Reducing imbalances between demand and supply of bed capacity for the clinic

Transcription

1 Einhoven University of Technology MASTER Reucing imbalances between eman an supply of be capacity for the clinic Kragten, T.C. Awar ate: 2015 Disclaimer This ocument contains a stuent thesis (bachelor's or master's), as authore by a stuent at Einhoven University of Technology. Stuent theses are mae available in the TU/e repository upon obtaining the require egree. The grae receive is not publishe on the ocument as presente in the repository. The require complexity or quality of research of stuent theses may vary by program, an the require minimum stuy perio may vary in uration. General rights Copyright an moral rights for the publications mae accessible in the public portal are retaine by the authors an/or other copyright owners an it is a conition of accessing publications that users recognise an abie by the legal requirements associate with these rights. Users may ownloa an print one copy of any publication from the public portal for the purpose of private stuy or research. You may not further istribute the material or use it for any profit-making activity or commercial gain Take own policy If you believe that this ocument breaches copyright please contact us proviing etails, an we will remove access to the work immeiately an investigate your claim. Downloa ate: 23. Nov. 2017

2 Einhoven, April 2015 Reucing imbalances between eman an supply of be capacity for the clinic By T.C. Kragten Stuent ientify number In partial fulfillment of the requirements for the egree of Master of Science In Operations Management an Logistics Supervisors: Dr.Ir. N.P. Dellaert, TU/e. OPAC Dr. M.J Reinorp, TU/e. OPAC Ir. J. Heijman van Gemert, Catharina Ziekenhuis

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4 TUE. School of Inustrial Engineering. Series Master Theses Operations Management an Logistics Subject heaings: healthcare, capacity planning, forecasting, resource allocation III

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6 PREFACE This report represents my master thesis, which is the last part of my stuy Operations at the Einhoven University. This master thesis has been conucte at the Catharina Hospital in Einhoven. Before moving on to the topic of the master thesis, I woul like to thank several people who supporte uring this project an uring my stuy. First, I woul like Jannie Heijman van Gemert, for being my supervisor at the Catharina Hospital. During the project, she gave me the freeom to set up my own project in a way which suite me. She provie useful input, an aske the right critical questions to trigger me to improve my project. From the TUE/e I woul like to thank my first supervisor Nico Dellaert for his criticism an the input he gave me for new ieas at moments I got stuck. Also I woul like to thank Matthew Reinorp for being my secon supervisor. Besies my supervisors, I woul like to thank my parents an my girlfrien Kathelijn for their support uring my whole stuy. Tim Kragten Einhoven, April 2015 V

7 MANAGEMENT SUMMARY This master thesis (1CM96) is conucte at the Catharina Hospital in Einhoven (CZE). The CZE is struggling in reacting on imbalances accoring to their be capacity. There are several ways in which the CZE can anticipate on an uner-provision of bes; however, especially for the situation of over-provisions of bes, the hospital experiences some problems how to eal with this. The hospital has no clear protocol for temporary closing bes. Information about the actual be occupancy, an the occupancy in the nearby feature is important to anticipate on these imbalances; however, the CZE has some ifficulties to create a correct overview of the be occupation. Despite the fact that the CZE has some effective methos to eal with overutilization of bes, the lack of a correct overview also affects the process for reacting on situations which are characterize by unerutilization. This is partially cause by the lack of information about the expecte length of stay per patient. Moreover, the CZE tries to anticipate in ifferent ways at the operational level; however, less is one at higher strategic levels. Creating a be allocation plan occurs once a year, an with exception from a seven week summer perio, seasonal patterns are not taken into account. Furthermore, clear insight in the optimal amount of flex-bes is missing. However, these flexbes play a major role in overcrowing situations. Therefore, the initial research problem is split up into two sub-problems. The first aim is to reuce the yearly variation between the eman an supply of bes in orer to reuce imbalances, an the secon aim is to generate insight on when to react on these imbalances In orer to solve the initial research problem following research objectives are establishe: The first objective is to efine proper performance measures. The secon objective is to ientify whether patient arrivals are influence by seasonal factors. Time series analysis an forecasting will be use for this. The thir objective is to fin a proper moel for the be allocation. Therefore, first a istribution for the patient arrivals an LOS has to be foun. The fourth objective is to create ifferent suitable scenarios for the be allocation. Different scenarios regaring to the number of flex-bes will be inclue. The fifth objective is relate to the operational level an is base on when to react on imbalances. Therefore, first a short term time series analysis an forecast will be one. The research focuses on the clinic of the CZE. Not all specialties will be taken into account. This research will only focus on the specialties that are able to exchange patients with each other an rely on regular bes. Moreover, the focus regaring the resources will be on the number of bes, an thus, for example not on the number of nurses. Furthermore, the focus of the research will VI

8 be on the clinic as a whole, instea of calculating an optimum for each unit iniviually, this will be one for the total clinic. SEASONAL PATTERNS In literature many ifferent moels are iscusse, where simple forecasting moels seems to perform better than complicate moels. To fin seasonal patterns a multiple regression moel is use. In total, 64 ifferent time perios are teste with a multiple regression moel to fin whether these perios o have a significant effect on the number of occupie bes in the clinic. From this analysis can be conclue that in total 30 ifferent perios o have a significant effect. By using these variables to forecast the maximum number of occupie bes, 75,3% of the variance is explaine. Furthermore, it can be conclue that the number of relevant OR sessions o contribute to a better moel. TACTICAL PLAN Base on the seasonal influence a forecast for 2014 is mae. However, we shoul not apply this forecast straightforwarly for two reasons. First, it is not preferable to change regular be capacity every ay of the year, an secon, the forecast is base on averages, thus, following the forecast will result in be shortages in approximately 50% of the ays. Therefore, first, the significant perios, which were foun by the multiple regression moel were compare to each other with the aim to reuce the amount of perios. After this reuction, a tactical plan is create. The tactical plan provies an optimal number of regular bes an flex bes, base on ifferent cost an perios scenarios. The ifferent cost scenarios show that: Decrease costs for active flex-bes result in less regular bes an more flex-bes. Increase costs of passive flex-bes result in less regular bes an less flex-bes. Increase costs for active flex-bes result in more regular bes an less flex-bes. Increase costs for patient refusals / elays result in the same amount of regular bes an an increase in flex-bes. In total four ifferent cost scenarios were teste: The actual situation in the Catharina hospital (benchmark moel), A scenario with all holiays, an special perios, which results in a reuction of costs of approximately 2,4%, epening on the cost scenarios, which is 800,- per ay (fictive costs) A scenario with all reuction perios an where the months are split into four perios, which results in an approximately 3,6% cost reuction, epening on the cost scenarios, which is 1200,- per ay (fictive costs) VII

9 a scenario with all reuction perios an each month as a separate perio, which results in approximately 3,6% cost reuction, epening on the cost scenarios, which is 1200,- per ay (fictive costs). Base on these results it can be conclue that anticipating on reuction perios results in the largest savings from 2,4%, an iviing the months into four ifferent clusters result in an aitional 1,2% savings. Furthermore, it can be conclue that the effect of iviing the months in to twelve ifferent clusters is negligible. OPERATIONAL PLAN For the operational plan, first, ifferent istributions were fitte for the emergency arrivals, elective arrivals, patients in hospital without a ischarge ate, an patients in the hospital with a ischarge ate. The emergency arrivals can be istribute with the Poisson process, where six ifferent perios per week are necessary. The elective arrivals, patients in hospital without a ischarge ate, an patients in the hospital with a ischarge ate, are istribute with an empirical istribution function (EDF). For the elective arrivals it can be conclue that a higher ifference in ays between now an the time, the patient is expecte, result in a larger eviation between the planne an actual arrival. For the patients in hospital with an expecte ischarge ate it can be conclue that on average, planne ischarges within 4 ays mostly occur slightly elaye, whereas patients with a ischarge ate larger than 4 ays ahea are ischarge on average earlier than expecte. For the patients in hospital without an expecte ischarge ate, it can be conclue that patients with a higher actual length of stay are expecte to stay for a longer perio in hospital, compare to patients that just arrive. To forecast the number of patients t ays ahea an operational moel is create, which epens on all the ifferent istribution functions relate to emergency arrivals, elective patients, length of stay an remaining length of stay. The output of the moel seems not useful for the hospital base on the results of the valiation. The average eviation in occupie bes between the forecast an realization shoul be at maximum aroun 10 bes; however, with the ata use for the valiation, the average ifference between the forecast an realization for all future perios is higher. An explanation of this eviation coul be that the use ata for the valiation originates from 2012, an that the information system was fille in ifferently. Therefore, more actual ata is neee. VIII

10 TABLE OF CONTENTS Preface... V Management Summary... VI 1. Introuction Organization Description The initial research problem Current situation Patient flow Planning an control Reucing be capacity Rules for creating an overview of the be capacity Research problem Problem efinition Research objectives Research scope Research approach Data collection Seasonal influences Literature Data Forecasting moel Results Valiation Conclusions on seasonal patterns Tactical plan Literature Determine baseline Performance measures Performance measures IX

11 5.3. Baseline perios Determination baseline Results Valiation Conclusions on tactical plan Operational plan Literature Arrival patterns Length of stay Data Distribution fitting Emergency arrivals Elective arrivals Length of stay with ischarge ate Length of stay without ischarge ate Operational moel Results Valiation Conclusions on operational plan Conclusions an recommenations Conclusions Seasonal influences Tactical plan Operational plan Recommenations Catharina Hospital Limitations an further research Bibliography List of abbreviations Appenix I: Framework for prouction control of hospitals X

12 Appenix II: Be occupancy per year Appenix III: Coefficients multiple regression moel with OR sessions Appenix IV: t-test Two-Sample Assuming Unequal Variances for the normal perios Appenix V: t-test Two-Sample Assuming Unequal Variances for the reuction perios Appenix VI: Distribution fitting for the occupancy of the clinic Appenix VII: Results for the ifferent cost scenarios per perio Appenix VIII: Results for the ifferent perios per cost scenario Appenix IX: Valiation results tables Appenix X Valiation graphs Appenix XI: Critical values for the Kolmogorov-Smirnov Test for gooness of fit Appenix XII: Empirical istributions elective arrivals Appenix XIII: Empirical istributions without Expecte ismiss ate (C1) Appenix XIV: Empirical istribution patients with expacte ismiss ate (C2) Appenix XV Probabilties elective patients without ischarge ate (C3) Appenix XVI Probabilties elective patients with ischarge ate (C4) XI

13 1. INTRODUCTION Due to the ageing population, price increases, an topics like technological evelopments, growing number of patients, an expane inications (RIVM 2012, Harper en Shahani 2002), a goo match between supply an eman in hospitals is important. The provision of aequate numbers of bes is therefore, a key concern for hospitals. The focus of this thesis is on clinics, where it is the aim to create a better balance between eman an supply of the number of bes use in the clinic by patients. Moreover, this thesis will focus on how hospitals can react in cases of imbalances, in orer to avoi uner- or overutilization in the nurse-clinic. This research is conucte at the Catharina Hospital in Einhoven an will be execute in completion of the master operations management an logistics at Einhoven University of Technology. This report consist of two parts, in the first part the main text is represente, an the secon part consists of the appenixes. In the first chapter, a escription is given about the organization in which this project is conucte. Moreover, the initial research problem will be introuce. Chapter 2 consists of the problem analysis, where the current situation is outline. In chapter 3, the research problem will be escribe. In chapter 4, it will be investigate which seasonal patterns affect the occupancy of the nurse-clinic on a tactical level. Base on the results of chapter 4, chapter 5 will provie ifferent scenarios in orer to make a tactical plan relate to the amount an types of bes for the nurse-clinic. Chapter 6 acts on an operational level an aims to provie a short term forecast for the be occupancy base on actual patient information. The last chapter, inclues the final conclusion, the limitations of this research an provies suggestions for further research options ORGANIZATION DESCRIPTION The Catharina hospital (CZE) is one of the two hospitals locate in Einhoven. The CZE is operationalize since Accoring to the annual report, the mission of CZE is: "together serving an innovative in the best specialist care an training". The core values of the CZE are: hospitable an approachable, reliable an riven, knowlegably an pioneering. Base on these core values, the Catharina Hospital has three ifferent overarching strategic programs. The hospitality program, the streamline work (lean manufacturing), an the program portfolio & partners. This master is conucte as part of the lean manufacturing program, this program focuses on aressing bottlenecks both primary an supportive. The program is

14 primarily riven by logistics. In aition, it is focuse on improving human cooperation between the various epartments. Figure 1: Organizational structure Catharina Hospital (Ziekenhuis 2013) The hospital consists of four ifferent care groups. Each care group consists of ifferent specialties, which can be overlapping. The care groups are supporte by six service units within the hospital. In aition, to the service units, there are three supporting sections which are the office boar, marketing & communication, an quality & safety. Some key numbers of the organization are presente in Table 1. 2

15 Table 1: Key numbers of the Catharina hospital (Jaarverslag Catharina Ziekenhuis 2013) 2013 Meical (sub)specialties 39 Meical specialists 211 Employees Nurses Junior octors 133 Number of authorize bes 696 First outpatient visit (excl. Psychiatry) Amissions per year ALOS in ays 4,8 OR Occupation 85,2% Number of scientific publications 343 Nationwie, the Catharina Hospital is known for their highly specialize care in cancer an heart isease. In the region, the hospital has a leaing position in the treatment of obesity an kiney failure. The Catharina hospital is part of the Santeon alliance. Santeon was foune in 2010 an emerge from the Association of Hospitals to encourage open collaboration between six clinical teaching hospitals (Canisius-Wilhelmina Ziekenhuis, Nijmegen; Catharina Ziekenhuis, Einhoven; Martini Ziekenhuis, Groningen; Meisch Spectrum Twente, Enschee; Onze Lieve Vrouwe Gasthuis, Amsteram; St. Antonius Ziekenhuis, Utrecht/Nieuwegein) with the aim to improve meical care through continuous innovation THE INITIAL RESEARCH PROBLEM The nursing units within the CZE are struggling to react on imbalances in their be capacity. There are several ways in which the CZE can anticipate on an uner-provision of bes; however, especially for the situation of over-provisions of bes, the hospital experiences some problems how to eal with this. 3

16 2. CURRENT SITUATION In this chapter, the current situation will be explaine. In the first paragraph, the patient flow will be iscusse. The secon paragraph contains a escription of the planning an control rules for the CZE relate to the be capacity within the clinic base on the moel from Vissers et al. (2001). The thir paragraph is about reucing be capacity, an in the last paragraph the rules for creating an overview of the be capacity are iscusse PATIENT FLOW The patient flow is the most important flow within a hospital. For the flow of patients, three ifferent phases can be ientifie; the arrival, the length of stay, an the outflow. Figure 2 represents an overview of this process; however, figure 2 is still a general moel, which implies that not all relations are isplaye in this figure. As can be seen in figure 2, the CZE eals with both elective an emergency patients. Both patient types follow a similar process; however, the arrivals are ifferent. Elective patients, refer to patients whose amission can be planne in avance, whereas the nonelective patients, are recore unexpecte, an hence the amission nees to be performe urgently. An overview of the patient numbers by specialism is given in table 2. Figure 2: patient flow for the clinic Department Number of hospitalizatio n at clinic Number of aytime hospitalization Number of clinical transfers to other location ALOS for clinical hospitalization Utilization General surgery ,9 85% Cariology ,1 77% Cariothoracic surgery ,7 73% Geriatrics ,7 91% Gynecology ,6 79% Internal meicine ,4 85% Respiratory meicine ,4 80% Gastroenterologist liver iseases ,3 82% Multiisciplinary oncology % Neurology % Orthopeics ,6 79% Urology ,2 73% Table 2: Key numbers for the regular epartments of the clinic for

17 2.2. PLANNING AND CONTROL Planning an control is an important aspect, without the right resources it is not possible to provie goo services to patients. Different frameworks have been evelope in orer to provie insight into the planning an control proceures relate to the healthcare sector (Vissers, Bertran en De Vries 2001, Hans, Van Houenhoven en Hulshof 2012). In this paragraph the framework from Vissers et al. (2001) is use to provie insight into the planning an control rules for the CZE relate to the be capacity within the clinic. The whole framework of Vissers et al. (2001) is isplaye in appenix I. The actual situation from the CZE regaring to planning an control will be escribe below base on this framework. Level 1: strategic planning, types of ecisions which shoul be mae at this level are ecisions about the range of offere services. The time perio relate to this level is 2-5 year, an oes therefore not affect the irect be planning. Level 2: patient volumes planning an control, is about the evelopment of hospital activities an how these activities are relate to volumes an capacity requirements for the upcoming year. In orer to make a sufficient be planning, the CZE takes into account the yearly patient volume growth, an an estimate ALOS (average length of stay). Level 3: resources planning & control, is relate to how resources are allocate to the specialties an patient groups. The time horizon of this level is 3 months till 1 year. The CZE ivies once a year the total number of bes to the ifferent nursing-units, resulting in a strict number of bes per nursing unit for one year. This allocation is base on averages per specialism of patient volumes, an length of stay; however, seasonal variation is not taken into account. The CZE assigns two types of bes to the ifferent nursing units, regular bes an flex-bes. The use of flex-bes will be iscusse in the next section. Moreover, one of the statements in the CZE regaring to allocating bes is; a be is a be. Clustering bes coul reuce variability (Green 2002). However, in the CZE, this statement applies especially to the lowest framework level of Vissers et al. (2001), where patients are assigne to any other suitable nursing units, in case the preferre nursing unit is full. Thus, this statement oes not result in really clustering bes. Level 4: Patient group planning an control, this level is relate to the projecte number of patients per perio an how the specialist-time shoul be scheule at patient group level an has a time horizon of several weeks till 3 months. Regaring to be capacity within the nursing clinic, the CZE only anticipates at the summer perio. In this perio, the CZE has a special protocol, where the hospital closes about 15% of their regular bes uring a 7 week perio. Further actions at this level are missing, which is experience as a weakness by the hospital. Level 5: patient planning & control, is about scheuling of patients for amissions an has a timehorizon of several ays. The hospital takes several actions in orer to eal with imbalances 5

18 between the eman of patients an the supply of bes. First, in cases where the preferre nursing unit is full, patients will be referre to other nursing units. There are some protocols in the CZE for referring patients to other units, one of the protocols is; search first into your own care group; however, in reality this oes not always seems to happen. Furthermore, in a vertical irection, communication takes place between the outpatient epartment an the nurse-unit manager, in case a patient from the outoor epartment shoul be place quickly at the inpatient epartment. Another action to react on imbalances is to open the flex-bes. Flex-bes are temporary bes which are normally not staffe, but may be use when the eman for bes is high. At this moment there are 23 flex-bes in the hospital ivie over 9 ifferent nursing units. In case eman is high, an less than 10 regular bes are available in the whole clinic, coe re is eclare, which implies opening the total number of flex-bes. In cases where patients at the nursing units have a low care eman, no extra personal is eploye for the flex bes. In a situation where the care eman is high, the epartment manager of that specific nursing unit will make an appeal to the flex office in orer to get temporary nurses. The flex office is a kin of temporary employment agency, an contains a atabase of on average 80 nurses all having a zero-hour contract. Depening on the traveling time, a nurse calle by the flex-office is available from 30 minutes till 90 minutes after the request for an extra nurse. In cases coe re is eclare, all flex-bes are at the same time. In cases where flex-bes are not necessary anymore, the flex-bes will be graually close REDUCING BED CAPACITY In case the hospital is facing a situation of over-provision of bes, a hospital can react on this uner-utilization by temporary sening nurses home, an closing bes. However, this is not a common practice. Many nursing-clinics o not look beyon their own clinic, especially when the eman is not far below average. However, unuse bes by ifferent clinics coul be combine in orer to reuce the total number of active nurses in the hospital. An interesting aspect is the fact that the hospital assumes that uner-provision in their nursingclinic results in higher probabilities of patient arrivals, compare with over-provision situations, This assumption can sometimes be true since patients enie access to or prematurely transferre out of a given unit may be place in other units (Cohen, Hershey en Weiss 1980). However, in cases where all care-units are ealing with unerutilization, an moreover, for a seclue clinic, this assumption oes not hol. In this case it seems reasonable to assume that the probability of arriving patients for a specific nursing-unit stays the same. However, it seems that sometimes managers are not aware of this an are therefore less willing to sen nurses home an close bes. 6

19 2.4. RULES FOR CREATING AN OVERVIEW OF THE BED CAPACITY The CZE is having ifficulties preicting whether the total be capacity is sufficient for the next ay, an even sometimes for the ay itself. In normal situations, with sufficient be capacity there are only two moments per ay a correct overview of the be capacity is available. The first moment of the ay is after a short counsel where all nurse epartment managers mention the number of available bes an expectations for that specific ay for their clinics. These managers often receive this information from their planner an report this information uring a short counsel to the officiating nurse epartment managers. The officiating nurse epartment manager is not an official function, it can be seen as a responsibility that the nurse epartment managers carry several weeks a year, an which rotates weekly. The secon moment of the ay, an overview is presente occur by or phone. In this case, the officiating nurse epartment managers receives an from all the other clinics about their number of available bes before 5:00 pm. In cases of tightness (less than ten regular bes available in the whole clinic) this also happens at 12:00 am. All this work is necessary because the information system oes not provie a clear view of the total number of available bes for the ifferent clinics. Moreover, ue to the lack of missing information, patients which are place off-service ue to a full nursing clinic, can provie a lot of extra work since the planner has to call other nursing clinics in orer to fin a be. Another isavantage of the current way of working is the probability of human errors, for example, a wrong quick calculation of the available bes by one of the planners, a wrong calculation by the officiating nurse epartment managers, or miscommunication between one of these actors can result in wrong be numbers. Different aspects contribute to this problem. First, all nursing units have their own planning. Due to this ecentralize planning, there are many ifferent actors all working slightly ifferent an with their own insights. An thus, all these actors have slightly ifferent ways to fill in the information system. Moreover, some of the specialisms experience ifficulties with preicting the provisional ate of ismissals, which again results in ifferent ways of filling in the information system. Another problem is the lack of taking into account unexpecte arrivals an unexpecte ismisses. Many arrivals an ismisses occur unexpecte, aing this information coul be helpful. 7

20 3. RESEARCH PROBLEM In the previous chapter, the current situation regaring to the be capacity was iscusse. In this chapter, ifferent problems will be erive. The initial research problem which is state in the introuction, is closely relate to the problems escribe in the current situation; however, it is not all-embracing. Base on literature, ata analysis an interviews, the first paragraph of this chapter will introuce the research problem for the thesis. In the secon section, the research objectives are state. The thir part of the chapter escribes the scope of this research PROBLEM DEFINITION As state in the introuction, the initial research problem, focusses on ealing with imbalances in the be capacity, especially for the situation in which the hospital has an unerutilization of bes. Base on the current situation it can be state that this is a problem, since the hospital has no clear protocol in orer to temporary close bes. Information about the actual be occupancy, an the occupancy in the nearby future is important to anticipate at these imbalances; however, the CZE has some ifficulties in orer to create a correct overview of the be occupation. Despite the fact that the CZE has some effective methos to eal with overutilization of bes, the lack of a correct overview also affects the process in orer to react on situations which are characterize by overutilization. This is partially cause by the lack of information about the expecte length of stay per patient. Moreover, the CZE tries to anticipate in ifferent ways at the operational level; however, less is one at higher strategic levels. The be istribution is performe once a year, an with exception from a seven week summer perio, seasonal patterns are not taken into account. Furthermore, clear insight in the optimal amount of flex-bes is missing, although, these flex-bes play a major role in orer to anticipate on overcrowing situations RESEARCH OBJECTIVES Base on the research problems, ifferent research objectives have been ientifie. The first three objectives will focus on the resource planning an control level from Vissers et al. (2001), these objectives aim to reuce the variation between the eman of patients an the supply of bes. The other objectives will focus on the patient planning an control level an will focus on when to react an how to react on imbalances. The first objective is to efine proper performance measures. The main part of the thesis is about creating a better match between eman an supply. Without efining performance measures it is impossible to have a proper evaluation between ifferent scenarios. 8

21 The secon objective is to fin whether the occupancy of the hospital clinic epens on any seasonal factors. The thir objective is to fin a proper moel to etermine the require amount of regular bes an flex-bes. Several techniques are iscusse in the literature; however, it is not possible to apply all these ifferent techniques in this master thesis. The fourth objective is to create ifferent suitable scenarios for calculating the optimum amount of regular bes an flex-bes. Now, be allocation at the CZE occurs once a year an contains a steay number of bes uring this year, where seasonal patterns are not taken into account (with exception from the 7 week summer perio). Therefore, epening on the outcome of the secon objective, one of the scenarios coul inclue seasonal patterns into the moel. Moreover, ifferent scenarios regaring to flex-bes coul be investigate, with the aim to fin the optimal number of flex-bes. Since the CZE has problems reacting to unerutilization, but it has capabilities to react on overutilization with flex-bes, it shoul be evaluate whether it is sufficient if these ifferent scenarios create a lower baseline, such that the CZE is facing less situations of unerutilization, but it still can anticipate at situations which inclue overutilization with their flex-bes. The fifth objective is relate to the operational level an is base on when to react on imbalances. Creating insight in when to react on these imbalances starts with a short term forecasting moel. Therefore, first, the arrivals of patients must be analyze an moele. Furthermore, information about the length of stay an the expecte remaining length of stay is necessary. The research objectives can be illustrate by the following two figures which aim to represent the actual be allocation proceure an one of the be allocation proceures that will be investigate in this master project. Figure 3, represents the actual be allocation, which is escribe in the current situation. Figure 4 represents the scenario to be investigate. In table 3, the ifferences between these two figures are shown. 9

22 Figure 3: Actual be allocation Figure 4: Possible be allocation Table 3: Differences between figure 3 an figure 4 Figure 3: Actual be allocation Figure 4: Possible be allocation No seasonal patterns Seasonal patterns High baseline in number of Lower baseline in number of available bes available bes Insight in number of available bes Insight in the number of available only for that specific ay base on bes for x ays ahea base on human insight forecasting an human insight 3.3. RESEARCH SCOPE A hospital is a complex institute with many ifferent proceures, epartments, an rules. Taking into account all these ifferent factors will result in a far too complex project, an moreover, the project will take too long to fit within the time span of the master thesis. Therefore, several limitations must be taken into account. The first limitation is base on which organizational parts shoul be inclue. The secon limitation is on the operational level. The research focuses on the clinic of the CZE. The clinic inclues ifferent specialties. However, not all these ifferent specialties will be taken into account, this research will only focus on the specialties that are able to exchange patients to each other an rely on regular bes. This means that epartments such as IC, psychiatry, maternity war, short stay, an the chilren's war will not be inclue in this research. Table 4 at the next page represents an overview of the ifferent epartments that are inclue an their relate number of regular bes, an flex-bes. 10

23 Table 4: Number of bes for the regular epartments Department Number of regular bes Number of flex-bes General surgery General surgery Cariology (7 west) 41 0 Cariothoracic Surgery 40 4 Geriatrics 23 1 Gynecology 22 0 Internal meicine 30 0 Respiratory meicine 37 6 Gastroenterologist liver iseases 30 2 multiisciplinary oncology 28 1 Neurology 32 0 Orthopeics 27 1 Urology 20 1 Total Moreover, there are some limitations mae from an operational perspective. First of all, the focus regaring the resources will be on the number of bes, an thus, for example not on the number of nurses. Furthermore, the focus of the research will be on the clinic as a whole, instea of calculating optima for each unit iniviually. The research will take into account both elective an non-elective patients RESEARCH APPROACH Mitroff et al. (1974) moel, which is isplaye in figure 5 below, will be use in orer to structure the master thesis. The moel consists of four phases, where Mitroff et al. (1974) argues that the research cycle can begin an en at any of the phases in the cycle. 11

24 Figure 5: Research moel by Mitroff et al. (1974) The conceptualization phase starts with interviews an analyzing ata in orer to sketch the actual situation. Base in this situation, research problems are erive an ecisions are mae about variables that nee to be inclue into the conceptual moel. The moeling phase is about actually builing a moel. For this master thesis, ifferent parameters have to be moele, such as the patient arrivals for both the short an long term, the length of stay, an the require amount of bes for both the long term an short term. Next the moel solving process takes place, where mathematics normally play an important rule. Finally, if the results satisfy the epartment managers an care group managers from the CZE, the solution coul be implemente. Moreover, as the moel of Mitroff et al. (1974) suggest, there will be interaction between reality an the evelope moel through valiation, an base on feeback, the solution from the moel solving can result in an aapte conceptual moel DATA COLLECTION An important aspect for this master thesis is the availability of useful ata. Without the right ata amount an quality, it is impossible to complete the research objectives. First, ata is collecte by interviews. Several epartments managers are interviewe an interview at the flex-office is conucte. Next to this, ata about the patient arrivals, whether these arrivals are elective or non-elective, the LOS, the amount of refusals, etc., were collecte. All hospitalize patients at the CZE are recore in the information system Ezis 5.2. The system contains personal information, arrival ate, ischarge ate, specialism, location, an type of patient (elective or non-elective). This ata is available from 2008 till now. From this ata, both arrival patterns an length of stay can be etermine. Data about the number of refusals an elaye patients is missing; however, accoring to the interviews, the number of refuse patients are negligible. Only ata about the inpatient epartments will be taken into account. 12

25 4. SEASONAL INFLUENCES The aim of this chapter is to iscover seasonal patterns in the occupancy of bes for the clinics. In the first paragraph, literature on forecasting is iscusse. The secon paragraph is about the ata is use to ientify seasonal patterns an trens. In the thir paragraph, a moel is chosen an ifferent variables are create. Paragraph four represent the results of the moel, in paragraph five, the results are valiate. An finally, in paragraph six, the conclusions on seasonal influences will be presente LITERATURE In this paragraph, relevant literature accoring to forecasting be occupancy will be iscusse. A forecast metho is a proceure for computing forecasts from present an past values (Chatfiel 2000). By analyzing an forecasting time series ifferent patterns can be iscovere. Chatfiel (2000) istinguishes four components to ecompose the variation in time series. The two main sources of variation are seasonal an tren variation. Healthcare relate examples of these variations are for example an increase number of patients in winter perios that suffer from a pneumonia (seasonal), or increasing healthcare eman ue to the ageing of population (tren). Moreover, Chatfiel (2000) iscusses other cyclic variations, which inclues regular cyclic variations at perios other than a year such as business cycles an irregular fluctuations. The last component, the irregular variation is often escribe as any variation that is left after removing tren, seasonality an cyclic variation. An example for an irregular fluctuation coul be a isaster, which is completely ranom an cannot be forecaste. Moeling an forecasting patient volumes provies useful information for hospitals in orer to allocate resources, scheuling staff an planning future expansion (Abel-Aal en Mangou 1998). Abek-Aak an Mangou (1998) use two univariate moels, the ARIMA moel an an a hoc approach base on extrapolating the growth curve of the annual means in orer to moel an forecast the monthly patient volume at a primary health care clinic. In their research Abek-Aak an Mangou (1998) foun that the ata follow a seasonal pattern with a minimum in the summer holiay season. The patient volume in their ata ha an upwar tren which was in line with the population increase. Their research inicates that a simple metho base on extrapolating the growth curve of the annual means shows better fitting results than the more complex ARIMA moel (0,55%-1.17% versus 1.86%-4.23%). Abek-Aak an Mangou (1998) argue that it is a result of the lack of strong ranom components that are require by an ARIMA process for moeling. In Jones et al. (2008) ifferent forecast methos are evaluate in orer to preict patient volumes for the emergency epartment. The researchers compare the accuracy of exponential smoothing, SARIMA, time series regression, time series regression with climatic variables, an an 13

26 artificial neural network moels with a linear regression moel, which was use as a benchmark. Jones et al. (2008) carrie out their research at three iverse hospital emergency epartments. Different forecasting methos were foun as best fitte for each of the three ifferent facilities. However, comparing these ifferent best fitte methos with the benchmark moel, Jones et al. (2008) foun that a simple regression moel is a reasonable approach to forecast patient volumes DATA Data from 2009 till 2013 is use to ientify trens an seasonal patterns in the occupancy of bes within the clinics. The ata set consists of more than a million lines incluing all mutations if patients are change from epartment or specialism. Before any analysis can be carrie out, the ata nee to be valiate. A few outliers were ientifie which have been remove or change. First, patients with negative length of stay have been remove. Moreover, accoring to the epartment manager, patients o not stay longer than 8 hours at the emergency epartment (ED); therefore, the assumption is mae that these patients were on a regular clinic instea of the ED. Base on the ataset, the be occupancies per hour (from 8:00 till 16:00) are specifie for 2009 till 2014, which inicates there were eight measurements each ay on historical ata. The results of 2009 are isplaye in figure 7 below as an example. The be occupancy of the other years are isplaye in appenix II Be occupancy Figure 6: Be occupancy for 2009 from 8:00 till 16: FORECASTING MODEL To fin out whether the be occupancy is influence by seasonal effects an trens, a multiple regression moel is execute. This metho is chosen because it can eal with holiays that cover 14

27 a ifferent time perio each year. The ata of 2009 till 2013 is use for the regression moel, an the ata 2014 is use for valiation. For the multiple regression moel, the maximum number of bes uring a ay is specifie as the epene variable. Both the log transformation an non-transforme maximum number of bes are teste as a epenent variable. Further, ifferent ummy variables are create which are relate to seasonal factors, holiays, off-ays, a tren in years, an the ay of the week. The teste perios are isplaye in table 5 below. Next to all seasonal relate variables, the number or OR sessions are ae as an inepenent variable. Table 5: Dummy variables Monay* Winter SummerVacationW6* Year Tuesay* Spring SummerVacationW7* AnesthesiaDay1 Wenesay* Summer ChristmasVacationW1* AnesthesiaDay2 Thursay* AscensionWeeken* ChristmasVacationW2* DayAfterAnesthesiaDay Friay* PentecostWeeken January* DayafterMayVacation Saturay* EasterWeeken* February* WeekAfterMayVacation* CarnivalVacation* Christmas* March* DayAfterCarnivalVacation Easter* EasterWeekenLong April* WeekAfterCarnivalVacation MayVacation* NewYear May DayAfterChristmasVacation* Pentecost* LiberationDay June* WeekAfterChristmasVacation* SummerVacation AnesthesiaDays July* InteractionNewYearNoSunay* AutumnVacation SummerVacationW1* August InteractionLiberationDayNoSunay ChristmasVacation SummerVacationW2* September* InteractionKingsDayNoSunay Ascension SummerVacationW3* October* InteractionNewYearNoWeeken Kingsay SummerVacationW4* November* InteractionLiberationayNoWeeken* Autumn SummerVacationW5* December* InteractionKingsDayNoWeeken* 4.4. RESULTS First a scenario is teste with only the seasonal relate variables from table 5. The results of these tests are shown below. Table 6 shows the results with the non-transforme epene variable, an table 7 is log-transforme. As can be seen the ifference between both moels is negligible, an therefore, the non-transforme epenent variable is chosen. The starre variables in table 5 above represent all variables that o have a significant effect on the be occupancy. Table 7: Moel summary Maxbes Table 6: Moel summary LN(Maxbes) 15

28 More etails of the results are isplaye on the next page. For the reliability of the moel an their results, the multiple regression assumptions must be teste. The first assumption assumes that variables shoul not inclue multicollinearity. Accoring to Fiel (2009), a VIF level of 10 is the maximum recommene level, an Rogerson (2001) even sets the VIF level of maximum of 5, to etect multicollinearity. Table 8 shows that all variables stay below these VIF levels. Moreover, the ata shoul be equally goo everywhere which implies homosceasticy an linearity. Figure 7, shows a ranom pattern which is an inication for homosceastic an linearity. The last assumption is that the noise must be normally istribute. Base on figure 9 it can be conclue that this assumption is met. For the secon scenario, the amount of OR sessions has been ae, to investigate whether the OR sessions o have an effect on the be occupancy or not. All OR sessions that are relevant for the clinic are counte per ay an ae to the multiple regression moel as an inepenent variable. The OR sessions o have a significant effect on the regression moel; however, by aing this variable the assumption of multicollinearity is violate since there is high correlation with the ifferent ays of the week, which result in a VIF larger than for this variable. The table of the coefficients an the VIF factors is shown appenix III. By eleting variables that have become nonsignificant after aing the OR sessions, an eleting the variables that contain multicollinearity, the moel with the OR sessions oes not show any improvement. The ajuste R² for the multiple regression moel with only seasonal patterns is 0,753, an the ajuste R² with OR sessions inclue is 0,752. Figure 7: Scatterplot Figure 8: P-P plot of regression stanarize resiual Figure 9: Histogram of the resiuals 16

29 Table 8: Multiple regression coefficients Moel 1 Unstanarize Coefficients Coefficients a Stanariz e Coefficient s 95,0% Confience Interval for B Lower Boun B St. Error Beta t Sig. (Constant) 285,855 1, ,554 0, , ,609 Collinearity Statistics Upper Boun Tolerance VIF Monay 30,013 1,200,384 25,006,000 27,659 32,367,572 1,748 Tuesay 33,738 1,201,432 28,091,000 31,383 36,094,571 1,750 Wenesay 36,841 1,202,471 30,648,000 34,483 39,198,572 1,748 Thursay 32,475 1,200,416 27,061,000 30,121 34,828,572 1,747 Friay 31,689 1,199,406 26,434,000 29,338 34,040,573 1,744 Saturay 5,935 1,204,076 4,928,000 3,572 8,297,568 1,760 CarnivalVacation -14,202 2,276 -,081-6,239,000-18,666-9,737,811 1,233 Easter -24,605 7,512 -,066-3,275,001-39,339-9,871,328 3,044 MayVacation -10,206 2,441 -,057-4,181,000-14,994-5,419,737 1,357 Pentecost -31,510 4,415 -,085-7,136,000-40,170-22,850,951 1,052 AscensionWeeken -12,506 3,184 -,048-3,928,000-18,751-6,261,919 1,088 EasterWeeken -14,615 6,203 -,048-2,356,019-26,781-2,449,322 3,105 Christmas -44,573 4,820 -,120-9,248,000-54,026-35,120,798 1,253 SummerVacationW1-17,708 2,675 -,089-6,620,000-22,954-12,462,751 1,332 SummerVacationW2-31,623 2,428 -,169-13,022,000-36,386-26,861,799 1,251 SummerVacationW3-38,927 2,421 -,208-16,080,000-43,675-34,179,804 1,244 SummerVacationW4-42,592 2,381 -,228-17,885,000-47,262-37,921,831 1,204 SummerVacationW5-37,689 2,401 -,202-15,700,000-42,397-32,981,818 1,223 SummerVacationW6-34,169 2,324 -,183-14,700,000-38,728-29,610,872 1,146 SummerVacationW7-4,940 2,323 -,026-2,127,034-9,496 -,384,873 1,145 ChristmasVacationW 1 ChristmasVacationW 2-30,653 2,735 -,164-11,208,000-36,018-25,289,630 1,587-44,146 2,501 -,233-17,649,000-49,051-39,240,772 1,295 January 16,557 1,751,169 9,457,000 13,123 19,991,424 2,358 February 23,517 1,713,230 13,730,000 20,158 26,876,483 2,070 March 22,158 1,588,226 13,957,000 19,044 25,271,516 1,939 April 17,493 1,602,176 10,919,000 14,351 20,635,522 1,916 June 6,163 1,569,062 3,928,000 3,086 9,240,544 1,839 July 4,185 1,618,043 2,586,010 1,011 7,359,496 2,015 September 5,682 1,517,057 3,746,000 2,707 8,657,582 1,718 October 9,235 1,581,094 5,842,000 6,135 12,335,520 1,922 November 13,459 1,593,135 8,448,000 10,334 16,583,528 1,895 December 13,774 1,741,140 7,910,000 10,359 17,190,429 2,333 WeekAfterMayVacatio n DayAfterChristmasVa cation WeekAfterChristmasV acation InteractionNewYearN osunay InteractionLiberationD aynoweeken -10,224 2,562 -,051-3,990,000-15,250-5,198,818 1,223-23,600 6,624 -,045-3,563,000-36,591-10,609,843 1,187-7,825 2,814 -,039-2,780,005-13,345-2,305,678 1,475-47,975 7,223 -,082-6,642,000-62,142-33,808,885 1,130-30,333 8,184 -,045-3,706,000-46,385-14,281,919 1,088 InteractionKingsDayN oweeken -24,370 7,258 -,042-3,358,001-38,604-10,136,877 1,140 a. Depenent Variable: MaxBesPerDay 17

30 4.5. VALIDATION In the previous paragraph, a multiple regression moel is mae, an is shown how this moel fits with the use ata. However, forecasting the future, cannot be one by using ata of the future. Therefore, a valiation perio (2014) is ae to test the valiity of the moel. Table 9: Gooness of fit measurements Gooness of fit Value MAPE 4,42 MAE 14,02 MaxAPE 18,18 MaxAE 61,09 The gooness of fits parameters from the forecast versus the realization are shown table 9. MAPE stans for a mean absolute percentage error an is calculate by: n MAPE = 1 n A t F t 100% A t t=1 MAE is the mean absolute error an is calculate by the formula: MAE = 1 n A t F t t=1 Both, the RMSE, MAPE an MAE are measurements for the variability of the ifference between forecast (F t ) an observe values(a t ). Smaller values inicates better moel performance. Furthermore, MaxAPE, is the maximum mean absolute percentage error: MaxAPE = max { A t F t A t } 100% MaxAE, is the maximum absolute error MaxAE = max { A t F t } The MaxAPE an MaxAE are worst-case measurements, where again hol that smaller values inicates better moel performance. Moreover a plot (figure 10) is mae. Figure 10 isplays the occupie bes in 2014, a forecast for 2014 base on the multiple regression moel, an the real available bes in As can be seen, the multiple regression forecast is much more relate to the real occupie bes than the real available bes. However, also the multiple regression moel oes have some large eviations, which especially occur just before the summer holiay. During this perio the hospital was contaminate with the VRE virus, which may resulte in more occupie bes. Moreover, October an December show some large eviations, however, there is no explanation for these perios. n 18

31 Total available bes vs forecaste bes vs real number of use bes 400, , , , , Recoring Amission stops Occupie bes Forecast Real available bes Figure 10: The forecaste bes versus the occupie bes versus the real available bes, incluing the amission stops (with the number of occupie bes for that moment) for CONCLUSIONS ON SEASONAL PATTERNS The aim of this chapter is to ientify seasonal patterns. In literature many ifferent moels are iscusse, where simple forecasting moels seem to perform better than more complicate moels. To fin seasonal patterns a multiple regression moel is use, an the following seasonal influence have been foun (table 10). The results show an ajuste R² of Table 10: Significant seasonal influences Monay SummerVacationW1 April 0.753, which inicates that 75,3% of Tuesay SummerVacationW2 June the variance for the occupie bes is Wenesay SummerVacationW3 July explaine. For the valiation perio Thursay SummerVacationW4 September Friay SummerVacationW5 October an average eviation of 14,02 bes, Saturay SummerVacationW6 November an a maximum eviation of 61,09 CarnivalVacation SummerVacationW7 December bes is shown. This may seem a lot; Easter ChristmasVacationW1 DayAfterChristmasVacation MayVacation ChristmasVacationW2 WeekAfterChristmasVacation however, compare with the actual Pentecost January InteractionNewYearNoSunay number of bes (figure 10), this is an AscensionWeeken February InteractionLiberationayNoWeeken enormous improvement. However, EasterWeeken March InteractionKingsDayNoWeeken base on the valiation perio one important thing shoul be taken into account. As can be seen in figure 10 there were several amission stops in In all cases the 390 be bounary was not met. So anticipating on seasonal influence will result in less variation between eman an supply; however, there are also many ifferent options for improvement with respect to the coorination, by creating a better insight in those bes that are not occupie. Furthermore, no set-up times, for cleaning an preparing bes for new patients were taken into account, which coul also be an explanation for the ifference. However, this effect, may be negligible since the moel uses the maximum occupie number of bes per ay, which may coul be seen as a compensation for the set-up times. 19

32 5. TACTICAL PLAN In chapter 4 the effects of seasonal influence are iscusse an a forecast for 2014 is mae. However, we shoul not apply this forecast for two reasons. First, it is not preferable to change regular be capacity every ay of the year, an secon, the forecast is base on averages, thus, following the forecast will result in be shortages in approximately 50% of the ays. In orer to eal with these two problems this chapter consists of seven parts to set up a tactical plan to etermine the amount of require regular bes an flex-bes. First, relevant literature is iscusse. In the secon part performance measures are introuce. In the thir part is stuie if an how ifferent perios coul be combine to reuce the number of times that the regular be capacity shoul change. The fourth part contains an integer linear programming moel which calculates the optimum number of regular bes an flex-bes base on ifferent cost scenarios an perios. The fifth part contains the results of the moel. In the sixth part the moel is valiate, an the last part represents the conclusions on the tactical plan LITERATURE DETERMINE BASELINE Harper & Shanani (2002) foun that many authors consiere the patient flow through hospitals an the resulting be requirements. They argue that a great amount of effort in the be capacity literature has been evote to queueing moels, which vary enormously in complexity an are often hospital or war specific. Other authors approache the be allocation problem by eploying a variety of operational techniques. These inclue integer programming, forecasting an simulation. Gorunescu et al. (2002), use an M/PH/c moel to etermine the optimal be numbers for a hospital system. The patient arrivals follow a Poisson process, the length of stay is moele by a phase-type istribution, an the bes are the servers. The moel oes not allow queueing an patients will leave the system when they arrive in case the care-unit is full. Gorunescu et al. (2002) aim to minimize the number of bes subject to maintaining the elay probability at a low level. In orer to fin a goo optimum between the occupancy rate of the bes an the minimum elay Gorunescu et al. (2002) use the base-stock policy, which implies holing costs for empty bes an penalty costs for lost eman. The optimal outcome, which is the outcome with the lowest cost, will therefore result in the optimal number of bes, while minimizing elaye patients, an optimizing be occupancy. Li et al. (2009) use the same queuing moel as Gorunescu et al. (2002); however, they combine their queueing moel with goal programming. First, Li et al. (2009) use the queueing moel to calculate the total number of bes in respect to 95% patient amission an the total number of 20

33 bes in respect to the optimal profit per ay. This is followe by a goal programming moel, where the researchers try to fin an optimum between a har be constraint an the profit. Their results aims for a maximum profit an show that in this case the patient amission probability will increase, while the occupancy rate will ecrease. Li et al. (2009) use piecewise linearization in orer to eal with the concave outcomes from their queueing moel. The research of Zhang et al. (2013) is a combination of queueing moeling an integer programming. Zhang et al. (2013) foun that the optimal be allocation uner uncertainty will involve etermining the level of two types of bes, namely; 1) bes that are always operational uner all scenarios; an 2) bes that are mae operational epening on a specific scenario. The work of Zhang et al. (2013) proposes a be allocation ecision making approach consisting of a two-step process. First, an Erlang loss queueing moel is presente, which is accoring to Zhang et al. (2013) a reasonable presentation of a hospital s in patient flow. The Erlang loss moel is an M/M/c system where the arrivals of patients are assume to be a Poisson process, the LOS is exponential, an where patients that o not fin a free be by their arrival are lost an have no further influence on the system. With the Erlang loss moel the theoretical be availability can be calculate. Thus, the probability of an arriving patient being refuse amission (or not) can be etermine, for a given number of operational bes. An moreover, ecie what be capacity is neee to achieve the preferre level of availability an be-occupancy (Zhang, et al. 2013). After calculating the minimum require number of bes neee to maintain a certain target level of be availability an be occupancy for each stochastic scenario, the outputs are use as one of the input parameters for a two-stage stochastic mixe integer linear programming (MILP) moel. This MILP-moel is use to etermine the allocation of the ifferent hospital bes (i.e. always operational, mothballe, etc.) by maintaining a balance between cost, accessibility an efficiency. The objective function of the propose stochastic moel is to minimize the expecte annualize be-cost PERFORMANCE MEASURES Due to many ifferent organizations within the healthcare sector, managing an measuring performance seems to be rather ifficult since ifferent stakeholers focus on ifferent types of performance (Curtright, Stolp-Smith en Eell 2000). Li an Benton (1996) reviewe performance measurement criteria in health care organizations, an trie to classify the ifferent performance measures. They argue that the performance measurements involve internal an external evaluations in two imensions, which are: cost / financial status performance an quality performance. Accoring to Li an Benton (1996) the internal performance criteria are usually evelope an measure internally an the external performance criteria can be evelope an measure by entities outsie the organization. The 21

34 internal measures are relate to prouction efficiency, utilization, an process an service of quality constructs, whereas external quality criteria focus on customer s perceptions an satisfaction of goos, an moreover, services provie by health care organizations. Caroen et al. (2010) i a literature review on operating room planning an scheuling in which they also wrote about performance criteria. Li an Benton (1996) an Caroen et al. (2010) both istinguish eight ifferent performance measures, however, the classification use by Caroen et al. (2010) is ifferent an they istinguish: waiting time, throughput, utilization, leveling, patient eferrals, financial measures an preferences as the main performance measures. Accoring to Li an Benton (1996), the occupancy rate is a key utilization ecision variable when planning the inpatient care facility size PERFORMANCE MEASURES Before analyzing an setting up a moel, first performance measures are presente. Base on the literature an interviews eight ifferent performance measures have been erive. I. Amount of regular bes: for comparing ifferent scenarios the amount of regular bes can be use as a performance measure. II. Amount of flex-bes: the amount of flex-bes tells something about the variability for the occupancy of the clinic. High variability in occupancy results in a high eman for flexibility, an thus a high number of flex-bes. III. Be utilization: utilization stans for the efficiency in which the bes are use. The be utilization is a ratio of the time that the bes are use an the time bes are available. IV. Number of times flex-bes use: the number of times flex-bes are tells something about the variability in the occupancy of the clinic. V. Amount of flex-bes use: again the amount of flex-bes use tells something about the variability of the occupancy of the clinic VI. Amission stops: the amount of amission stops stans for the times the clinic is full. The higher the amount of amission stops, the higher the amount refuse an elaye patients. The amount of amission stops gives information about the quality of the system, more amission stops result in a lower quality. VII. The amount of refuse / elaye patients: this tells something about the quality of the process, more refuse / elaye patients result in a lower quality of the services. VIII. Costs: an optimal scenario between the amount of regular bes an flex-bes will be foun base on fictive costs, since the exact cost structures are unknown. Scenarios base on ifferent costs regaring to regular bes, available an use flex-bes, an reject patients will be teste. The costs represent a combination of all escribe performance measures above, where higher costs stans for weaker overall results. 22

35 5.3. BASELINE PERIODS As shown in the previous chapter, many ifferent time perios have a significant effect on the be capacity. This paragraph aims to reuce the amount of perios. Therefore, first a istinction is mae between reuction perios an normal perios. The reuction perios consists of off-ays, holiays an weekens. The normal perios consists of all the other time perios. First, the normal perio will be split into ifferent timespans. For these normal perios, the number of occupie forecaste bes per month is taken as starting point. Data is use from the forecasts for the perios from , where holiays, off-ays an weekens are filtere out to fin possible ways to combine ifferent months with the aim to reuce the amount of perios. The means of the forecaste be occupancy of each month are compare with each other. The following hypotheses are teste; H 0 : μ X = μ Y, H 1 : μ X μ Y with α = 0,05 where x an y are ifferent perios. In case the H 0 is accepte, a possible cluster is introuce. In case a month can be combine with ifferent months, also larger clusters will be teste. The test statistic that is use is the two sample t-test with unequal variances, because the variance is unknown, an it is not likely that the variance for each month is the same ue to possible external influences which are seasonal relate, for example a flu epiemic. The formulas that are use are isplaye below. The test statistic is: The egree of freeom: f = t x y 0 = s x 2 n + s 2 y m (s 2 x 2 n + s y m )² s y 2 ( s x 2 n )² n 1 + ( m )² m 1 The results of all the performe t-tests are shown in appenix IV. The possible clusters are given in table 11 below. This table also inclues the MAE. Which is in this situation the error in number of bes in case the average number of bes is use for that specific cluster, compare to the real occupie number of bes. The next step is to fin the optimal clusters. Therefore, an integer linear programming moel is mae. This moel calculates the clusters base on a restricte number of perios which can be fille in as a constraint. The moel aims to minimize the mean absolute error an is isplaye 23

36 below. Base on the possible clusters to reuce the amount of perios a minimum of 4 perios is require. Table 11: Possible clusters to reuce the amount of perios #(p) Cluster (C p ) MAE(M p ) Days(D p ) #(p) Cluster (C p ) MAE(M p ) Days(D p ) 1 January 10, February + April 10, February 9, April + December 11, March 8, May + August 11, April 11, June + September 11, May 11, July + September 11, June 12, January + December 10, July 11, May + September 11, August 10, July + October 11, September 11, January + April + November 11, October 11, April + November + December 11, November 10, May + June + August 11, December 10, June + August + September 12, January + April 11, July + August + September 11, February + March 9, January + April + December 11, April + November 11, May + June + September 11, May + June 11, July + August + October 11, June + August 11, January + November + December 10, July + August 11, May + August + September 11, August + September 11, January + April + November + December 10, November + 20 December 10, May + June + August + September 11, January + November 10, Minimize: 41 t=1 M p C p D p 41 t=1 C p D p Decision variables: C p t #Perios Subject to: C C p Binary t 41 C t =1 C p = #Perios 41 j=1 X i,p C p = 1 i, where X i,p = 1 if month i is in cluster p An: C p = Cluster, p = perio, M p = MAE at perio p, D p = total ays for perio p The optimal clusters Ω for a given number of perios p are isplaye on the next page: 24

37 Table 12: Optimal clusters for a given number of perios # MAE Clusters 12 10, , , , , , , , ,88 Ω 12 = ({January}, {February}, {March}, {April}, {May}, { June}, {July}, {August}, { September}, {October}, {November}, {December}) Ω 11 = ({January}, {February}, {March}, {April}, {May}, { June}, {July, August}, { September}, {October}, {November}, {December}) Ω 10 = ({January, November}, {February}, {March}, {April}, {May}, {June}, {July, August}, { September}, {October}, {December}) Ω 9 = ({January, November, December}, {February}, {March}, {April}, {May}, { June}, {July, August}, { September}, {October}) Ω 8 = ({January, November, December}, {February}, {March}, {April}, {May, June}, {July, August}, { September}, {October}) Ω 7 = ({January, November, December}, {February}, {March}, {April}, {May, June}, { July, October}, { August, September}) Ω 6 = ({January, November, December}, {February, April}, {March}, {May, June}, { July, October}, { August, September}) Ω 5 = ({January, April, November, December}, {February, March}, {May, June}, { July, October}, { August, September}) Ω 4 = ({January, April, November, December}, {February, March}, {May, June, August, September}, { July, October}) This table shows that a reuction of the number of perios only has a small effect on the error in the range from 12 to 4 clusters, smaller clusters are not possible base on perios that o not significantly iffer from each other. As well as the normal perios, the amount of reuction perios will be reuce. Again, a t-test is use. The results of the t-test are summarize in table 13 below. The ifferent t-tests itself can be foun in Appenix V. For the weekens, it is assume that the optimal clusters are the same as the clusters for the normal perios Ω 4, ue to the lack of sufficient ata for a larger ifferentiation. Reuction perios Carnival holiay Pentecost Easter weeken / Ascension weeken Christmas / New Year Summerholiay W1 Summer holiay W2 Summer holiay W3+W4 Summer holiay W5+W6 Table 13 clusters for the reuction perios 25 Summer holiay W7 Christmas holiay W1 Christmas holiay W2 Week after May holiay Week after Christmas holiay Saturay Sunay / Kingsay / Liberation ay To generate more insight into the ifferent reuction options, some of these clusters will be compare in the next paragraph. First, the perios from the current work metho of the

38 Catharina Hospital are chosen as a benchmark, this option implies one single amount of available bes uring the whole year, excluing a reuction for the summer holiay. The secon scenario, also inclues a single normal perio; however, now all reuction perios are inclue, where the number of reuction perios has been reuce by table 13. This scenario aims to generate insight into the effect of aing only special ays an holiays. These reuction perios are inclue as well in scenario three an four, where scenario three consists of Ω 4 for the normal perios as state in table 12. This scenario is chosen because it is the option with the lowest number of clusters base on significant results. Scenario four contains a ifferent baseline every month (Ω 12 ), to see the results of extremely anticipating on the ifferent time perios. For the weekens, the same clusters are use as for the normal perios, except for a ifferent baseline every month. In this case, the months are split up into four clusters to avoi the effect of over fitting because for some months, only a few number of weekens were counte DETERMINATION BASELINE With the multiple regression moel many ifferent perios have been iscovere that o have a significant effect on the eman for bes. In the previous paragraph, all these ifferent perios have been clustere. In this paragraph, the optimal amount of regular bes an flex-bes will be calculate base on ifferent cost scenarios an perios. As mentione in the literature stuy, a great amount of effort in the be capacity literature has been evote to queueing moels; however, with all the reuction perios it is har to apply these queueing moels ue to ifferent arrival patterns an ALOS for each perio. Therefore, an integer linear programming moel is mae to fin the optimum amount of bes. The moel is closely relate to the traitional newsboy problem; however, now four ifferent cost types are inclue. First, for regular be costs (C rb ) is assume that these bes are always manne with nurses, this implies the costs for occupie an unoccupie bes are the same. For the active flexbes (C fa ) it is assume that these are only manne with nurses when the bes are occupie. This coul be more expensive ue to the type of contract for these nurses. Costs for passive flexbes (C fp ) are also inclue, since there must be a pool of nurses who are always available in cases these flex-bes must be quickly. Coorination of this pool also nees to be pai. The final cost type is the costs for refuse patients (C rf ), these costs are relate to both the costs of missing profit, costs relate to searching for another hospital for that refuse patient, an costs for reputation amage. The exact cost structures are unknown. Therefore, the moel will be execute with ifferent scenarios relate to the costs which will be explaine in table

39 Table 14: Five ifferent costs scenarios Sce nar io Costs of regular bes Costs of active flexbes Costs of passive flex-bes Refusu al costs Explanation Estimate relative cost values To iscover the impact of relatively cheap flexible nurses To iscover the impact of expensive passive flex-bes (coorination costs) To iscover the impact of expensive flexible nurses To iscover the impact of very high refusal costs. The moel uses a probability ensity function for every single perio. This probability ensity function can be base on any istribution. For the input of the moel, all ifferent perios were teste on a normal istribution. In case the normal istribution i not fit the Gamma, Weibull an lognormal istribution were teste. The chi square statistic is use as gooness of fit parameter: k Χ 0 2 = (O i E i )² i=1 Where k is the number of bins, calculate by k = 1 + log 2 N, an O i is the observe frequency for bin i, an E i is the expecte frequency for bin i calculate by E i = F(x 2 ) F(x 1 ) where F is the cumulative istribution function (CDF) of the probability istribution being teste, an x 1, x 2 are the limits for bin i. The hypotheses teste are: H 0 : The be occupancy ata follow the specifie istribution, H 1 : the be occupancy ata o not follow the specifie istribution E i With α = 0,05. Where H 0 will hol if Χ < Χ 1 α,k 1 From the tests, it can be conclue that all perios follow a normal istribution, except one. This is the actual situation in the Catharina hospital, were only the summer holiay is exclue. In that 27

40 case a Weibull istribution is use. This one can be seen below as an example, all other results are shown in appenix VI. 0,26 0,24 0,22 0,2 Probability Density Function 1 perioe excluing s Weibull Alpha 16,006 Beta 329,04 0,18 f(x) 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 Gooness of fit Deg of free 10 Statistics 14,441 P-value 0,15379 Alpha 0,05 Critical val 18, Figure 11: Distribution fitting, one perio excluing summer holiay Base on these ifferent istributions, costs, an time perios, the integer linear programming moel below is execute to fin the optimal number of regular bes an flex-bes for every specific perio. A constraint for the maximum amount of flex-bes is built in case a hospital wants to restrict the total number of flex-bes for non-cost reasons. However, in this analysis this constraint is not taken into account. Base on the istributions an ifferent costs the following moel is create: MAX Minimize: b MAX R i C b MAX b MAX b rb C rf i=1 + i=1 F i C fp + i=1 F i F(x) C fa + i=1 P i F(x) Decision variables: F i i R i i Subject to: i binary i F i + R i 1 MAX b F=1 F i MAX f F i + R i + P i = 1 Where: F i = patient in flex bes R i = patient in regular bes P i = patient not in be C rb = Cost regular bes C fp = Costs passive flex bes F(x) = Distribution function on [0, MAX b ] 28 i = patient C fa = Costs active flex bes C rf = Costs refusuals f(x) = Corresponing PDF Weibull PDF: f(x) = βxβ 1 α β e x/αβ PDF: f(x) = 1 e (x μ)β 2σ 2 σ 2π MAX f = Maximum esirable number of flex bes MAX b = Maximum esirable number of bes, which is in this case 450. For the results, the ifferent performance measures escribe in section 5.2 are use, the calculations for the performance measures are shown below: MAX b Total regular bes = R i i=1 MAX b Total flex bes = F i i=1 Occupancy regular bes = x MAX b i=1 R i MAX b i=1 330 F(X) 100% R i 340 Percentage of time flexbes = (1 min { 1, R i = 1, i) 100% f(x), R i

41 5.5. RESULTS MAX b Expecte amount of flex bes = F i F(x) Percentage of recoring stops = (1 min { 1, R i + F i = 1, i) 100% f(x), R i + F i 1 Expecte amount of refuse elaye patiets = P i F(x) Bases on the moel escribe above, the optimal number of regular bes an flex-bes are calculate for all the ifferent time perios an cost scenarios. To compare the effect of the ifferent cost scenarios an example of the results is given. After calculating the optimal number of bes base on the cost scenarios, the costs per ay in all tables are correcte for the ifferent scenarios to make them comparable. This example inclues the one perio with only summer exclue (table 16). More etaile results can be foun in appenix VII. i=1 MAX b Table 15: Results of the ifferent cost scenarios for one perio with only summer as a reuction perio i=1 Regu lar bes Flex be s Occupancy rate regular bes % of time flexbes One perio only summer holiay as reuction Expecte refuse/ Expecte Probability elaye Costs per #flexbes Amission patients ay for stop per ay scenario 1 The results of table 15 show that e.g. the costs from scenario 1 result in 320 regular bes an 32 flex-bes per ay for With this amount of bes, the expecte weighte average occupancy rate per ay is 95,86% an the flex-bes are for 42,94% of the time. On average 6,36 flexbes per ay are in use, an there is a 2,48% probability for an amission stop per ay. The weighte average of the expecte elaye / refuse patients per ay is 0,17, which results in 0, = 62,05 elaye / refuse patients per year. Analyzing the ifferences between scenario 1 an 2, the results show that lower costs of flex-bes result in a lower amount of regular bes, an a higher amount of flex-bes. Therefore, the occupancy rate of the regular bes, as well as the number of times flex-bes are, an the amount of flex-bes is will all increase. Because of the lower cost ratio, comparing the flex-bes with refuse / elaye patients, the probability of an amission stop, the expecte refuse / elaye patients all ecrease. Comparing scenario 1 with 3, it shows that increase costs of passive flex-bes not only results in a ecrease in flex-bes but also in a ecrease in regular bes. This results in a higher occupancy 29 Costs per ay for scenario 2 Costs per ay for scenario 3 Costs per ay for scenario 4 Costs per ay for scenario 5 Cost scen ,86% 42,94% 6,36 2,48% 0, Cost scen ,64% 76,71% 21,32 2,13% 0, Cost scen ,31% 47,83% 7,49 5,13% 0, Cost scen ,22% 27,42% 3,06 2,87% 0, Cost scen ,86% 42,94% 6,52 0,27% 0,

42 of regular bes, flex-bes are use more often, the probability of amission stops increases, an the expecte number of refuse / elaye patients increases. Scenario 4 shows that an increase of costs for active flex-bes result in a higher amount of regular bes an a lower amount of flex-bes. Therefore, less flex-bes are use. The amount of amission stops an refuse / elaye patients increases. Increasing the refusal costs (scenario 5), results in exactly the same amount of regular bes as in scenario 1. The amount of flex-bes is higher. Therefore, the occupancy rate for the regular bes, an the amount of time flex-bes are are the same. The higher amount of flex-bes result in less amission stops an less refuse / elaye patients. Besies the cost scenarios, also the effect of ifferent time perios are teste. The results from these perios with cost scenario 1 as an example can be foun in table 16 on the next page. The results from the other cost scenarios are given in appenix VIII. These tables show that incluing more perios, results in less expecte weighte average costs. Especially aing the reuction perios results in better performances on the number of regular bes, the frequency an average amount of use flex-bes an the refusal rate (on average 772, base on the fictive costs), where Easter / Ascension weeken, Pentecost an the Christmas perio show the largest improvements. An extra extension by splitting up the regular months into four perios oes have a smaller effect but still shows improvements (on average, an extra 117, base on the fictive costs). Especially by anticipating on the busy months, February an March, an the most quiet months, June an September. The most etaile level, creating a new be level for each month separately, harly shows any improvements (on average, an extra 7). 30

43 Table 16: Results per perio for cost scenario 1 Time perio Regu lar Scen 1 1 perio only summer holiay as reuction 1 perio with all reuction perios 4 perios with all reuction perios 12 perios with all reuction perios Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts Costs Regu per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expec te refus e/ elay e patie nts Costs Regu per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie Costs Regu nts per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie Costs nts per ay 4Perios1Saturay ,81% 9,06% 0,71 0,02% 0, ,51% 41,54% 4,78 2,16% 0, ,66% 43,02% 4,94 2,17% 0, ,66% 43,02% 4,94 2,17% 0, Perios1Sunay ,09% 2,36% 0,15 0,00% 0, ,71% 44,73% 5,21 2,36% 0, ,53% 42,03% 4,77 2,00% 0, ,53% 42,03% 4,77 2,00% 0, Perios2Saturay ,94% 13,50% 1,10 0,04% 0, ,41% 54,10% 6,70 3,50% 0, ,77% 42,83% 4,75 2,14% 0, ,77% 42,83% 4,75 2,14% 0, Perios2Sunay ,40% 5,54% 0,32 0,00% 0, ,55% 78,74% 10,84 5,54% 0, ,02% 39,52% 3,46 2,08% 0, ,02% 39,52% 3,46 2,08% 0, Perios3Saturay ,78% 6,12% 0,46 0,01% 0, ,91% 34,09% 3,67 1,35% 0, ,49% 41,69% 4,82 2,21% 0, ,49% 41,69% 4,82 2,21% 0, Perios3Sunay ,05% 0,10% 0,00 0,00% 0, ,62% 17,08% 1,32 0,10% 0, ,71% 40,71% 3,99 1,95% 0, ,71% 40,71% 3,99 1,95% 0, Perios4Saturay ,19% 8,17% 0,66 0,03% 0, ,16% 38,30% 4,40 2,08% 0, ,35% 40,79% 4,83 2,08% 0, ,35% 40,79% 4,83 2,08% 0, Perios4Sunay ,91% 0,26% 0,01 0,00% 0, ,25% 30,84% 2,64 0,26% 0, ,88% 40,29% 3,70 2,13% 0, ,88% 40,29% 3,70 2,13% 0, Januari ,51% 78,35% 12,27 4,63% 0, ,62% 53,60% 6,19 2,33% 0, ,18% 44,40% 4,66 1,93% 0, ,02% 41,38% 4,20 1,93% 0, Februari ,79% 88,61% 15,90 8,24% 0, ,25% 68,30% 8,83 4,33% 0, ,07% 39,99% 3,81 2,08% 0, ,42% 44,46% 4,19 2,04% 0, March ,88% 92,23% 17,16 8,80% 0, ,46% 73,92% 9,70 4,46% 0, ,42% 44,46% 4,19 2,04% 0, ,25% 41,06% 3,73 2,04% 0, April ,49% 79,09% 13,35 7,22% 0, ,66% 56,80% 7,22 4,06% 0, ,25% 48,35% 5,60 3,48% 0, ,94% 42,73% 4,73 2,13% 0, May ,26% 35,65% 3,88 0,54% 0, ,33% 16,31% 1,42 0,24% 0, ,44% 38,22% 4,20 1,61% 0, ,62% 40,85% 4,58 2,25% 0, June ,41% 38,80% 4,48 0,83% 0, ,55% 19,00% 1,76 0,39% 0, ,58% 41,35% 4,81 2,28% 0, ,58% 41,35% 4,83 1,95% 0, July ,48% 54,68% 7,11 1,82% 0, ,97% 30,70% 3,11 0,89% 0, ,54% 38,32% 4,16 1,82% 0, ,71% 40,98% 4,56 2,15% 0, August ,50% 33,24% 3,08 0,14% 0, ,47% 12,44% 0,90 0,05% 0, ,69% 36,19% 3,43 0,60% 0, ,05% 42,34% 4,19 2,10% 0, September ,03% 44,87% 5,08 0,71% 0, ,27% 21,71% 1,92 0,31% 0, ,19% 47,75% 5,47 2,19% 0, ,86% 42,01% 4,52 2,19% 0, October ,76% 59,94% 8,08 2,23% 0, ,38% 35,04% 3,64 1,10% 0, ,91% 43,17% 4,81 2,23% 0, ,74% 40,41% 4,37 2,23% 0, November ,31% 72,80% 10,97 3,98% 0, ,27% 47,73% 5,40 2,03% 0, ,78% 39,04% 4,03 1,69% 0, ,95% 41,90% 4,44 2,03% 0, December ,32% 72,87% 10,79 3,54% 0, ,28% 47,19% 5,21 1,75% 0, ,79% 38,33% 3,86 1,45% 0, ,96% 41,24% 4,25 2,10% 0, Carnival holiay ,71% 30,14% 3,95 1,58% 0, ,84% 41,49% 6,14 2,29% 0, ,84% 41,49% 6,14 2,29% 0, ,84% 41,49% 6,14 2,29% 0, Easter / Ascension ,18% 1,48% 0,11 0,00% 0, ,94% 42,31% 5,73 2,25% 0, ,94% 42,31% 5,73 2,25% 0, ,94% 42,31% 5,73 2,25% 0, May holiay ,49% 11,16% 1,27 0,36% 0, ,50% 43,52% 7,27 2,29% 0, ,50% 43,52% 7,27 2,29% 0, ,50% 43,52% 7,27 2,29% 0, Week after may holiay ,21% 9,08% 0,96 0,20% 0, ,58% 42,80% 6,79 2,23% 0, ,58% 42,80% 6,79 2,23% 0, ,58% 42,80% 6,79 2,23% 0, Pentecost ,19% 0,01% 0,00 0,00% 0, ,36% 42,25% 4,72 2,22% 0, ,36% 42,25% 4,72 2,22% 0, ,36% 42,25% 4,72 2,22% 0, Summer holiay W ,19% 42,70% 5,58 2,19% 0, ,19% 42,70% 5,58 2,19% 0, ,19% 42,70% 5,58 2,19% 0, ,19% 42,70% 5,58 2,19% 0, Summer holiay W ,58% 52,05% 7,87 3,72% 0, ,87% 43,21% 6,01 2,24% 0, ,87% 43,21% 6,01 2,24% 0, ,87% 43,21% 6,01 2,24% 0, Summer W3+W ,01% 32,29% 3,77 0,70% 0, ,88% 41,38% 5,22 2,11% 0, ,88% 41,38% 5,22 2,11% 0, ,88% 41,38% 5,22 2,11% 0, Summer W5+W ,20% 47,90% 7,05 3,16% 0, ,64% 41,42% 5,73 2,16% 0, ,64% 41,42% 5,73 2,16% 0, ,64% 41,42% 5,73 2,16% 0, Summer holiay W ,52% 42,14% 6,85 2,23% 0, ,52% 42,14% 6,85 2,23% 0, ,52% 42,14% 6,85 2,23% 0, ,52% 42,14% 6,85 2,23% 0, Christmas / New Year ,82% 0,00% 0,00 0,00% 0, ,65% 41,72% 5,11 2,13% 0, ,65% 41,72% 5,11 2,13% 0, ,65% 41,72% 5,11 2,13% 0, Christmas holiay W ,69% 1,30% 0,10 0,00% 0, ,95% 43,24% 6,02 2,26% 0, ,95% 43,24% 6,02 2,26% 0, ,95% 43,24% 6,02 2,26% 0, Christmas holiay W ,85% 0,25% 0,02 0,00% 0, ,33% 42,24% 6,39 2,26% 0, ,33% 42,24% 6,39 2,26% 0, ,33% 42,24% 6,39 2,26% 0, Week after Christmas ,20% 30,72% 4,45 2,64% 0, ,49% 42,44% 7,18 2,14% 0, ,49% 42,44% 7,18 2,14% 0, ,49% 42,44% 7,18 2,14% 0, Weighte average (year) ,86% 42,94% 6,36 2,48% 0, ,35% 42,65% 5,31 2,11% 0, ,52% 42,17% 5,00 2,14% 0, ,51% 41,85% 4,93 2,13% 0,

44 5.6. VALIDATION In this paragraph, the results from the previous paragraph will be valiate. First, the weighte averages per year will be compare, an further, a more in epth valiation will take place for all the specific time perios. Table 17 represents the performance measures for The first column, realization 2014, represents the output of the moel escribe in previous chapter with ata of the occupie bes in The secon column, represents the output where ifferent istributions are use as input base on ata from 2009 till Table 17: the weighte average performance measures of the realization for 2014 versus expecte performance measures Scen 1 Scen 2 Scen 3 Scen 4 Scen 5 Occupancy % of time rate regular flexbes bes Realization 2014 #flexbes % of ays a Amissio refuse / n stop elaye occure patients Cost per ay As can be seen, the occupancy rate for the regular bes are preicte very well. The largest eviation (0,41%) occurs for cost scenario 2 with one perio an all reuction perios are inclue. The percentage of time a flex be is seems a little higher for the realization, except for scenario 2, where it is slightly lower. Incluing more perios results in a larger eviation. The number of flex-bes is in all cases higher than expecte as well as the amission stops. However, the number of refuse / elaye patients is lower. The overall performance measure costs for the non-reuction are closely corresponing. For the higher etaile scenarios with more perios, the ifferences in costs increases. Table 18 represents the valiation results on a more etaile level. The performance measures of the realization per perio for cost scenario 1 with all reuction perios inclue versus the expecte performance measures are given. For completeness, all other valiation results are given in appenix IX, these results follow the same pattern as the example below. 32 Expecte occupancy rate regular bes Expecte % of time flexbes Expecte Expecte #flexbes Expecte probability Amission stop for a specific ay Expecte refuse / elaye patients Expecte costs per ay No reuction 95,93% 42,47% 6,50 3,01% 0, ,86% 42,94% 6,36 2,48% 0, p 97,06% 50,14% 6,54 4,11% 0, ,35% 42,65% 5,31 2,11% 0, p 97,32% 47,67% 5,96 4,93% 0, ,52% 42,17% 5,00 2,14% 0, p 97,29% 47,40% 5,84 4,93% 0, ,51% 41,85% 4,93 2,13% 0, No reuction 98,61% 76,44% 21,64 3,01% 0, ,64% 76,71% 21,32 2,13% 0, p 98,85% 75,07% 16,58 4,11% 0, ,26% 77,35% 15,13 1,82% 0, p 99,06% 77,53% 15,49 4,93% 0, ,35% 77,94% 14,38 1,88% 0, p 99,08% 76,16% 15,36 4,93% 0, ,35% 77,91% 14,34 1,88% 0, No reuction 96,38% 47,95% 7,61 6,03% 0, ,31% 47,83% 7,49 5,13% 0, p 97,38% 52,88% 7,28 8,77% 0, ,72% 48,02% 6,16 4,79% 0, p 97,63% 50,68% 6,55 8,49% 0, ,86% 47,07% 5,68 4,86% 0, p 97,63% 51,23% 6,59 8,49% 0, ,88% 47,37% 5,72 4,79% 0, No reuction 94,31% 29,59% 3,28 3,84% 0, ,22% 27,42% 3,06 2,87% 0, p 95,93% 35,62% 3,73 5,21% 0, ,07% 27,82% 2,83 2,46% 0, p 96,17% 32,60% 3,35 5,21% 0, ,25% 26,79% 2,61 2,48% 0, p 96,13% 32,05% 3,27 5,21% 0, ,21% 26,29% 2,55 2,41% 0, No reuction 95,93% 42,47% 6,67 0,27% 0, ,86% 42,94% 6,52 0,27% 0, p 97,06% 50,14% 6,85 0,55% 0, ,35% 42,69% 5,45 0,13% 0, p 97,32% 47,67% 6,32 0,55% 0, ,52% 42,17% 5,14 0,17% 0, p 97,29% 47,40% 6,22 0,55% 0, ,49% 41,60% 5,04 0,17% 0,

45 Table 18: the performance measures of the realization of 2014 versus expecte performance measures Occupa ncy rate regular bes % of time flexbe s Realization 2014 #flex bes open e % of ays a Amiss ion stop occur 12 perios with all reuction perios Refuse / elaye patient s per Occupa ncy rate regular bes Time perio Reg ular Flex Costs per ay Reg ular Flex Costs per ay 4Perios1Saturay ,38% 63,64% 6,45 9,09% 0, ,66% 43,02% 4,94 2,17% 0, Perios1Sunay ,82% 90,91% 12,36 18,18% 1, ,53% 42,03% 4,77 2,00% 0, Perios2Saturay ,22% 71,43% 6,57 0,00% ,77% 42,83% 4,75 2,14% 0, Perios2Sunay ,20% 28,57% 3,00 0,00% ,02% 39,52% 3,46 2,08% 0, Perios3Saturay ,03% 30,00% 2,50 0,00% ,49% 41,69% 4,82 2,21% 0, Perios3Sunay ,62% 20,00% 4,10 10,00% 0, ,71% 40,71% 3,99 1,95% 0, Perios4Saturay ,30% 83,33% 13,50 16,67% 0, ,35% 40,79% 4,83 2,08% 0, Perios4Sunay ,89% 83,33% 11,17 33,33% 3, ,88% 40,29% 3,70 2,13% 0, Januari ,37% 33,33% 2,47 0,00% ,02% 41,38% 4,20 1,93% 0, Februari ,33% 40,00% 3,55 0,00% ,42% 44,46% 4,19 2,04% 0, March ,39% 62,50% 5,31 0,00% ,25% 41,06% 3,73 2,04% 0, April ,91% 55,56% 5,67 0,00% ,94% 42,73% 4,73 2,13% 0, May ,25% 23,08% 2,46 0,00% ,62% 40,85% 4,58 2,25% 0, June ,06% 0,00% - 0,00% ,58% 41,35% 4,83 1,95% 0, July ,66% 77,78% 12,78 11,11% 0, ,71% 40,98% 4,56 2,15% 0, August ,05% 42,34% 4,19 2,10% 0, September ,03% 50,00% 5,14 0,00% ,86% 42,01% 4,52 2,19% 0, October ,64% 47,83% 6,43 4,35% 0, ,74% 40,41% 4,37 2,23% 0, November ,67% 75,00% 7,55 0,00% ,95% 41,90% 4,44 2,03% 0, December ,99% 60,00% 5,27 13,33% 0, ,96% 41,24% 4,25 2,10% 0, Carnival holiay ,05% 11,11% 0,44 0,00% ,84% 41,49% 6,14 2,29% 0, Easter / Ascension ,37% 42,86% 11,86 14,29% 0, ,94% 42,31% 5,73 2,25% 0, May holiay ,30% 75,00% 10,75 0,00% ,50% 43,52% 7,27 2,29% 0, Week after may holiay ,40% 57,14% 8,71 0,00% ,58% 42,80% 6,79 2,23% 0, Pentacost ,61% 0,00% - 0,00% ,36% 42,25% 4,72 2,22% 0, Summer holiay W ,81% 57,14% 11,57 14,29% 1, ,19% 42,70% 5,58 2,19% 0, Summer holiay W ,15% 57,14% 4,71 0,00% ,87% 43,21% 6,01 2,24% 0, Summer W3+W ,19% 35,71% 0,93 0,00% ,88% 41,38% 5,22 2,11% 0, Summer W5+W ,64% 7,14% 0,43 0,00% ,64% 41,42% 5,73 2,16% 0, Summer holiay W ,70% 14,29% 0,29 0,00% ,52% 42,14% 6,85 2,23% 0, Christmas / New Year ,36% 33,33% 9,67 33,33% 8, ,65% 41,72% 5,11 2,13% 0, Christmas holiay W ,87% 83,33% 24,00 50,00% 4, ,95% 43,24% 6,02 2,26% 0, Christmas holiay W ,81% 75,00% 16,00 12,50% 13, ,33% 42,24% 6,39 2,26% 0, Week after Christmas ,25% 57,14% 6,00 0,00% ,49% 42,44% 7,18 2,14% 0, Weighte average (year) ,29% 47,40% 5,84 4,93% 0, ,51% 41,85% 4,93 2,13% 0, The results show that in particular for the perios: 4Perios1Sunay, December, Easter / Ascension, summer holiay W1, Christmas / New Year, Christmas Holiay W1 an Christmas holiay W2, the eman was higher than expecte at some ays. This resulte in a higher percentage of amission stops an more refuse / elaye patients. The perios: Carnival, June, Pentecost, Summer holiay W3+W4, Summer holiay W5 + W6, Summer holiay W7 show a lower eman than expecte, resulting in a lower occupancy rate for the regular bes an a reuce use of flex-bes. A graphical presentation of the occupie bes for scenario 1 with the corresponing perios versus the realization can be foun in figure 12 an 13 below, in figure 12 only the regular bes have been inclue an in figure 13 the regular + flexbes have been inclue. The figures from the other cost scenarios can be foun in appenix X. % of time flexbe s Expecte Expec te #flex bes open e Proba bility Amis sion stop Expect e refuse / elaye 33

46 Scenario 1 Regular Bes 1-jan 1-feb 1-mrt 1-apr 1-mei 1-jun 1-jul 1-aug 1-sep 1-okt 1-nov 1-ec Realisation 1 perio no reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Figure 12: Realization versus the regular bes for cost scenario 1 incluing all ifferent perios Scenario 1 Regular + Flex Bes jan 1-feb 1-mrt 1-apr 1-mei 1-jun 1-jul 1-aug 1-sep 1-okt 1-nov 1-ec Realisation 1 perio no reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Figure 13: Realization versus the regular bes + flex-bes for cost scenario 1 incluing all ifferent perios 5.7. CONCLUSIONS ON TACTICAL PLAN The aim of this chapter was to provie a tactical plan for the optimal number of bes an flexbes. In literature, the main focus for etermining the optimal amount of bes is relate to queueing moels. The occupancy rate is a key utilization ecision variable when planning the inpatient care facility size (Li en Benton 1996). First, the significant perios, which were foun in chapter 4 were compare to each other with the aim to reuce the amount of perios. Base on a t-test ifferent perios were clustere. For the normal perios, with ifferent cluster probabilities, the optimal combinations have been foun by using an integer linear programming moel. Base on this moel, the ifferent months can be clustere in 4 perios (Ω4= ({January, April, November, December}, {February, March}, {May, June, August, September}, {July, October})). Easter an Ascension, Summer Holiay W3 an W4, Summer Holiay W5 an W6, an Sunay, Kingsay an Liberation ay can also be combine. 34

47 For ifferent costs scenarios, an ifferent perio scenarios, the optimal amount of regular bes an flex-bes is calculate via an integer linear programming moel. Because the exact costs for regular bes, flex-bes, an refuse patients are unknown ifferent cost scenarios were create to show how changes in the cost structure effect the amount of regular bes an flex-bes. The ifferent cost scenarios show that: Decrease costs for active flex-bes result in less regular bes an more flex-bes. Increase costs of passive flex-bes result in less regular bes an less flex-bes. Increase costs for active flex-bes result in more regular bes an less flex-bes. Increase costs for patient refusals / elays result in the same amount of regular bes an an increase in flex-bes. Four scenarios with ifferent perios were teste. 1. The actual situation, 2. A scenario with all holiays, an special perios, 3. A scenario with all reuction perios an where the months are split into four perios, 4. A scenario with all reuction perios an each month as a separate perio. The results show that anticipating on weekens, holiays an special ays result in a ecrease of the fictive costs for approximately 770,- per ay. Moreover, iviing the months into four ifferent perios results in an aitional ecrease of 120,- per ay. The efficiency increase for an even more etaile version with each month as a separate perio is negligible. Since aing more perios also requires more coorination, the last scenario will be rejecte as a possible solution for the Catharina Hospital ue to the negligible improvements. The valiation process shows that in general, flex-bes are more often than expecte, where incluing more perios result in a higher eviation between the expectation an realization. However, the expecte refuse/ elaye patients are higher compare to the reality. Therefore, the istribution may have a slightly negative kurtosis. The valiation results show a smaller ifference in costs between the ifferent scenarios than the expecte results. The main cause are some single unexpecte very busy ays (in total 6 ays) in the perios 4Perios1Sunay, Christmas / New Year, an Christmas Holiay W1, where the costs are highly increase ue to refuse/ elaye patients. Especially New Year, with a eman of 299 patients an therefore 26 refusals seems to be exceptional. The perio Summer Holiay W1 shows some large eviations. A possible explanation coul be the VRE-virus where the hospital was ealing with at that moment. Overall, the moel provies a proper tactical plan for the amount of require regular bes an flex-bes for the long term. However, ue to for example external influences such as a virus, or other causes also an operational plan shoul be evelope to eal with extreme unexpecte emans for very short perios. 35

48 6. OPERATIONAL PLAN After setting up a tactical plan for the number of bes in the previous chapter, this chapter aims to eal with the short term be occupancy by generating more insight into the occupancy of bes for t ays ahea. Therefore, first some relevant literature is iscusse. In paragraph 6.2 the use ata will be explaine. Base on this ata ifferent istributions for the arrivals, LOS, an remaining LOS will be calculate in paragraph 6.3. Paragraph 6.4 will combine the ifferent istributions into a moel to create a forecast of the number of occupie bes t ays ahea. The next paragraph will present the results of the moel. In paragraph 6.6 the valiation will take place, an finally the chapter ens with a conclusion on this operational plan LITERATURE In this paragraph, literature about the arrival patterns of an the length of stay of patients will be iscusse briefly ARRIVAL PATTERNS There are two ways in which patients can arrive, ranom arrivals an scheule arrivals. Alexopoulos et al. (2008) foun that researchers, from history till present, assume that the interarrival times of unscheule patients are inepenent an ientically istribute ranom variables from the exponential istribution. Accoring to Gorunescu et al. (2002) it is reasonable to assume that the ranom patients follow Poisson istribution in orer to create a stable hospital system. De Bruin et al. (De Bruin, et al. 2010) moele both the elective an emergency patients as a Poisson process. For the elective patients the ata is split up into weekays an weekens. Despite the fact that elective patients are planne, it seems that the arrivals of elective patients are quite variable for most epartments LENGTH OF STAY The length of stay (LOS) is the time a patient spens in war an is an easily available inicator of hospitals an is use for various purposes, such as quality control, appropriateness of hospital use, management of hospital care, an hospital planning (Marazzi, et al. 1998). Due to increasing costs, the efficient use of bes is becoming more important. Accoring to Lapierre et al. (1999) the average length of stay in hospitals has been reuce rastically. The length of stay has a typical istribution where most patients only stay short in the hospital; however, a small group of patients will be in a hospital for a longer perio. Therefore, the LOS istribution is skewe, contains outliers an has a large stanar eviation. There is a large variety of istribution patterns of the LOS such as Weibull, lognormal, normal, gamma, Erlang, or negative exponential. Accoring to Vissers an Beech (2005) the Erlang or Gamma istribution which are both characterize by an early peak an a long tail to the right are often use to arrive a goo fit 36

49 with this type of istributions. However, Marazzi et al. (1998), foun that the lognormal moel fits best, an moreover, the Weibull istribution is sufficient in most cases DATA For this chapter, ata about the arrivals, the expecte LOS, an the ALOS is require. From the interviews can be conclue that information about the patient arrival types, whether a patient is elective or an emergent patient is not completely reliable. The only way to have an inication base on numbers on the reliability of the patient arrival types are the arrivals at the emergency epartment. In reality elective patients never arrive at the ED. Accoring to the ata from 2009 till 2014, arrivals emerge through the ED, of which 789 arrivals were inicate as elective. This results in an % = 1,35% error. To calculate the arrivals of emergency patients, the same ataset is use as for chapter 4 an 5, where only ata from the regular epartments within the clinic are taken into account. For the reliability of the elective arrivals, snapshots of the epartment occupation overview are mae, since the store ata oes not contain changes in the expecte arrival ate. Snapshots were taken in the perio from till to progress the reliability for the elective patients. No snapshots were mae on Friays an weekens. In total, 14 snapshots were mae. For these ays one snapshot occurre in the morning aroun 9am, an one in the afternoon aroun 16:30. Figure 15 shows the total measure patients planne 1 till 14 ays in avance from the ata create with snapshots. Base on the ata from 2009 till 2014, on average about elective patients arrive at the regular epartments of the hospital. Which is in total about 60% of the total arrivals. Therefore, the reliability of the input for the elective patients is extremely important. Figure 14 shows that about 50% of the patients is planne only one ay in avance Number of elective patients planne x ays in avance <1 (1,2] (2,3] (3,4] (4,5] (5,6] (6,7] (7,14] Ach1 Ach2 Car1 CCH1 Ger1 Gyn1 Int1 Lon1 MDL1 MDO1 Neu1 Ort1 Uro1 Figure 14: Number of elective patients planne x ays avance per epartment Moreover, snapshots were taken to calculate the reliability of the expecte LOS, because again, changes for the expecte ischarge ate are not save in the system. In total 38 snapshots of the epartment occupation overview are mae. This is one in the perio till No snapshots were mae on Friay till Sunay. In total, on 19 ays snapshots were taken. For these ays one snapshot occurre in the morning aroun 9am, an one in the afternoon 37

50 aroun 16:30. Figure 15 shows the number of patients with an without an expecte LOS from the ataset create with snapshots. Where it can be notice that many patients o not contain an expecte ischarge ate Number of patients with an without an expecte LOS Ach1 Ach2 Car1 CCH1 Ger1 Gyn1 Int1 Lon1 MDL1 MDO1 Neu1 Ort1 Uro1 Patients with an expecte LOS Patients with no expecte LOS Figure 15: The number of patients with an expecte LOS per epartment 6.3. DISTRIBUTION FITTING In this paragraph, ata of the arrivals, length of stay, an remaining length of stay will be fitte to ifferent istributions. First, the emergency arrival will be fitte, an thereafter the elective arrivals. After the ifferent arrivals, the remaining LOS an the LOS will be fitte to a istribution EMERGENCY ARRIVALS Emergency arrivals occur unexpecte. Accoring to the literature, emergency arrivals are mostly moele with the Poisson istribution. Therefore, the Poisson istribution will be use. Accoring to the ata of 2013, 9964 arrivals occurre unexpecte. All these emergency arrivals were trie to fit with the Poisson istribution as one category first. The chi square statistic has been use as gooness of fit parameter. However, the ata i not match with the Poisson istribution. To generate more insight into the ata, 2 graphs are presente. Figure 16 represents the total emergency arrivals per ay, whereas figure 17 represents the emergency arrivals per hour. Base Emergency arrivals per ay for Emergency arrivals per hour for Figure 16: total emergency arrivals per ay for 2013 Figure 17: total emergency arrivals per hour for

51 on these two graphs, more specifie clusters are mae, to fin a corresponing Poisson istribution function that fits. These teste clusters are shown in table 19 below, where the starre clusters are significant. The mean stans for the expecte number of minutes between the arrivals, where lamba stans for the expecte number of patient arrivals per hour. Table 19: Poisson istributions for the emergency arrivals Incluing Sample size Ran ge Mea n Variance Distribution P value Lamb a per hour All Arrivals , Poisson 0,00 1,19 Workays , Poisson 0,00 1,26 Workays; 8:00-16: , Poisson 0,00 1,84 Workays; 16:00-8: , Poisson 0,00 1,47 Workays; 0-08: , Poisson 0,57* 0,86 λ 1 Workays; 8:00-12: , Poisson 0,21* 1,96 λ 2 Workays; 12:00-16: , Poisson 0,05* 2,83 λ 3 Workays; 16: , Poisson 0,06* 1,83 λ 4 Weekens , Poisson 0,00 1,02 102,1 Weekens; 1:00-08: Poisson 0,59* 0,59 λ 5 Weekens; 16:00-8: , Poisson 0,00 0,69 Weekens; 08: , Poisson 0,43* 1,28 λ 6 Weekens; - 01: , Poisson 0,00 1,29 Base on the significant time perios, the whole week can be covere with the Poisson istribution except from till 1:00 in weekens. As can be seen in figure 16, the amount of arrivals at hour is much higher than the amount of arrivals at 23:00 or 1:00. Base on this large eviation, it is assume that this is the effect of aministration errors, which also effects the Poisson istribution fitting for till 1:00. Therefore, it is assume that the perio Weekens; 8:00 till also covers the time perio till 1:00 in this report. λ i ELECTIVE ARRIVALS Because elective arrivals are known in avance, the istribution for these arrivals is base on the reliability of the planne patients. Figure 18 below, with on the X-axis the number of ays before the amission is planne, an on the Y-axis the eviation between the planne amission ate an the realization, where Y-axis presents positive values for the postpone arrivals, provies more insight in the elective patient arrivals. 39

52 Deviation between planne arrival ate an realization Scatterplot Number of ays before planne amission Figure 18: scatterplot of the number of ays before the planne amission an the eviation between the planne arrival ate an the realization In orer to fit this ata, an EDF is chosen. Where the input is: the realization of arrival ate the planne arrival ay for patients that are expecte to arrive x ays ahea. For this istribution hols that: Where n F n = 1 n 1{X 1 x} i=1 1{X 1 x} = { 1 if X 1 x 0 otherwise The upper (F u (X)) an lower (F L (X)) confience intervals for F n are given by F u (X) = { F n(x) +, if F n (X) + < 1 1, if F n (X) + 1 F L (X) = { F n(x), if F n (X) + > 0 0, if F n (X) + 0 Where the value of can be foun via the table of Kolmogorov-Smirnov Acceptance Limits, which can be foun in Appenix XI. This results in fifteen ifferent EDF s, how patients arrive that are expecte toay, till how patients arrive that are expecte in 14 ays. The graph from the EDF for the patients that are expecte within 7 ays is ae as an example an isplaye below, where 78% of the patients arrive in time. The probabilities of all other ays can be foun in appenix XII. 40

53 Deviation between planne ismissate an realization -14,5-13,5-12,5-11,5-10,5-9,5-8,5-7,5-6,5-5,5-4,5-3,5-2,5-1,5-0,5 0 0,5 1 1,5 2,5 3,5 4,5 5,5 6,5 7,5 8,5 9,5 10,5 11,5 12,5 13,5 14,5 Cancelle Waitinglist 100,00% 90,00% 80,00% 70,00% 60,00% 50,00% 40,00% 30,00% 20,00% 10,00% 0,00% EDF Elective arrivals 7 ays ahea Probability Lower boun Cummulative Upper boun Figure 19: The probabilities of the eviation between the planne arrival ates versus the real arrival ate for patients planne 7 ays ahea LENGTH OF STAY WITH DISCHARGE DATE Figure 20 represents a scatterplot, with on the X-axis the number of ays before the ismissal is planne an on the Y-axis the eviation between the planne ismiss ate an the real ismiss ate, where positive values stans for postpone ismisses. Scatterplot Number of ays before planne ismiss Figure 20: scatterplot of the number of ays before the planne ismiss an the eviation between the planne ismiss ate an the realization For the length of stay with expecte ismiss ate, the same metho is use as for the elective patients. Again, an example of the probabilities for the expecte ismisses is given below in figure 21. The other results can be foun in appenix XIII. 41

54 Time till ismiss -14,5-13,5-12,5-11,5-10,5-9,5-8,5-7,5-6,5-5,5-4,5-3,5-2,5-1,5-0,5 0 0,5 1 1,5 2,5 3,5 4,5 5,5 6,5 7,5 8,5 9,5 10,5 11,5 12,5 13,5 14,5 100,00% EDF Expecte issmis ate 7 ays ahea 80,00% 60,00% 40,00% 20,00% 0,00% Probability Cumalative Lower boun Upper boun Figure 21: The probabilities of the eviation between the planne ismiss ates versus the real ismiss ates for patients planne 7 ays ahea LENGTH OF STAY WITHOUT DISCHARGE DATE The following scatterplot (figure 22) represents the number of ays a patient is in the hospital on the x-axis an the number of ays till the patient is ismisse on the y-axis. Scatterplot Time patients without expexte ismiss ate in hospital Figure 22: scatterplot of the number of ays a patient without expecte ismiss ate is in the hospital versus the time till the ismissal Figure 15 has shown that a large amount of the patients oes not have an expecte ismiss ate. The Catharina Hospital has a general rule in which is state that a patient shoul have an expecte ismiss ate within 24 hours after amission. However, about 15% of the patients that are longer than 24 hours in hospital o not have an expecte ismiss ate, an about 6% of the patients is ismisse within 24 hours after amission. Therefore, also the probability istributions for the patients without an expecte ismiss ate are very important. The scatterplot in figure 22 shows that in general, patients planne in avance have a short length 42

55 of stay, whereas patients lying in the hospital for a longer time also have a longer remaining time. To calculate the probabilities, again the EDF is use. Different istributions are calculate from the planne patients till patients lying in the hospital for at least 10 ays. The other results can be foun in appenix XIV. 100,00% EDF Expecte issmis ate for patients lying alreay 7 ays in hospital 80,00% 60,00% 40,00% 20,00% 0,00% 0,5 1 1,5 2,5 3,5 4,5 5,5 6,5 7,5 8,5 9,5 10,5 11,5 12,5 13,5 14,5 Probability Lower boun Cummulative Upper boun Figure 23: The probabilities a ismissal occurs in x ays for patients that are lying for 7 ays in the hospital 6.4. OPERATIONAL MODEL In the previous paragraph, all ifferent probabilities for arrivals are explaine. This paragraph aims to combine these ifferent probabilities into a moel to forecast the expecte number of patients within t ays. Base on the available patient information an the calculate istributions in the previous paragraph, each patient will be assigne to one of the following categories (C x ): (1) Patients P i in hospital with ischarge ate, (2) patients P i in hospital without ischarge ate, (3) Elective patients P i with ischarge ate, (4) elective patients P i without ischarge ate, an (5) acute patients P i. Each patient category has a corresponing probability, where all probabilities epen of the number of ays ahea a preiction in the future will be mae ( t). Furthermore, C 1 epens on the actual length of stay (a i ) for patient P i. C 2 epens on the ifference in ays between the ischarge ate (D i ) an t = 0 ( D i ). C 3 epens on the ifferences between the planne amission ate (E i ) an t = 0 ( E i ) an the actual length of stay where a = 1. C 4 epens on E i an D i E i = DE i. The acute patient category, C 5 epens on the actual length of stay where a = 0 an the time perios with their corresponing λ i (table 19) between t an t = 0. 43

56 The patient category can be calculate via: C 1, E i > t, an f i is 0 C C x = { 2, E i > t, an f i is > t C 3, E i < t, an f i is 0 C 4, E i < t, an f i is > t TC x = total patients in categorie x So the expecte number of patients (S), t ays ahea for category C x is: TC 1 S C1,t = i=1 P i, t,ai S C1,t = i=1 P i, t, Di TC 3 S C1,t = i=1 P i, t, Ei,a i S C1,t = i=1 P i, t, Ei, DE i Where: P i, t,ai is the probability that patient i with actual length of stay a i is now (t = 0) + time t in the hospital. For the acute patients counts that: TC 2 TC 4 t 7 S C5,t = λ i P t,a F t,i t=0 λ i =1 Where the values for λ i can be foun in table 19, P t,a is the probability that the patients are still in hospital after time t, with a = 0, an F t,i is the percentage of time λ i is in the perio between time t an t + 1. All probabilities can be foun in appenix XIV till XVIII. The total expecte arrivals on time t are: 6.5. RESULTS x=5 S total,t = S Cx, t The moel escribe above results in an expecte number of patients t ays ahea. Figure 24, gives a graphical representation of these results base on the patients in the system for 11 march 2015, at 8:45. x=1 44

57 400 Expecte patients t ays ahea ,5 1 1,5 2,5 3,5 4,5 5,5 6,5 7,5 8,5 9,5 10,5 11,5 12,5 13,5 14,5 Patients in the system Acute arrivals + expecte stay in the future Total patients Figure 24: Expecte number of patients t ays ahea These results generate insight into the number of bes which are require t ays ahea for the acute patients which are not entere in the information system yet. Furthermore, the number of bes require for the patients that are planne in the system an those patients that are in the hospital for this moment is given VALIDATION To provie insight into the reliability of the results from the previous paragraph, the moel will be valiate. For the valiation, ata of 2012 is use. Different snapshots of the information system, with ata about the number of patients with their corresponing arrival ate, a possible expecte ischarge ate, an the planne elective patients were use as input for the moel escribe in this chapter. The results of the moel are compare with the occupancy of bes for 2012, which was also use in chapter 4 an 5. In total, 20 snapshots where use as input to compare the forecaste occupie be numbers versus the real occupie be numbers. For this chapter, the same gooness of fit variables are use as in chapter 4. These are the Mape, MAE, MaxApe, an the MaxAE. The results are presente in table 20 below: Table 20: gooness of fit parameters for the operational moel t MAE 9,94 11,8 18,50 12,40 16,49 20,93 25,80 33,31 42,00 52,44 63,52 67,43 71,10 77,95 82,13 84,62 96,06 MaxA E 27,67 26,4 44,36 34,64 50,25 54,15 49,77 58,00 68,49 81,64 82,81 89,72 96,98 105,1 110,8 112,7 124,8 MAPE MaxA pe 3,43 % 10,77 % 3,66 % 8,24 % 5,37 % 13,20 % 3,87 % 10,50 % 4,98 % 14,87 % 6,24 % 15,74 % 7,81 % 14,78 % 9,87 % 18,65 % As can be seen in table 20, the error strongly increases if time t increases. An explanation for this coul be that most elective patients are planne only one ay ahea as we saw in figure 14. Since the moel only uses the planne patients foun in the system, an oes not provie an aitional istribution for the expecte elective patients for more than t + 1 ays ahea, the results of the valiation for t + 1 ays ahea are not comparable to each other. Furthermore, 45 12,41 % 21,40 % 16,03 % 24,37 % 19,92 % 24,87 % 21,55 % 26,54 % 22,77 % 28,69 % 24,86 % 31,10 % 25,86 % 32,81 % 26,72 % 33,06 % 30,13 % 36,92 %

58 the table shows an average eviation of approximately 10 bes at time t = 0 an even a MaxAE of 27,67 bes. These results are striking. The average eviation in bes between the forecast an realization shoul be at maximum aroun 10 bes to be useful for the hospital. It shoul be expecte that an overview create at time t=0 base on a snapshot of the patients in the information system are the same as the be occupancy base on historical ata; however, this is not the case. Therefore, base on the available ata, it is not possible to make conclusions on the reliability of the operational moel CONCLUSIONS ON OPERATIONAL PLAN This chapter aims to provie more insight into the short term be occupancy. First, ifferent istributions were fitte for the emergency arrivals, elective arrivals, patients in hospital without a ischarge ate, an patients in the hospital with a ischarge ate. For the emergency arrivals, in total six ifferent time perios were selecte to fulfill the whole week to calculate unexpecte arrivals by the Poisson process. The istribution for elective arrivals is base on the ifferences in ays between the actual ay an the number of ays the patient is planne ahea. By using this istribution, it can be conclue that higher ifference in ays, result in a larger eviation between the planne an actual arrival. For the patients in hospital with an expecte ischarge ate it can be conclue that on average, planne ischarges within 4 ays mostly occurs slightly elaye, whereas patients with a ischarge ate larger than 4 ays ahea are ischarge on average earlier than expecte. For the patients in hospital without an expecte ischarge ate, it can be conclue that patients with a higher actual length of stay are expecte to stay for a longer perio in hospital, compare to patients that just arrive. To forecast the number of patients t ays ahea an operational moel is create, which epens on all the ifferent istribution functions relate to emergency arrivals, elective patients, length of stay an remaining length of stay. The output of the moel seems not useful for the hospital base on the results of the valiation. The average eviation in occupie bes between the forecast an realization shoul be maximum aroun 10; however, with the ata use for the valiation, the average ifference between the forecast an realization for all future perios is higher. An explanation for this coul be that relevant information about planne patients for more than t = 1ays ahea is missing. Therefore, aing an extra istribution for the elective patients that are not in the system coul provie useful information. Aitionally, the results from the two ifferent atasets vary too much at time t = 0. An explanation of this eviation coul be that the use ata for the valiation originates from 2012, an that the information system was fille in ifferently. Therefore, more actual ata is neee. 46

59 7. CONCLUSIONS AND RECOMMENDATIONS The aim of this research has been to create a better match between the eman an supply of bes for the regular clinic at the Catharina hospital. After iscussing the current situation, the research approach, iscovering seasonal influences, an creating a moels on both the tactical an operational level this report ens with the conclusion. Furthermore, limitations an possible options for further research as well as recommenations for the Catharina Hospital will get attention in this chapter CONCLUSIONS In this section, the project is reflecte by rawing conclusions on the ifferent steps execute uring this project SEASONAL INFLUENCES In total, 64 ifferent time perios are teste with a multiple regression moel to fin whether these perios o have a significant effect on Table 21: significant seasonal influences the number of occupie bes in the clinic. From this analyze can be conclue that in total 30 ifferent variables o have a Monay Tuesay SummerVacationW1 SummerVacationW2 April June significant effect (table 21). Wenesay SummerVacationW3 July By using these variables to forecast the maximum number of occupie bes, 75,3% of the variance is explaine. Furthermore, it can be conclue that the number of relevant OR sessions o contribute to a better moel. Thursay SummerVacationW4 September Friay SummerVacationW5 October Saturay SummerVacationW6 November CarnivalVacation SummerVacationW7 December Easter ChristmasVacationW1 DayAfterChristmasVacation MayVacation ChristmasVacationW2 WeekAfterChristmasVacation Pentecost January InteractionNewYearNoSunay AscensionWeeken February InteractionLiberationayNoWeeken EasterWeeken March InteractionKingsDayNoWeeken TACTICAL PLAN The tactical plan provies an optimal number of regular bes an flex bes, base on ifferent cost an perios scenarios. The ifferent cost scenarios show that: Decrease costs for active flex-bes result in less regular bes an more flex-bes. Increase costs of passive flex-bes result in less regular bes an less flex-bes. Increase costs for active flex-bes result in more regular bes an less flex-bes. Increase costs for patient refusals / elays result in the same amount of regular bes an an increase in flex-bes. In total four ifferent cost scenarios where teste: The actual situation in the Catharina hospital (benchmark moel), 47

60 a scenario with all holiays, an special perios, which results in a reuction of costs of approximately 2,3%, epening on the cost scenarios, which is 770,- per ay (fictive costs) a scenario with all reuction perios an where the months are split into four perios, which results in an approximately 2,6% cost reuction, epening on the cost scenarios, which is 890,- per ay (fictive costs) a scenario with all reuction perios an each month as a separate perio, which results in approximately 2,6% cost reuction, epening on the cost scenarios, which is 900,- per ay (fictive costs). Base on these results it can be conclue that anticipating on reuction perios results in the largest savings from 2,4%, an iviing the months into four ifferent clusters result in an aitional 1,2% savings. Furthermore, it can be conclue that the effect of iviing the months in to twelve ifferent clusters is negligible. Overall, the moel provies a proper tactical plan for the amount of require regular bes an flex-bes for the long term. However, ue to for example external influences such as a virus, or other causes also an operational plan shoul be evelope to eal with extreme unexpecte emans for very short perios OPERATIONAL PLAN For the operational plan, first, ifferent istributions were fitte for the emergency arrivals, elective arrivals, patients in hospital without a ischarge ate, an patients in the hospital with a ischarge ate. The emergency arrivals can be istribute with the Poisson process, where six ifferent perios per week are necessary: (1) Workays; 0-08:00, (2), Workays; 8:00-12:00 (3) Workays; 12:00-16:00, (4) Workays; 16:00-0, (5) Weekens; 1:00-08:00, an (6) Weekens; 08:00 -. The elective arrivals, patients in hospital without a ischarge ate, an patients in the hospital with a ischarge ate, are istribute with an EDF. For the elective arrivals it can be conclue that higher ifference in ays between now an the time, the patient is expecte, result in a larger eviation between the planne an actual arrival. For the patients in hospital with an expecte ischarge ate it can be conclue that on average, planne ischarges within 4 ays mostly occurs slightly elaye, whereas patients with a ischarge ate larger than 4 ays ahea are ischarge on average earlier than expecte. For the patients in hospital without an expecte ischarge ate, it can be conclue that patients with a higher actual length of stay are expecte to stay for a longer perio in hospital, compare to patients that just arrive. 48

61 To forecast the number of patients t ays ahea an operational moel is create. The output of the moel seems not useful for the hospital base on the results of the valiation. The average eviation in occupie bes between the forecast an realization shoul be maximum aroun 10; however, with the ata use for the valiation, the average ifference between the forecast an realization for all future perios is higher. An explanation for this coul be that relevant information about planne patients for more than t = 1ays ahea is missing. Aitionally, the results from the two ifferent atasets vary too much at time t = 0. An explanation of this eviation coul be that the use ata for the valiation originates from 2012, an that the information system was fille in ifferently. Therefore, more actual ata is neee RECOMMENDATIONS In this last paragraph of this rapport recommenations for both the Catharina Hospital, as well as for acaemics for further research are given CATHARINA HOSPITAL Base on the conclusions, several recommenations can be mae for the Catharina Hospital. First of all, it is highly recommen to anticipate on seasonal patterns. By anticipating on holiays an special ays, the ifference between eman an supply uring these perios can be rastically reuce. Aitionally, clustering the normal perios into four perios will result in cost savings. Therefore, the perio scenario with all reuction perios inclue an four ifferent clusters for the normal months is recommen. Regaring to the cost scenarios, all ifferent scenarios result in less regular bes, more flexbes, an a higher usage of flex-bes. Therefore, it is recommen that the amount regular bes ecreases an the amount of flex-bes increases. Comparing the results of the ifferent cost scenarios in appenix VII, using the formation of bes from scenario 5 for all ifferent cost an perio scenarios results on average in a small increase of 0,98% in costs. However, the expecte refuse / elaye patients by always using the be formation from cost scenario 5 results in a ecrease of 92,33%. Since the satisfaction of patient is the major concern of the hospital, the formation from cost scenario 5 is recommen. Furthermore, more attention for filling in the information system is recommen. Due to the lack of correct information, coorination requires more time. Aitionally, register information from refuse an elaye patients coul help in orer to create a more reliable planning LIMITATIONS AND FURTHER RESEARCH The results provie in this stuy are limite to the regular epartments of the clinic at the Catharina hospital, which limits the generalizability of the finings. The research only focuses on 49

62 number of bes for all regular epartments within the clinic as a whole. No further ifferentiation between epartments is mae. The tactical plan provies optimums of be capacity per time perios, which results in most scenarios in changing be capacities several times per year. By changing be capacities, it is reasonable to assume that some patients have to be transferre to other epartments. However, costs for transferring patients ue to capacity changes were not taken into account. Aitionally, no set-up times were taken into account for cleaning an preparing bes for a new patients. In this research, this effect may be negligible since the moel uses the maximum occupie number of bes per ay, which may coul be seen as a compensation for the set-up times. However, more research shoul be conucte to prove this assumption. For the operational moel, no external variables are use. However, Jones et al. (2002) foun out that two external variables; mean aytime temperature an the influenza illness rate are relate to the number of emergency occupie bes an the number of emergency amissions. Aitionally, the istributions for the length of stay an remaining length of stay are both generalize for all patients. A higher level of ifferentiation, for example splitting up patients per epartment, sort arrival, or even further, by conition may result in a higher reliability. As state in the conclusion, not much can be sai about the reliability of the operational moel ue to missing ata. Therefore, the concept of this operational plan coul be use as a start-up for a new project. Important for that new project is to take into account a patient flow with new elective arrivals. Since this research only takes into account the planne arrivals, not much can be sai about the number of occupie bes one week ahea. Moreover, the operational moel coul be combine with the tactical moel an the seasonal influence that are foun to increase the reliability. With a more reliable operational moel, ifferent rules coul be set up for closing regular bes in cases of expecte unerutilization, or opening flex-bes in cases of expecte overutilization. 50

63 8. BIBLIOGRAPHY Abel-Aal, R. E., en A. M. Mangou Moeling an forecasting monthly patient volume at a primary health care clinic using univariate time-series analysis. Computer methos an programs in biomeicine, 56(3) Alexopoulos, Christos, D. Golsman, J. Fontanesi, D. Kopal, en J. R. Wilson Moelling patient arrivals in community clinics. Omega Caroen, Brecht, Erik Demeulemeester, en Jeroen Beliën Operating room planning an scheuling: A literature review. European Journal of Operational Research Cohen, M. A., J. C. Hershey, en E. N. Weiss Analysis of capacity ecisions for progressive patient care hospital facilities. Health Services Research, 15(2) 145. Curtright, J. W., S. C. Stolp-Smith, en E. S. Eell Strategic performance management: Development of a performance measurement system at the Mayo Clinic. Journal of Healthcare Management, De Bruin, A. M., R. Bekker, L. Van Zanten, en G. M. Koole Dimensioning hospital wars using the Erlang loss moel. Annals of Operations Research, 178(1) Fiel, Any Discovering statistics using SPSS. Lonon: Sage Publications. Gorunescu, F., S. U. McClean, en P. H. Millar A queueing moel for be-occupancy management an planning of hospitals. Journal of the Operational Research Society Green, Lina V How Many Hospital Bes? The Journal of Health Care Organization, Provision, an Financing, 39(4) Hans, E. W., M. Van Houenhoven, en P. J. Hulshof A framework for healthcare planning an control. Hanbook of healthcare system scheuling. Springer US Harper, P.R, en A.K. Shahani Moelling for the planning an management of be capacities in hospitals. Journal of the operational Research Society Jones, Simon Anrew, Mark Patrich Joy, en Jon Pearson Forecasting eman of emergency care. Health care management science, 5(4) Jones, Spencer S., A. Thomas, R. S. Evans, S. J. Welch, en P. J. Haug Forecasting aily patient volumes in the emergency epartment. Acaemic Emergency Meicine, 15(2)

64 Lapierre, Sophie D., D Golsman, R Cochran, en J Dubow Be allocation techniques base on census ata. Socio-Economic Planning Sciences Li, L. X., en W. C. Benton Performance measurement criteria in health care organizations: review an future research irections. European Journal of Operational Research, 93(3) Marazzi, A., F Paccau, C. Ruffieux, en C. Beguin Fitting the istributions of length of stay by parametric moels. Meical care, 36(6) Miroff, I I, F. Betz, L. R. Pony, en F. Sagasti On managing science in the systems age: two schemas for the stuy of science as a whole systems phenomenon. Interfaces RIVM Infographic Zorgkosten juni Geopen November 1, Rogerson, P. A Statistical methos for geography. Lonon: Sage. Vissers, J. M., J. W. M. Bertran, en G. De Vries A framework for prouction control in health care organizations. Prouction Planning & Control, 12(6) Vissers, Jan, en Roger Beech Health Operations Management. Oxon: Routlege. Ziekenhuis, Cathatina Jaarverslag Catharina Ziekenhuis. Einhoven. 52

65 9. LIST OF ABBREVIATIONS ALOS ARIMA CDF CZE ED EDF IC LOS MAE MAPE MaxAE MaxApe MILP MRI MRP OM OR SARIMA Average length of stay Auto-Regressive Integrate Moving Average Cumulative istribution function Catharina Hospital Emergency Department Empirical istribution function Intensive Care Length of Stay Mean absolute error Mean absolute percentage error Max absolute error Max absolute percentage error Mixe integer linear programming Magnetic Resonance Imaging Manufacturing Resources Planning Operations Management Operations room Seasonal Auto-Regressive Integrate Moving Average 53

66 APPENDIX I: FRAMEWORK FOR PRODUCTION CONTROL OF HOSPITALS Figure 25: Framework for prouction control of hospitals (Vissers en Beech 2005) 54

67 Table 22 Framework for prouction control of hospitals (Vissers, Bertran en De Vries 2001) 55

68 APPENDIX II: BED OCCUPANCY PER YEAR Be Occupancy Be Occupancy Be Occupancy

69 Be Occupancy Be Occupancy 2014

70 APPENDIX III: COEFFICIENTS MULTIPLE REGRESSION MODEL WITH OR SESSIONS Moel 1 Unstanarize Coefficients Coefficients a Stanariz e Coefficient s 95,0% Confience Interval for B Lower Boun B St. Error Beta t Sig. (Constant) 284,424 1, ,673 0, , ,150 Collinearity Statistics Upper Boun Tolerance VIF Monay 12,924 2,386,165 5,417,000 8,245 17,603,140 7,164 Tuesay 16,119 2,442,206 6,600,000 11,329 20,909,133 7,507 Wenesay 18,595 2,510,238 7,410,000 13,673 23,517,127 7,902 Thursay 15,449 2,379,198 6,494,000 10,784 20,115,140 7,123 Friay 14,618 2,383,187 6,134,000 9,944 19,292,140 7,148 Saturay 6,252 1,183,080 5,285,000 3,932 8,572,568 1,762 CarnivalVacation -11,083 2,267 -,063-4,890,000-15,528-6,637,788 1,269 Easter -15,720 7,454 -,042-2,109,035-30,339-1,100,322 3,109 MayVacation -6,344 2,442 -,035-2,598,009-11,133-1,555,710 1,409 Pentecost -21,369 4,507 -,058-4,742,000-30,207-12,530,880 1,137 AscensionWeeken -6,709 3,204 -,026-2,094,036-12,994 -,425,875 1,143 EasterWeeken -13,021 6,093 -,043-2,137,033-24,972-1,071,322 3,108 Christmas -36,640 4,829 -,099-7,587,000-46,111-27,168,766 1,305 SummerVacationW1-13,877 2,667 -,070-5,203,000-19,108-8,646,728 1,374 SummerVacationW2-28,103 2,422 -,150-11,602,000-32,854-23,353,774 1,292 SummerVacationW3-35,023 2,424 -,188-14,451,000-39,777-30,270,773 1,293 SummerVacationW4-37,996 2,404 -,203-15,807,000-42,710-33,282,786 1,272 SummerVacationW5-33,159 2,420 -,178-13,701,000-37,906-28,413,776 1,289 SummerVacationW6-32,122 2,296 -,172-13,993,000-36,625-27,620,862 1,160 SummerVacationW7-5,203 2,281 -,028-2,281,023-9,676 -,729,873 1,145 ChristmasVacationW1-26,509 2,732 -,142-9,703,000-31,867-21,151,609 1,643 ChristmasVacationW2-40,048 2,506 -,212-15,983,000-44,962-35,134,742 1,348 January 16,196 1,720,165 9,419,000 12,823 19,568,424 2,360 February 23,331 1,682,228 13,872,000 20,032 26,629,483 2,071 March 21,867 1,559,223 14,026,000 18,809 24,924,515 1,940 April 16,964 1,574,170 10,777,000 13,877 20,051,521 1,920 June 5,608 1,542,056 3,637,000 2,584 8,632,543 1,842 July 4,694 1,590,048 2,952,003 1,575 7,813,495 2,018 September 5,792 1,489,058 3,889,000 2,871 8,713,582 1,718 October 9,397 1,552,096 6,054,000 6,353 12,441,520 1,923 November 12,877 1,566,129 8,224,000 9,806 15,947,527 1,899 December 13,598 1,710,139 7,953,000 10,244 16,951,429 2,333 WeekAfterMayVacation -7,750 2,534 -,039-3,059,002-12,719-2,781,806 1,240 DayAfterChristmasVacation -24,181 6,504 -,046-3,718,000-36,936-11,425,843 1,187 WeekAfterChristmasVacation -6,624 2,767 -,033-2,394,017-12,051-1,197,676 1,479 InteractionNewYearNoSunay -37,432 7,206 -,064-5,194,000-51,565-23,298,857 1,166 InteractionLiberationDayNoW eeken InteractionKingsDayNoWeeke n -15,135 8,245 -,022-1,836,067-31,305 1,035,873 1,146-9,072 7,364 -,016-1,232,218-23,514 5,370,821 1,218 ORSessions,736,089,324 8,239,000,561,912,084 11,890 a. Depenent Variable: MaxBesPerDay 58

71 59

72 Moel 1 Unstanarize Coefficients Coefficients a Stanariz e Coefficient s 95,0% Confience Interval for B Lower Boun B St. Error Beta t Sig. (Constant) 284,231 1, ,221 0, , ,717 Collinearity Statistics Upper Boun Tolerance VIF Saturay 5,000 1,152,064 4,340,000 2,740 7,259,624 1,603 CarnivalVacation -8,924 2,290 -,051-3,897,000-13,415-4,432,804 1,243 Pentecost -14,798 4,440 -,040-3,333,001-23,507-6,089,944 1,059 EasterWeeken -18,783 3,700 -,062-5,076,000-26,039-11,526,909 1,100 Christmas -30,289 4,847 -,082-6,249,000-39,796-20,782,792 1,262 SummerVacationW1-10,754 2,682 -,054-4,010,000-16,013-5,495,750 1,333 SummerVacationW2-25,014 2,421 -,134-10,333,000-29,762-20,266,807 1,239 SummerVacationW3-31,808 2,418 -,170-13,154,000-36,551-27,066,809 1,236 SummerVacationW4-34,175 2,364 -,183-14,455,000-38,811-29,538,847 1,181 SummerVacationW5-28,870 2,368 -,155-12,192,000-33,514-24,226,844 1,185 SummerVacationW6-29,691 2,307 -,159-12,871,000-34,215-25,166,889 1,125 SummerVacationW7-4,856 2,307 -,026-2,105,035-9,380 -,331,889 1,125 ChristmasVacationW1-23,408 2,748 -,125-8,518,000-28,798-18,018,626 1,596 ChristmasVacationW2-37,244 2,523 -,197-14,762,000-42,192-32,296,762 1,312 January 16,658 1,692,170 9,847,000 13,340 19,976,456 2,193 February 23,999 1,653,234 14,521,000 20,757 27,240,521 1,920 March 22,424 1,522,229 14,735,000 19,439 25,408,564 1,774 April 17,110 1,559,172 10,976,000 14,053 20,168,553 1,807 June 5,891 1,516,059 3,886,000 2,918 8,864,585 1,709 July 5,661 1,593,058 3,552,000 2,535 8,786,514 1,946 September 6,459 1,466,065 4,406,000 3,584 9,335,626 1,599 October 10,250 1,513,105 6,776,000 7,283 13,216,570 1,753 November 13,141 1,527,132 8,604,000 10,146 16,137,576 1,735 December 14,250 1,682,145 8,470,000 10,951 17,550,461 2,169 WeekAfterMayVacation -5,413 2,528 -,027-2,141,032-10,372 -,455,844 1,185 WeekAfterChristmasVacation -9,225 2,656 -,046-3,473,001-14,435-4,015,764 1,309 InteractionNewYearNoSunay -28,644 7,235 -,049-3,959,000-42,834-14,454,886 1,129 ORSessions 1,309,035,576 37,270,000 1,240 1,378,567 1,762 a. Depenent Variable: MaxBesPerDay 60

73 APPENDIX IV: T-TEST TWO-SAMPLE ASSUMING UNEQUAL VARIANCES FOR THE NORMAL PERIODS January February January March January April January May January June January July January August Mean 336,17 340,87 336,17 342,39 336,17 337,42 336,17 320,61 336,17 321,68 336,17 327,70 336,17 320,58 Variance 168,38 152,09 168,38 133,08 168,38 198,83 168,38 214,96 168,38 230,14 168,38 209,48 168,38 156,27 Observations 87,00 101,00 87,00 120,00 87,00 113,00 87,00 71,00 87,00 123,00 87,00 50,00 87,00 12,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 179,00 172,00 192,00 141,00 201,00 93,00 14,00 t Stat -2,53-3,56-0,65 6,99 7,43 3,42 4,03 P(T<=t) two-tail 0,01 0,00 0,52 0,00 0,00 0,00 0,00 t Critical two-tail 1,97 1,97 1,97 1,98 1,97 1,99 2,14 February March February April February May February June February July February August February September Mean 340,87 342,39 340,87 337,42 340,87 320,61 340,87 321,68 340,87 327,70 340,87 320,58 340,87 324,22 Variance 152,09 133,08 152,09 198,83 152,09 214,96 152,09 230,14 152,09 209,48 152,09 156,27 152,09 189,99 Observations 101,00 120,00 101,00 113,00 101,00 71,00 101,00 123,00 101,00 50,00 101,00 12,00 101,00 99,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 207,00 212,00 134,00 222,00 85,00 14,00 195,00 t Stat -0,94 1,91 9,52 10,44 5,52 5,32 9,00 P(T<=t) two-tail 0,35 0,06 0,00 0,00 0,00 0,00 0,00 t Critical two-tail 1,97 1,97 1,98 1,97 1,99 2,14 1,97 March April March May March June March July March August March September March October Mean 342,39 337,42 342,39 320,61 342,39 321,68 342,39 327,70 342,39 320,58 342,39 324,22 342,39 329,56 Variance 133,08 198,83 133,08 214,96 133,08 230,14 133,08 209,48 133,08 156,27 133,08 189,99 133,08 200,29 Observations 120,00 113,00 120,00 71,00 120,00 123,00 120,00 50,00 120,00 12,00 120,00 99,00 120,00 133,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 217,00 121,00 228,00 76,00 13,00 191,00 249,00 t Stat 2,94 10,71 12,00 6,38 5,80 10,44 7,93 P(T<=t) two-tail 0,00 0,00 0,00 0,00 0,00 0,00 0,00 t Critical two-tail 1,97 1,98 1,97 1,99 2,16 1,97 1,97 April May April June April July April August April September April October April November Mean 337,42 320,61 337,42 321,68 337,42 327,70 337,42 320,58 337,42 324,22 337,42 329,56 337,42 334,23 Variance 198,83 214,96 198,83 230,14 198,83 209,48 198,83 156,27 198,83 189,99 198,83 200,29 198,83 183,90 Observations 113,00 71,00 113,00 123,00 113,00 50,00 113,00 12,00 113,00 99,00 113,00 133,00 113,00 123,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 145,00 234,00 92,00 14,00 207,00 238,00 230,00 t Stat 7,68 8,26 3,98 4,38 6,88 4,35 1,77 P(T<=t) two-tail 0,00 0,00 0,00 0,00 0,00 0,00 0,08 t Critical two-tail 1,98 1,97 1,99 2,14 1,97 1,97 1,97 May June May July May August May September May October May November May December Mean 320,61 321,68 320,61 327,70 320,61 320,58 320,61 324,22 320,61 329,56 320,61 334,23 320,61 334,07 Variance 214,96 230,14 214,96 209,48 214,96 156,27 214,96 189,99 214,96 200,29 214,96 183,90 214,96 175,57 Observations 71,00 123,00 71,00 50,00 71,00 12,00 71,00 99,00 71,00 133,00 71,00 123,00 71,00 74,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 150,00 106,00 17,00 145,00 139,00 137,00 140,00 t Stat -0,49-2,64 0,01-1,63-4,21-6,41-5,79 P(T<=t) two-tail 0,63 0,01 1,00 0,11 0,00 0,00 0,00 t Critical two-tail 1,98 1,98 2,11 1,98 1,98 1,98 1,98 June July June August June September June October June November June December January September Mean 321,68 327,70 321,68 320,58 321,68 324,22 321,68 329,56 321,68 334,23 321,68 334,07 336,17 324,22 Variance 230,14 209,48 230,14 156,27 230,14 189,99 230,14 200,29 230,14 183,90 230,14 175,57 168,38 189,99 Observations 123,00 50,00 123,00 12,00 123,00 99,00 123,00 133,00 123,00 123,00 123,00 74,00 87,00 99,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 95,00 14,00 217,00 249,00 241,00 170,00 183,00 t Stat -2,44 0,28-1,30-4,29-6,84-6,01 6,09 P(T<=t) two-tail 0,02 0,78 0,19 0,00 0,00 0,00 0,00 t Critical two-tail 1,99 2,14 1,97 1,97 1,97 1,97 1,97 61

74 July August July September July October July November July December January October February October Mean 327,70 320,58 327,70 324,22 327,70 329,56 327,70 334,23 327,70 334,07 336,17 329,56 340,87 329,56 Variance 209,48 156,27 209,48 189,99 209,48 200,29 209,48 183,90 209,48 175,57 168,38 200,29 152,09 200,29 Observations 50,00 12,00 50,00 99,00 50,00 133,00 50,00 123,00 50,00 74,00 87,00 133,00 101,00 133,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 19,00 94,00 86,00 86,00 99,00 195,00 228,00 t Stat 1,72 1,41-0,78-2,74-2,49 3,56 6,52 P(T<=t) two-tail 0,10 0,16 0,44 0,01 0,01 0,00 0,00 t Critical two-tail 2,09 1,99 1,99 1,99 1,98 1,97 1,97 August September August October August November August December January November February November March November Mean 320,58 324,22 320,58 329,56 320,58 334,23 320,58 334,07 336,17 334,23 340,87 334,23 342,39 334,23 Variance 156,27 189,99 156,27 200,29 156,27 183,90 156,27 175,57 168,38 183,90 152,09 183,90 133,08 183,90 Observations 12,00 99,00 12,00 133,00 12,00 123,00 12,00 74,00 87,00 123,00 101,00 123,00 120,00 123,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 14,00 14,00 14,00 15,00 190,00 220,00 237,00 t Stat -0,94-2,36-3,58-3,44 1,05 3,84 5,06 P(T<=t) two-tail 0,36 0,03 0,00 0,00 0,30 0,00 0,00 t Critical two-tail 2,14 2,14 2,14 2,13 1,97 1,97 1,97 September October September November September December January December February December March November April December Mean 324,22 329,56 324,22 334,23 324,22 334,07 336,17 334,07 340,87 334,07 342,39 334,23 337,42 334,07 Variance 189,99 200,29 189,99 183,90 189,99 175,57 168,38 175,57 152,09 175,57 133,08 183,90 198,83 175,57 Observations 99,00 133,00 99,00 123,00 99,00 74,00 87,00 74,00 101,00 74,00 120,00 123,00 113,00 74,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 214,00 209,00 161,00 154,00 151,00 237,00 163,00 t Stat -2,89-5,41-4,75 1,01 3,45 5,06 1,65 P(T<=t) two-tail 0,00 0,00 0,00 0,31 0,00 0,00 0,10 t Critical two-tail 1,97 1,97 1,97 1,98 1,98 1,97 1,97 October November October December November December Mean 329,56 334,23 329,56 334,07 334,23 334,07 Variance 200,29 183,90 200,29 175,57 183,90 175,57 Observations 133,00 123,00 133,00 74,00 123,00 74,00 Hypothesize Mean Difference 0,00 0,00 0,00 f 254,00 160,00 157,00 t Stat -2,69-2,29 0,08 P(T<=t) two-tail 0,01 0,02 0,94 t Critical two-tail 1,97 1,97 1,98 62

75 January - April November January - April December February - March April February - April March April - November December January - November December July - August September Mean 336,88 334,23 336,88 334,07 341,70 337,42 339,05 342,39 335,75 334,07 335,20 334,07 326,32 324,22 Variance 185,05 183,90 185,05 175,57 141,69 198,83 178,95 133,08 192,78 175,57 171,71 175,57 204,48 189,99 Observations 200,00 123,00 200,00 74,00 221,00 113,00 214,00 120,00 236,00 74,00 161,00 74,00 62,00 99,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 259,00 134,00 195,00 278,00 127,00 140,00 126,00 t Stat 1,70 1,55 2,76-2,40 0,94 0,61 0,92 P(T<=t) two-tail 0,09 0,12 0,01 0,02 0,35 0,54 0,36 t Critical two-tail 1,97 1,98 1,97 1,97 1,98 1,98 1,98 May - June September May - August September July - October September January - April - November December May - June - August September July - August - September October July - August - October September Mean 321,29 324,22 320,60 324,22 329,05 324,22 335,87 334,07 321,25 324,22 325,03 329,56 328,53 324,22 Variance 223,71 189,99 204,46 189,99 202,36 189,99 185,70 175,57 219,03 189,99 195,38 200,29 202,87 189,99 Observations 194,00 99,00 83,00 99,00 183,00 99,00 323,00 74,00 206,00 99,00 161,00 133,00 195,00 99,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 212,00 172,00 207,00 111,00 206,00 280,00 203,00 t Stat -1,67-1,73 2,78 1,05-1,72-2,75 2,51 P(T<=t) two-tail 0,10 0,09 0,01 0,30 0,09 0,01 0,01 t Critical two-tail 1,97 1,97 1,97 1,98 1,97 1,97 1,97 July - August October July - September October June - August September May - June August Mean 326,32 329,56 325,39 329,56 321,59 324,22 321,29 320,58 Variance 204,48 200,29 197,87 200,29 222,45 189,99 223,71 156,27 Observations 62,00 133,00 149,00 133,00 135,00 99,00 194,00 12,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 f 118,00 276,00 220,00 13,00 t Stat -1,48-2,48-1,40 0,19 P(T<=t) two-tail 0,14 0,01 0,16 0,85 t Critical two-tail 1,98 1,97 1,97 2,16 63

76 APPENDIX V: T-TEST TWO-SAMPLE ASSUMING UNEQUAL VARIANCES FOR THE REDUCTION PERIODS Summer holliay W3 + W4 Interaction liberation ay no weeken Summer holliay Summer holliay Easter Day after Christmas Week after Christmas Summer Summer Zomervak Ascension Easter Christmas holliay Christmas holliay W3 W4 Easter weeken holliay holliay Christmas New Year holliay W6 holliay W5 W5 + 6 Weeken weeken Saturay Sunay week 1 week 2 May April Mean 270,78 270,03 279,60 284,93 301,00 314,74 244,40 233,20 279,90 274,18 270,40 277,04 289,55 284,93 305,81 295,82 285,94 270,10 279,67 283,33 300,75 302,79 Variance 386,18 167,36 192,27 242,35 478,50 499,02 281,82 151,20 429,43 230,30 273,41 333,99 370,47 242,35 222,91 217,20 324,00 396,64 202,33 238,27 151,58 162,95 Observations 40,00 40,00 10,00 15,00 5,00 35,00 10,00 5,00 40,00 40,00 80,00 80,00 20,00 15,00 225,00 165,00 31,00 30,00 3,00 6,00 4,00 14,00 Hypothesize Mean Difference 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 f 67,00 21,00 5,00 11,00 71,00 156,00 33,00 356,00 58,00 4,00 5,00 t Stat 0,20-0,90-1,31 1,47 1,41-2,41 0,78 6,58 3,25-0,35-0,29 P(T<=t) one-tail 0,42 0,19 0,12 0,09 0,08 0,01 0,22 0,00 0,00 0,37 0,39 t Critical one-tail 1,67 1,72 2,02 1,80 1,67 1,65 1,69 1,65 1,67 2,13 2,02 P(T<=t) two-tail 0,84 0,38 0,25 0,17 0,16 0,02 0,44 0,00 0,00 0,74 0,78 t Critical two-tail 2,00 2,08 2,57 2,20 1,99 1,98 2,03 1,97 2,00 2,78 2,57 Interaction kingsay no weeken 64

77 APPENDIX VI: DISTRIBUTION FITTING FOR THE OCCUPANCY OF THE CLINIC 0,26 0,24 0,22 0,2 0,18 Probability Density Function 1 perio excluing summer holliay Probability Density Function 1 perio excluing all reuction perios Weibull 0,22 Alpha 16,006 0,2 Beta 329,04 0,18 SD 14,808 0,16 Mean 332 f(x) 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0, x Gooness of fit 0,12 Deg of freeom 10 Gooness of fit 0,1 Statistics 14,441 Deg of freeom 9 0,08 P-value 0,15379 Statistics 25,85 0,06 Alpha 0,05 P-value 0,002 0,04 Critical value 18,307 Alpha 0,05 0,02 Critical value 16,91 f(x) 0, x Histogram Weibull Histogram 0,24 0,22 0,2 0,18 0,16 Probability Density Function 4 perios, p1 excluing all reuction perios Probability Density Function 4 perios, p2 excluing all reuction perios 0,36 0,32 SD 13,559 0,28 SD 11,904 Mean 335,53 Mean 341,7 0,24 0,14 0,2 f(x) 0,12 0,1 0,08 0,06 0,04 0, x f(x) Gooness of fit Gooness of fit 0,16 Deg of freeom 8 Deg of freeom 7 0,12 Statistics 6,0144 Statistics 8,9494 P-value 0,64562 P-value 0,2563 0,08 Alpha 0,05 Alpha 0,05 0,04 Critical value 15,507 Critical value 14, x Histogram Histogram 0,24 0,22 0,2 0,18 0,16 0,14 Probability Density Function 4 perios, p3 excluing all reuction perios Probability Density Function 4 perios, p4 excluing all reuction perios 0,24 0,22 0,2 SD 14,522 SD 14,225 0,18 Mean 322,21 Mean 329,05 0,16 0,14 f(x) 0,12 0,1 0,08 0,06 0,04 0, x f(x) 0,12 Gooness of fit Gooness of fit 0,1 Deg of freeom 8 Deg of freeom 7 0,08 Statistics 8,9538 Statistics 3,8622 0,06 P-value 0,34583 P-value 0, ,04 Alpha 0,05 Alpha 0,05 0,02 Critical value 15,507 Critical value 14, x Histogram Histogram 65

78 Probability Density Function 12 perios, p1 excluing all reuction perios Probability Density Function 12 perios, p2 excluing all reuction perios 0,28 0,26 0,24 0,22 0,2 0,32 SD 12,976 SD 12,33 0,28 Mean 337,17 Mean 340,87 0,24 0,18 0,16 0,2 f(x) 0,14 0,12 0,1 0,08 0,06 0,04 0, x f(x) Gooness of fit Gooness of fit 0,16 Deg of freeom 6 Deg of freeom 6 0,12 Statistics 7,7023 Statistics 2,9228 P-value 0,26073 P-value 0, ,08 Alpha 0,05 Alpha 0,05 0,04 Critical value 12,592 Critical value 12, x Histogram Histogram Probability Density Function 12 perios, p3 excluing all reuction perios Probability Density Function 12 perios, p4 excluing all reuction perios f(x) 0,4 0,36 0,32 0,28 0,24 0,2 0,16 0,12 0,08 0,04 0,28 0,26 SD 11,536 0,24 SD 14,101 0,22 Mean 342,39 Mean 337,42 Gooness of fit 0,16 Gooness of fit Deg of freeom 6 0,14 Deg of freeom 6 0,12 Statistics 5,8926 Statistics 6,3747 0,1 P-value 0,43533 P-value 0, ,08 Alpha 0,05 0,06 Alpha 0,05 0,04 Critical value 12,592 Critical value 12,592 f(x) 0,3 0,2 0,18 0, x x Histogram Histogram Probability Density Function 12 perios, p5 excluing all reuction perios Probability Density Function 12 perios, p6 excluing all reuction perios f(x) 0,32 0,28 0,24 0,2 0,16 0,12 0,08 0,04 0,32 SD 14,661 SD 15,17 0,28 Mean 320,61 Mean 321,68 Gooness of fit Gooness of fit 0,2 Deg of freeom 6 Deg of freeom 6 0,16 Statistics 3,6404 Statistics 1,6459 P-value 0,7252 P-value 0, ,12 Alpha 0,05 Alpha 0,05 0,08 Critical value 12,592 Critical value 12,592 0,04 f(x) 0,36 0, x x Histogram Histogram 0,3 Probability Density Function 12 perios, p7 excluing all reuction perios Probability Density Function 12 perios, p8 excluing all reuction perios 0,64 f(x) 0,28 0,26 0,24 0,22 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0,56 SD 14,473 SD 12,501 0,48 Mean 327,7 Mean 320,58 Gooness of fit Gooness of fit 0,32 Deg of freeom 5 Deg of freeom 1 Statistics 7,2156 Statistics 0, ,24 P-value 0,20509 P-value 0, ,16 Alpha 0,05 Alpha 0,05 Critical value 11,07 Critical value 3,8145 0,08 f(x) 0, x x Histogram 66 Histogram

79 Probability Density Function 12 perios, p9 excluing all reuction perios Probability Density Function 12 perios, p10 excluing all reuction perios f(x) 0,26 0,24 0,22 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0,22 0,2 SD 13,784 SD 14,152 0,18 Mean 324,22 Mean 329,56 0,14 Gooness of fit Gooness of fit 0,12 Deg of freeom 6 Deg of freeom 7 0,1 Statistics 6,4492 Statistics 0, ,08 P-value 0,37479 P-value 0, ,06 Alpha 0,5 Alpha 0,05 0,04 Critical value 12,592 Critical value 14,067 f(x) 0,24 0,16 0, x x Histogram Histogram Probability Density Function 12 perios, p11 excluing all reuction perios Probability Density Function 12 perios, p12 excluing all reuction perios f(x) 0,3 0,28 0,26 0,24 0,22 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0,24 0,22 SD 13,561 SD 13,25 0,2 Mean 334,23 Mean 334,07 Gooness of fit 0,14 Gooness of fit Deg of freeom 6 0,12 Deg of freeom 6 0,1 Statistics 2,2627 Statistics 3,7118 0,08 P-value 0,89403 P-value 0, ,06 Alpha 0,05 Alpha 0,05 0,04 Critical value 12,592 Critical value 12,592 f(x) 0,26 0,18 0,16 0, x x Histogram Histogram Probability Density Function Carnival Probability Density Function May holliay f(x) 0,28 0,26 0,24 0,22 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0,32 SD 19,644 SD 21,802 Mean 315,78 Mean 299,44 0,28 Gooness of fit Gooness of fit 0,2 Deg of freeom 5 Deg of freeom 5 0,16 Statistics 5,191 Statistics 1,037 P-value 0,39302 P-value 0, ,12 Alpha 0,05 Alpha 0,05 0,08 Critical value 11,07 Critical value 11,07 0,04 f(x) 0,36 0, x x Histogram Histogram f(x) 0,44 0,4 0,36 0,32 0,28 0,24 0,2 0,16 0,12 0,08 0,04 Probability Density Function Pentecost Probability Density Function Summer holliay W1 0,3 0,28 SD 16,918 0,26 SD 14,328 0,24 Mean 296,89 0,22 Mean 271,2 0,2 Gooness of fit 0,18 Gooness of fit? 0,16 Deg of freeom 4 Deg of freeom? 0,14 Statistics 0, ,12 Statistics? P-value 0, ,1 P-value? Alpha 0,05 0,08 Alpha? 0,06 Critical value 9,4877 0,04 Critical value? f(x) 0, x x Histogram Histogram 67

80 0,3 0,28 0,26 0,24 0,22 Probability Density Function Summer holliay W2 Probability Density Function Summer holliay W3 +4 0,26 0,24 SD 17,981 SD 16,535 0,22 Mean 278,93 Mean 270,4 0,2 f(x) 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0,18 Gooness of fit Gooness of fit 0,16 Deg of freeom 4 Deg of freeom 6 0,14 Statistics 0, ,12 Statistics 4,2182 P-value 0, ,1 P-value 0, ,08 Alpha 0,05 Alpha 0,05 0,06 Critical value 9,4877 Critical value 12,592 f(x) 0,04 0, x x Histogram Histogram 0,3 0,28 0,26 0,24 0,22 Probability Density Function Summer holliay W5 +6 Probability Density Function Summer holliay W7 0,32 SD 18,275 0,28 SD 21,55 Mean 277,04 Mean 308,73 0,24 f(x) 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 Gooness of fit Gooness of fit 0,2 Deg of freeom 6 Deg of freeom 4 Statistics 9,8817 Statistics 5,4013 0,16 P-value 0,12972 P-value 0, ,12 Alpha 0,05 Alpha 0,05 0,08 Critical value 12,592 Critical value 9,4877 f(x) 0, x x Histogram Histogram 0,44 0,4 0,36 0,32 Probability Density Function Week after may holliay Probability Density Function Week after Christmas holliay 0,3 0,28 SD 20,793 SD 22,339 0,26 Mean 298,23 Mean 314,74 0,24 0,22 f(x) 0,28 0,24 0,2 0,16 0,12 0,08 0,2 Gooness of fit Gooness of fit 0,18 Deg of freeom Deg of freeom 3 0,16 Statistics 4,1395 0,14 Statistics 1,0425 0,12 P-value 0,38745 P-value 0, ,1 Alpha 0,05 Alpha 0,05 0,08 Critical value 9,4877 0,06 Critical value 7,8147 f(x) 0,04 0,04 0, x x Histogram Histogram 0,36 0,32 0,28 Probability Density Function Christmas / new year Probability Density Function Easter weeken / Ascension weeken 0,24 0,22 SD 15,945 SD 17,669 0,2 Mean 240,67 Mean 287,57 0,18 f(x) 0,24 0,2 0,16 0,12 0,08 0,04 0,16 Gooness of fit Gooness of fit 0,14 Deg of freeom 1 Deg of freeom 4 0,12 Statistics 0,48861 Statistics 3,162 0,1 P-value 0,48455 P-value 0, ,08 Alpha 0,05 Alpha 0,05 0,06 Critical value 3,8415 Critical value 9,4877 f(x) 0,04 0, x x Histogram Histogram 68

81 f(x) 0,3 0,28 0,26 0,24 0,22 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 Probability Density Function Probability Density Function Saturay Summer W2-6 0,22 SD 14,93 0,2 SD 17,824 Mean 305,81 0,18 Mean 274,76 0,16 Gooness of fit 0,14 Gooness of fit Deg of freeom 7 0,12 Deg of freeom 7 Statistics 6,2446 0,1 Statistics 3,9091 P-value 0,5115 0,08 P-value 0,79019 Alpha 0,05 0,06 Alpha 0,05 Critical value 14,067 0,04 Critical value 14,067 f(x) 0, x x Histogram Histogram 0,28 0,26 0,24 0,22 Probability Density Function Saturay P1 Probability Density Function Saturay P2 0,28 0,26 SD 14,643 SD 14,096 0,24 Mean 306,43 Mean 310,46 0,22 f(x) 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,18 Gooness of fit Gooness of fit 0,16 Deg of freeom 6 Deg of freeom 4 0,14 Statistics 2,8487 Statistics 2,5302 0,12 P-value 0,82759 P-value 0, ,1 Alpha 0,05 0,08 Alpha 0,05 0,06 Critical value 12,592 Critical value 9,4877 f(x) 0,2 0,04 0,02 0, x x Histogram Histogram 0,32 0,28 0,24 Probability Density Function Saturay P3 Probability Density Function Saturay P4 0,28 0,26 SD 14,976 0,24 SD 15,512 Mean 302,86 0,22 Mean 304,38 0,2 f(x) 0,2 0,16 0,12 0,08 0,04 0,18 Gooness of fit Gooness of fit 0,16 Deg of freeom 5 Deg of freeom 4 0,14 Statistics 1,3257 Statistics 0, ,12 P-value 0, ,1 P-value 0,98557 Alpha 0,05 0,08 Alpha 0,05 0,06 Critical value 11,07 Critical value 9,4877 f(x) 0,04 0, x x Histogram Histogram 0,22 0,2 0,18 0,16 Probability Density Function Sunay Probability Density Function Sunay P1 0,26 0,24 SD 14,738 SD 14,582 0,22 Mean 295,82 Mean 297,07 0,2 f(x) 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0,18 Gooness of fit Gooness of fit 0,16 Deg of freeom 7 Deg of freeom 5 0,14 Statistics 9,4226 0,12 Statistics 1,9089 P-value 0, ,1 P-value 0,8616 0,08 Alpha 0,05 Alpha 0,05 0,06 Critical value 14,067 Critical value 11,07 f(x) 0,04 0, x x Histogram Histogram 69

82 0,3 0,28 0,26 0,24 Probability Density Function Sunay P2 Sunay P3 Probability Density Function 0,32 SD 11,285 SD 12,572 Mean 308 Mean 287,05 0,28 f(x) 0,22 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 Gooness of fit Gooness of fit Deg of freeom 3 Deg of freeom 5 0,2 Statistics 1,4134 Statistics 0, ,16 P-value 0,70241 P-value 0, ,12 Alpha 0,05 Alpha 0,05 Critical value 7,8147 Critical value 11,07 0,08 f(x) 0,24 0,04 0,04 0, x x Histogram Histogram 0,32 0,28 Probability Density Function Sunay P4 SD 11,785 Mean 293,1 f(x) 0,24 0,2 0,16 0,12 0,08 0,04 Gooness of fit Deg of freeom 2 Statistics 2,2473 P-value 0,32509 Alpha 0,05 Critical value 9, x Histogram 70

83 APPENDIX VII: RESULTS FOR THE DIFFERENT COST SCENARIOS PER PERIOD Table 23: Results ifferent cost scenarios for 1 perio with all reuction perios Regu lar bes Flex be s Occupancy rate regular bes % of time flexbes One perio with all reuction perios Expecte refuse/ Probability elaye Amission patients stop per ay Expecte #flexbes Costs per ay for scenario 1 Costs per ay for scenario 2 Costs per ay for scenario 3 Costs per ay for scenario 4 Costs per ay for scenario 5 Cost scen ,35% 42,65% 5,31 2,11% 0, , , , , Cost scen ,26% 77,35% 15,13 1,82% 0, , , , , Cost scen ,72% 48,02% 6,16 4,79% 0, , , , , Cost scen ,07% 27,82% 2,83 2,46% 0, , , , , Cost scen ,35% 42,69% 5,45 0,13% 0, , , , , Table 24: Results ifferent cost scenarios for 4 perios with all reuction perios Regu lar bes Flex be s Occupancy rate regular bes % of time flexbes Four perios with all reuction perios Expecte #flexbes Probability Amission stop Expecte refuse/ elaye patients per ay Costs per ay for scenario 1 Costs per ay for scenario 2 Costs per ay for scenario 3 Costs per ay for scenario 4 Costs per ay for scenario 5 Cost scen ,52% 42,17% 5,00 2,14% 0, , , , , Cost scen ,35% 77,94% 14,38 1,88% 0, , , , , Cost scen ,86% 47,07% 5,68 4,86% 0, , , , , Cost scen ,25% 26,79% 2,61 2,48% 0, , , , , Cost scen ,52% 42,17% 5,14 0,17% 0, , , , ,

84 Table 25: Results ifferent cost scenarios for 12 perios with all reuction perios Twelve perios with all reuction perios Regu lar bes Flex be s Occupancy rate regular bes % of time flexbes Expecte #flexbes Probability Amission stop Expecte refuse/ elaye patients per ay Costs per ay for scenario 1 Costs per ay for scenario 2 Costs per ay for scenario 3 Costs per ay for scenario 4 Costs per ay for scenario 5 Cost scen ,51% 41,85% 4,93 2,13% 0, , , , , Cost scen ,35% 77,91% 14,34 1,88% 0, , , , , Cost scen ,88% 47,37% 5,72 4,79% 0, , , , , Cost scen ,21% 26,29% 2,55 2,41% 0, , , , , Cost scen ,49% 41,60% 5,04 0,17% 0, , , , ,

85 APPENDIX VIII: RESULTS FOR THE DIFFERENT PERIODS PER COST SCENARIO Table 26: Results per perio for cost scenario 2 Time perio Regu lar Scenario 2 1 perio only summer holiay as reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per ay Occupa ncy rate regular Costs Regu per ay lar Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expec te refus e/ elay e patie nts per Costs ay per ay 73 Occupa ncy rate regular Regu lar Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per ay Occupa ncy rate regular Costs Regu per ay lar Flex bes 4Perios1Saturay ,83% 64,45% 9,60 0,02% 0, ,45% 80,19% 14,73 1,84% 0, ,38% 78,24% 13,92 1,84% 0, ,38% 78,24% 13,92 1,84% 0, Perios1Sunay ,34% 39,37% 4,47 0,00% 0, ,48% 81,49% 15,21 2,36% 0, ,34% 77,60% 13,61 2,00% 0, ,34% 77,60% 13,61 2,00% 0, Perios2Saturay ,30% 74,88% 12,33 0,03% 0, ,71% 87,84% 17,99 2,98% 0, ,38% 77,08% 13,00 1,80% 0, ,38% 77,08% 13,00 1,80% 0, Perios2Sunay ,39% 73,25% 9,59 0,00% 0, ,98% 98,33% 24,73 5,54% 0, ,47% 76,08% 10,27 1,67% 0, ,47% 76,08% 10,27 1,67% 0, Perios3Saturay ,31% 54,94% 7,51 0,01% 0, ,13% 72,29% 12,08 1,13% 0, ,37% 78,58% 14,36 1,88% 0, ,37% 78,58% 14,36 1,88% 0, Perios3Sunay ,08% 13,35% 0,99 0,00% 0, ,72% 59,57% 7,29 0,10% 0, ,45% 78,79% 12,25 1,95% 0, ,45% 78,79% 12,25 1,95% 0, Perios4Saturay ,46% 58,64% 8,62 0,02% 0, ,21% 74,84% 13,36 1,77% 0, ,36% 78,77% 14,93 1,77% 0, ,36% 78,77% 14,93 1,77% 0, Perios4Sunay ,79% 25,14% 2,03 0,00% 0, ,48% 78,01% 11,37 0,26% 0, ,48% 78,01% 11,29 1,73% 0, ,48% 78,01% 11,29 1,73% 0, Januari ,00% 99,66% 35,94 3,93% 0, ,76% 87,89% 16,72 1,93% 0, ,57% 80,54% 13,29 1,60% 0, ,51% 78,35% 12,46 1,93% 0, Februari ,00% 99,94% 40,41 7,08% 0, ,91% 94,64% 20,88 3,64% 0, ,41% 73,83% 10,48 1,71% 0, ,55% 78,83% 12,06 1,71% 0, March ,00% 99,98% 41,92 7,50% 0, ,96% 96,82% 22,30 3,70% 0, ,59% 79,22% 11,46 1,65% 0, ,53% 76,65% 10,66 1,65% 0, April ,99% 99,51% 36,98 6,29% 0, ,74% 87,78% 17,92 3,48% 0, ,55% 81,07% 14,51 2,97% 0, ,42% 76,99% 12,97 1,80% 0, May ,80% 90,94% 21,11 0,44% 0, ,12% 48,93% 6,14 0,19% 0, ,27% 74,38% 12,52 1,61% 0, ,42% 78,57% 14,07 1,91% 0, June ,80% 91,36% 22,16 0,69% 0, ,22% 51,80% 6,91 0,32% 0, ,31% 75,93% 13,45 2,28% 0, ,38% 77,94% 14,26 1,95% 0, July ,94% 96,75% 27,76 1,53% 0, ,06% 67,83% 10,38 0,74% 0, ,32% 74,86% 12,54 1,53% 0, ,39% 77,01% 13,30 1,82% 0, August ,90% 94,14% 20,84 0,11% 0, ,38% 48,67% 5,28 0,03% 0, ,49% 77,83% 11,93 0,60% 0, ,49% 77,83% 11,87 1,73% 0, September ,91% 95,40% 24,41 0,58% 0, ,74% 59,24% 7,85 0,25% 0, ,60% 83,13% 15,17 2,19% 0, ,42% 77,08% 12,72 1,84% 0, October ,96% 97,82% 29,54 1,88% 0, ,26% 72,74% 11,62 0,91% 0, ,48% 79,31% 13,90 1,88% 0, ,42% 77,23% 13,10 1,88% 0, November ,99% 99,29% 34,04 3,39% 0, ,63% 83,53% 15,15 1,69% 0, ,38% 75,19% 11,91 1,41% 0, ,46% 77,46% 12,65 2,03% 0, December ,99% 99,37% 33,90 2,99% 0, ,65% 83,80% 14,96 1,45% 0, ,40% 75,31% 11,71 1,19% 0, ,47% 77,63% 12,46 1,75% 0, Carnival holiay ,15% 77,41% 18,01 1,39% 0, ,22% 78,91% 18,75 2,03% 0, ,22% 78,91% 18,75 2,03% 0, ,22% 78,91% 18,75 2,03% 0, Easter / Ascension ,78% 22,36% 2,51 0,00% 0, ,18% 77,88% 16,46 1,96% 0, ,18% 77,88% 16,46 1,96% 0, ,18% 77,88% 16,46 1,96% 0, May holiay ,84% 47,15% 8,40 0,32% 0, ,07% 78,81% 20,67 2,05% 0, ,07% 78,81% 20,67 2,05% 0, ,07% 78,81% 20,67 2,05% 0, Week after may holiay ,76% 44,70% 7,43 0,17% 0, ,08% 78,24% 19,43 1,98% 0, ,08% 78,24% 19,43 1,98% 0, ,08% 78,24% 19,43 1,98% 0, Pentecost ,07% 1,88% 0,12 0,00% 0, ,32% 78,28% 13,65 1,88% 0, ,32% 78,28% 13,65 1,88% 0, ,32% 78,28% 13,65 1,88% 0, Summer holiay W ,23% 77,69% 15,71 1,90% 0, ,23% 77,69% 15,71 1,90% 0, ,23% 77,69% 15,71 1,90% 0, ,23% 77,69% 15,71 1,90% 0, Summer holiay W ,42% 84,06% 20,01 3,29% 0, ,15% 78,07% 16,82 1,96% 0, ,15% 78,07% 16,82 1,96% 0, ,15% 78,07% 16,82 1,96% 0, Summer W3+W ,88% 71,51% 13,02 0,59% 0, ,24% 79,11% 16,02 1,82% 0, ,24% 79,11% 16,02 1,82% 0, ,24% 79,11% 16,02 1,82% 0, Summer W5+W ,27% 80,99% 18,54 2,79% 0, ,12% 77,88% 17,00 1,89% 0, ,12% 77,88% 17,00 1,89% 0, ,12% 77,88% 17,00 1,89% 0, Summer holiay W ,08% 78,12% 20,03 2,00% 0, ,08% 78,12% 20,03 2,00% 0, ,08% 78,12% 20,03 2,00% 0, ,08% 78,12% 20,03 2,00% 0, Christmas / New Year ,96% 0,01% 0,00 0,00% 0, ,15% 78,65% 15,27 1,83% 0, ,15% 78,65% 15,27 1,83% 0, ,15% 78,65% 15,27 1,83% 0, Christmas holiay W ,32% 20,13% 2,23 0,00% 0, ,17% 78,06% 16,84 1,97% 0, ,17% 78,06% 16,84 1,97% 0, ,17% 78,06% 16,84 1,97% 0, Christmas holiay W ,56% 6,04% 0,58 0,00% 0, ,07% 79,06% 19,09 2,00% 0, ,07% 79,06% 19,09 2,00% 0, ,07% 79,06% 19,09 2,00% 0, Week after Christmas ,78% 73,08% 17,93 2,38% 0, ,08% 78,24% 19,43 1,98% 0, ,08% 78,24% 19,43 1,98% 0, ,08% 78,24% 19,43 1,98% 0, Weighte average (year) ,64% 76,71% 21,32 2,13% 0, ,26% 77,35% 15,13 1,82% 0, ,35% 77,94% 14,38 1,88% 0, ,35% 77,91% 14,34 1,88% 0, % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per ay Costs per ay

86 Table 27: Results per perio for cost scenario 3 Time perio Regu lar Scen 3 1 perio only summer holiay as reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per ay Costs Regu per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expec te refus e/ elay e patie nts per ay Costs Regu per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per Costs Regu ay per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per Costs ay per ay 4Perios1Saturay ,58% 12,88% 1,07 0,07% 0, ,00% 48,43% 5,72 4,66% 0, ,00% 48,43% 5,72 4,66% 0, ,00% 48,43% 5,72 4,66% 0, Perios1Sunay ,90% 3,77% 0,26 0,01% 0, ,05% 50,18% 5,94 5,79% 0, ,89% 47,45% 5,49 5,04% 0, ,89% 47,45% 5,49 5,04% 0, Perios2Saturay ,67% 18,67% 1,63 0,13% 0, ,68% 59,67% 7,59 7,25% 0, ,38% 46,47% 4,23 4,61% 0, ,38% 46,47% 4,23 4,61% 0, Perios2Sunay ,21% 9,19% 0,58 0,00% 0, ,67% 83,52% 11,85 14,38% 0, ,38% 46,47% 4,23 4,61% 0, ,38% 46,47% 4,23 4,61% 0, Perios3Saturay ,57% 8,93% 0,71 0,04% 0, ,31% 39,11% 4,33 3,01% 0, ,84% 46,96% 5,56 4,66% 0, ,84% 46,96% 5,56 4,66% 0, Perios3Sunay ,87% 0,21% 0,01 0,00% 0, ,13% 21,42% 1,74 0,44% 0, ,09% 46,97% 4,74 4,78% 0, ,09% 46,97% 4,74 4,78% 0, Perios4Saturay ,97% 11,51% 0,99 0,09% 0, ,53% 43,31% 5,09 4,31% 0, ,87% 48,42% 6,01 4,93% 0, ,87% 48,42% 6,01 4,93% 0, Perios4Sunay ,74% 0,56% 0,03 0,00% 0, ,68% 37,05% 3,33 1,12% 0, ,24% 46,97% 4,48 4,57% 0, ,24% 46,97% 4,48 4,57% 0, Januari ,68% 84,50% 14,38 9,73% 0, ,88% 59,66% 7,17 5,42% 0, ,34% 47,46% 4,96 4,63% 0, ,34% 47,46% 4,96 4,63% 0, Februari ,87% 92,63% 17,98 16,27% 1, ,41% 73,83% 9,92 9,55% 0, ,23% 43,15% 4,11 4,33% 0, ,39% 46,35% 4,59 4,33% 0, March ,93% 95,36% 19,26 17,89% 1, ,59% 79,22% 10,87 10,27% 0, ,57% 47,90% 4,54 4,46% 0, ,57% 47,90% 4,54 4,46% 0, April ,65% 84,67% 15,30 13,45% 1, ,89% 62,29% 8,12 8,24% 0, ,39% 51,18% 5,83 7,22% 0, ,25% 48,35% 5,51 4,72% 0, May ,80% 43,51% 5,09 1,36% 0, ,79% 19,90% 1,79 0,65% 0, ,80% 43,51% 4,88 4,16% 0, ,96% 46,21% 5,31 4,81% 0, June ,92% 46,54% 5,76 1,95% 0, ,00% 22,78% 2,18 1,00% 0, ,92% 46,54% 5,48 5,45% 0, ,92% 46,54% 5,54 4,76% 0, July ,85% 62,73% 8,79 4,02% 0, ,36% 35,71% 3,74 2,15% 0, ,88% 43,69% 4,87 4,02% 0, ,04% 46,42% 5,29 4,66% 0, August ,05% 42,34% 4,28 0,48% 0, ,95% 16,03% 1,21 0,18% 0, ,05% 42,34% 4,19 2,10% 0, ,22% 45,49% 4,46 5,12% 0, September ,48% 53,53% 6,57 1,84% 0, ,71% 26,21% 2,41 0,87% 0, ,48% 53,53% 6,28 5,71% 0, ,19% 47,75% 5,27 4,92% 0, October ,08% 67,86% 9,87 4,89% 0, ,74% 40,41% 4,34 2,63% 0, ,22% 48,77% 5,59 4,89% 0, ,07% 45,96% 5,09 4,89% 0, November ,52% 79,61% 12,98 8,31% 0, ,55% 53,61% 6,28 4,66% 0, ,95% 41,90% 4,31 3,98% 0, ,27% 47,73% 5,21 4,66% 0, December ,54% 79,82% 12,83 7,65% 0, ,57% 53,21% 6,11 4,18% 0, ,96% 41,24% 4,15 3,54% 0, ,28% 47,19% 5,00 4,89% 0, Carnival holiay ,29% 35,66% 4,86 2,91% 0, ,33% 47,52% 7,26 5,05% 0, ,33% 47,52% 7,26 5,05% 0, ,33% 47,52% 7,26 5,05% 0, Easter / Ascension ,99% 2,25% 0,17 0,01% 0, ,31% 46,78% 6,43 4,79% 0, ,31% 46,78% 6,43 4,79% 0, ,31% 46,78% 6,43 4,79% 0, May holiay ,23% 14,00% 1,64 0,70% 0, ,01% 48,98% 8,39 5,15% 0, ,01% 48,98% 8,39 5,15% 0, ,01% 48,98% 8,39 5,15% 0, Week after may holiay ,96% 11,68% 1,28 0,42% 0, ,10% 48,52% 7,90 5,22% 0, ,10% 48,52% 7,90 5,22% 0, ,10% 48,52% 7,90 5,22% 0, Pentecost ,96% 0,01% 0,00 0,00% 0, ,75% 47,77% 5,47 4,83% 0, ,75% 47,77% 5,47 4,83% 0, ,75% 47,77% 5,47 4,83% 0, Summer holiay W ,54% 47,37% 6,30 4,83% 0, ,54% 47,37% 6,30 4,83% 0, ,54% 47,37% 6,30 4,83% 0, ,54% 47,37% 6,30 4,83% 0, Summer holiay W ,90% 56,46% 8,55 8,16% 0, ,24% 47,62% 6,73 4,72% 0, ,24% 47,62% 6,73 4,72% 0, ,24% 47,62% 6,73 4,72% 0, Summer W3+W ,46% 36,74% 4,40 2,11% 0, ,45% 48,55% 6,42 4,75% 0, ,45% 48,55% 6,42 4,75% 0, ,45% 48,55% 6,42 4,75% 0, Summer W5+W ,54% 52,26% 7,71 7,01% 0, ,20% 47,90% 6,87 5,06% 0, ,20% 47,90% 6,87 5,06% 0, ,20% 47,90% 6,87 5,06% 0, Summer holiay W ,02% 47,64% 7,95 5,08% 0, ,02% 47,64% 7,95 5,08% 0, ,02% 47,64% 7,95 5,08% 0, ,02% 47,64% 7,95 5,08% 0, Christmas / New Year ,51% 0,00% 0,00 0,00% 0, ,09% 46,67% 5,81 4,93% 0, ,09% 46,67% 5,81 4,93% 0, ,09% 46,67% 5,81 4,93% 0, Christmas holiay W ,48% 1,97% 0,15 0,01% 0, ,31% 47,64% 6,74 4,74% 0, ,31% 47,64% 6,74 4,74% 0, ,31% 47,64% 6,74 4,74% 0, Christmas holiay W ,61% 0,40% 0,03 0,00% 0, ,90% 48,20% 7,53 4,93% 0, ,90% 48,20% 7,53 4,93% 0, ,90% 48,20% 7,53 4,93% 0, Week after Christmas ,78% 35,58% 5,31 4,34% 0, ,98% 47,76% 8,24 5,23% 0, ,98% 47,76% 8,24 5,23% 0, ,98% 47,76% 8,24 5,23% 0, Weighte average (year) ,31% 47,83% 7,49 5,13% 0, ,72% 48,02% 6,16 4,79% 0, ,86% 47,07% 5,68 4,86% 0, ,88% 47,37% 5,72 4,79% 0,

87 Table 28: Results per perio for cost scenario 4 Time perio Regu lar Scen 4 1 perio only summer holiay as reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per ay Costs Regu per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expec te refus e/ elay e patie nts per ay Costs Regu per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per Costs Regu ay per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per Costs ay per ay 4Perios1Saturay ,43% 2,55% 0,17 0,03% 0, ,48% 27,91% 2,65 2,55% 0, ,26% 25,66% 2,36 2,55% 0, ,26% 25,66% 2,36 2,55% 0, Perios1Sunay ,67% 0,46% 0,03 0,00% 0, ,52% 29,32% 2,81 2,77% 0, ,29% 27,01% 2,53 2,36% 0, ,29% 27,01% 2,53 2,36% 0, Perios2Saturay ,60% 4,08% 0,27 0,05% 0, ,40% 37,35% 3,75 4,08% 0, ,58% 27,21% 2,47 2,53% 0, ,58% 27,21% 2,47 2,53% 0, Perios2Sunay ,93% 0,84% 0,04 0,00% 0, ,96% 60,48% 6,38 6,60% 0, ,19% 26,75% 2,01 2,08% 0, ,19% 26,75% 2,01 2,08% 0, Perios3Saturay ,38% 1,59% 0,10 0,02% 0, ,59% 20,88% 1,88 1,59% 0, ,27% 27,08% 2,62 2,21% 0, ,27% 27,08% 2,62 2,21% 0, Perios3Sunay ,69% 0,01% 0,00 0,00% 0, ,97% 7,66% 0,51 0,13% 0, ,62% 26,35% 2,15 2,36% 0, ,62% 26,35% 2,15 2,36% 0, Perios4Saturay ,82% 2,42% 0,17 0,03% 0, ,91% 24,69% 2,36 2,42% 0, ,13% 26,77% 2,64 2,42% 0, ,13% 26,77% 2,64 2,42% 0, Perios4Sunay ,49% 0,02% 0,00 0,00% 0, ,78% 15,64% 1,11 0,34% 0, ,79% 25,14% 1,92 2,13% 0, ,79% 25,14% 1,92 2,13% 0, Januari ,62% 53,60% 5,98 5,42% 0, ,67% 35,49% 3,32 2,79% 0, ,09% 27,32% 2,32 2,33% 0, ,89% 24,82% 2,04 2,33% 0, Februari ,25% 68,30% 8,44 9,55% 0, ,54% 49,58% 5,04 5,13% 0, ,13% 25,49% 2,01 2,52% 0, ,13% 25,49% 2,01 2,52% 0, March ,46% 73,92% 9,29 10,27% 0, ,85% 54,80% 5,58 5,34% 0, ,52% 28,34% 2,19 2,50% 0, ,32% 25,48% 1,89 2,50% 0, April ,66% 56,80% 6,88 8,24% 0, ,77% 39,97% 4,10 4,72% 0, ,23% 32,03% 2,99 4,06% 0, ,84% 27,13% 2,46 2,52% 0, May ,33% 16,31% 1,40 0,65% 0, ,86% 8,21% 0,62 0,29% 0, ,24% 23,92% 2,19 1,91% 0, ,45% 26,08% 2,44 2,25% 0, June ,55% 19,00% 1,72 1,00% 0, ,12% 10,14% 0,81 0,48% 0, ,43% 26,96% 2,60 2,66% 0, ,43% 26,96% 2,63 2,28% 0, July ,97% 30,70% 3,02 2,15% 0, ,69% 17,91% 1,53 1,07% 0, ,35% 23,83% 2,14 2,15% 0, ,57% 26,03% 2,38 2,53% 0, August ,47% 12,44% 0,89 0,18% 0, ,93% 5,12% 0,32 0,06% 0, ,43% 20,23% 1,59 0,75% 0, ,87% 25,04% 2,01 2,10% 0, September ,27% 21,71% 1,89 0,87% 0, ,86% 11,18% 0,84 0,38% 0, ,12% 31,15% 2,92 2,60% 0, ,71% 26,21% 2,32 2,19% 0, October ,38% 35,04% 3,53 2,63% 0, ,15% 20,95% 1,82 1,32% 0, ,79% 27,56% 2,52 2,63% 0, ,59% 25,25% 2,26 2,23% 0, November ,27% 47,73% 5,21 4,66% 0, ,23% 30,87% 2,86 2,42% 0, ,62% 23,56% 1,99 2,03% 0, ,83% 25,89% 2,24 2,42% 0, December ,28% 47,19% 5,05 4,18% 0, ,23% 30,04% 2,71 2,10% 0, ,61% 22,67% 1,87 1,75% 0, ,82% 25,01% 2,08 2,52% 0, Carnival holiay ,75% 16,39% 1,73 1,79% 0, ,30% 26,69% 3,25 2,58% 0, ,30% 26,69% 3,25 2,58% 0, ,30% 26,69% 3,25 2,58% 0, Easter / Ascension ,84% 0,36% 0,02 0,00% 0, ,26% 25,89% 2,83 2,57% 0, ,26% 25,89% 2,83 2,57% 0, ,26% 25,89% 2,83 2,57% 0, May holiay ,25% 5,15% 0,49 0,41% 0, ,54% 26,70% 3,58 2,55% 0, ,54% 26,70% 3,58 2,55% 0, ,54% 26,70% 3,58 2,55% 0, Week after may holiay ,93% 3,85% 0,34 0,24% 0, ,79% 26,95% 3,48 2,50% 0, ,79% 26,95% 3,48 2,50% 0, ,79% 26,95% 3,48 2,50% 0, Pentecost ,96% 0,00% 0,00 0,00% 0, ,01% 26,95% 2,50 2,22% 0, ,01% 26,95% 2,50 2,22% 0, ,01% 26,95% 2,50 2,22% 0, Summer holiay W ,77% 27,50% 2,96 2,52% 0, ,77% 27,50% 2,96 2,52% 0, ,77% 27,50% 2,96 2,52% 0, ,77% 27,50% 2,96 2,52% 0, Summer holiay W ,06% 34,70% 4,19 4,20% 0, ,16% 26,90% 3,03 2,55% 0, ,16% 26,90% 3,03 2,55% 0, ,16% 26,90% 3,03 2,55% 0, Summer W3+W ,01% 17,27% 1,66 0,83% 0, ,30% 26,07% 2,70 2,43% 0, ,30% 26,07% 2,70 2,43% 0, ,30% 26,07% 2,70 2,43% 0, Summer W5+W ,58% 31,19% 3,69 3,56% 0, ,12% 27,43% 3,17 2,45% 0, ,12% 27,43% 3,17 2,45% 0, ,12% 27,43% 3,17 2,45% 0, Summer holiay W ,78% 26,89% 3,59 2,49% 0, ,78% 26,89% 3,59 2,49% 0, ,78% 26,89% 3,59 2,49% 0, ,78% 26,89% 3,59 2,49% 0, Christmas / New Year ,84% 0,00% 0,00 0,00% 0, ,89% 25,85% 2,58 2,47% 0, ,89% 25,85% 2,58 2,47% 0, ,89% 25,85% 2,58 2,47% 0, Christmas holiay W ,35% 0,32% 0,02 0,00% 0, ,28% 26,94% 3,04 2,57% 0, ,28% 26,94% 3,04 2,57% 0, ,28% 26,94% 3,04 2,57% 0, Christmas holiay W ,63% 0,06% 0,00 0,00% 0, ,58% 27,51% 3,44 2,54% 0, ,58% 27,51% 3,44 2,54% 0, ,58% 27,51% 3,44 2,54% 0, Week after Christmas ,29% 18,23% 2,12 2,93% 0, ,80% 27,64% 3,87 2,38% 0, ,80% 27,64% 3,87 2,38% 0, ,80% 27,64% 3,87 2,38% 0, Weighte average (year) ,22% 27,42% 3,06 2,87% 0, ,07% 27,82% 2,83 2,46% 0, ,25% 26,79% 2,61 2,48% 0, ,21% 26,29% 2,55 2,41% 0,

88 Table 29: Results per perio for cost scenario 5 Scen 5 1 perio only summer holiay as reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Time perio Regu lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per ay Costs Regu per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expec te refus e/ elay e patie nts per ay Costs Regu per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per Costs Regu ay per ay lar Occupa ncy rate regular Flex bes % of time flexbe s Expec te #flexb es Proba bility Amis sion stop Expe cte refus e/ elay e patie nts per Costs ay per ay 4Perios1Saturay ,81% 9,06% 0,71 0,00% 0, ,66% 43,02% 5,08 0,15% 0, ,66% 43,02% 5,08 0,18% 0, ,66% 43,02% 5,08 0,18% 0, Perios1Sunay ,09% 2,36% 0,15 0,00% 0, ,71% 44,73% 5,35 0,20% 0, ,53% 42,03% 4,89 0,16% 0, ,53% 42,03% 4,89 0,16% 0, Perios2Saturay ,94% 13,50% 1,10 0,00% 0, ,41% 54,10% 6,92 0,25% 0, ,77% 42,83% 4,87 0,16% 0, ,77% 42,83% 4,87 0,16% 0, Perios2Sunay ,40% 5,54% 0,32 0,00% 0, ,55% 78,74% 11,15 0,30% 0, ,02% 39,52% 3,56 0,17% 0, ,02% 39,52% 3,56 0,17% 0, Perios3Saturay ,78% 6,12% 0,46 0,00% 0, ,91% 34,09% 3,75 0,08% 0, ,49% 41,69% 4,95 0,16% 0, ,49% 41,69% 4,95 0,16% 0, Perios3Sunay ,05% 0,10% 0,00 0,00% 0, ,62% 17,08% 1,33 0,00% 0, ,71% 40,71% 4,09 0,16% 0, ,71% 40,71% 4,09 0,16% 0, Perios4Saturay ,19% 8,17% 0,66 0,00% 0, ,16% 38,30% 4,54 0,16% 0, ,35% 40,79% 4,96 0,16% 0, ,35% 40,79% 4,96 0,16% 0, Perios4Sunay ,91% 0,26% 0,01 0,00% 0, ,25% 30,84% 2,65 0,00% 0, ,88% 40,29% 3,80 0,15% 0, ,88% 40,29% 3,80 0,15% 0, Januari ,51% 78,35% 12,55 0,46% 0, ,62% 53,60% 6,33 0,11% 0, ,18% 44,40% 4,76 0,14% 0, ,02% 41,38% 4,30 0,18% 0, Februari ,79% 88,61% 16,40 0,91% 0, ,25% 68,30% 9,09 0,22% 0, ,07% 39,99% 3,92 0,17% 0, ,07% 39,99% 3,92 0,17% 0, March ,88% 92,23% 17,68 0,84% 0, ,46% 73,92% 9,95 0,18% 0, ,42% 44,46% 4,30 0,13% 0, ,25% 41,06% 3,83 0,13% 0, April ,49% 79,09% 13,82 1,04% 0, ,66% 56,80% 7,48 0,31% 0, ,25% 48,35% 5,81 0,38% 0, ,94% 42,73% 4,86 0,16% 0, May ,26% 35,65% 3,91 0,04% 0, ,33% 16,31% 1,43 0,01% 0, ,44% 38,22% 4,30 0,12% 0, ,62% 40,85% 4,72 0,15% 0, June ,41% 38,80% 4,53 0,07% 0, ,55% 19,00% 1,78 0,02% 0, ,58% 41,35% 4,95 0,21% 0, ,58% 41,35% 4,95 0,17% 0, July ,48% 54,68% 7,21 0,17% 0, ,97% 30,70% 3,16 0,04% 0, ,54% 38,32% 4,26 0,14% 0, ,71% 40,98% 4,69 0,17% 0, August ,50% 33,24% 3,08 0,00% 0, ,47% 12,44% 0,90 0,00% 0, ,69% 36,19% 3,46 0,02% 0, ,05% 42,34% 4,30 0,18% 0, September ,03% 44,87% 5,11 0,04% 0, ,27% 21,71% 1,94 0,01% 0, ,19% 47,75% 5,60 0,15% 0, ,86% 42,01% 4,65 0,15% 0, October ,76% 59,94% 8,21 0,21% 0, ,38% 35,04% 3,70 0,05% 0, ,91% 43,17% 4,95 0,17% 0, ,74% 40,41% 4,50 0,17% 0, November ,31% 72,80% 11,21 0,42% 0, ,27% 47,73% 5,52 0,10% 0, ,78% 39,04% 4,13 0,13% 0, ,95% 41,90% 4,56 0,17% 0, December ,32% 72,87% 10,99 0,33% 0, ,28% 47,19% 5,31 0,08% 0, ,79% 38,33% 3,94 0,10% 0, ,96% 41,24% 4,37 0,17% 0, Carnival holiay ,71% 30,14% 4,05 0,29% 0, ,84% 41,49% 6,32 0,18% 0, ,84% 41,49% 6,32 0,18% 0, ,84% 41,49% 6,32 0,18% 0, Easter / Ascension ,18% 1,48% 0,11 0,00% 0, ,94% 42,31% 5,89 0,18% 0, ,94% 42,31% 5,89 0,18% 0, ,94% 42,31% 5,89 0,18% 0, May holiay ,49% 11,16% 1,29 0,06% 0, ,50% 43,52% 7,46 0,18% 0, ,50% 43,52% 7,46 0,18% 0, ,50% 43,52% 7,46 0,18% 0, Week after may holiay ,21% 9,08% 0,97 0,03% 0, ,58% 42,80% 6,97 0,17% 0, ,58% 42,80% 6,97 0,17% 0, ,58% 42,80% 6,97 0,17% 0, Pentecost ,19% 0,01% 0,00 0,00% 0, ,36% 42,25% 4,85 0,18% 0, ,36% 42,25% 4,85 0,18% 0, ,36% 42,25% 4,85 0,18% 0, Summer holiay W ,19% 42,70% 5,73 0,18% 0, ,19% 42,70% 5,73 0,18% 0, ,19% 42,70% 5,73 0,18% 0, ,19% 42,70% 5,73 0,18% 0, Summer holiay W ,58% 52,05% 8,15 0,38% 0, ,87% 43,21% 6,17 0,16% 0, ,87% 43,21% 6,17 0,16% 0, ,87% 43,21% 6,17 0,16% 0, Summer W3+W ,01% 32,29% 3,81 0,03% 0, ,88% 41,38% 5,37 0,16% 0, ,88% 41,38% 5,37 0,16% 0, ,88% 41,38% 5,37 0,16% 0, Summer W5+W ,20% 47,90% 7,29 0,31% 0, ,64% 41,42% 5,89 0,16% 0, ,64% 41,42% 5,89 0,16% 0, ,64% 41,42% 5,89 0,16% 0, Summer holiay W ,52% 42,14% 7,05 0,17% 0, ,52% 42,14% 7,05 0,17% 0, ,52% 42,14% 7,05 0,17% 0, ,52% 42,14% 7,05 0,17% 0, Christmas / New Year ,82% 0,00% 0,00 0,00% 0, ,65% 41,72% 5,25 0,18% 0, ,65% 41,72% 5,25 0,18% 0, ,65% 41,72% 5,25 0,18% 0, Christmas holiay W ,69% 1,30% 0,10 0,00% 0, ,95% 43,24% 6,18 0,16% 0, ,95% 43,24% 6,18 0,16% 0, ,95% 43,24% 6,18 0,16% 0, Christmas holiay W ,85% 0,25% 0,02 0,00% 0, ,33% 42,24% 6,57 0,18% 0, ,33% 42,24% 6,57 0,18% 0, ,33% 42,24% 6,57 0,18% 0, Week after Christmas ,20% 30,72% 4,65 0,67% 0, ,49% 42,44% 7,36 0,17% 0, ,49% 42,44% 7,36 0,17% 0, ,49% 42,44% 7,36 0,17% 0, Weighte average (year) ,86% 42,94% 6,52 0,27% 0, ,35% 42,69% 5,45 0,13% 0, ,52% 42,17% 5,14 0,17% 0, ,49% 41,60% 5,04 0,17% 0,

89 APPENDIX IX: VALIDATION RESULTS TABLES Table 30: Results valiation for cost scenario 1 Scen 1 1 perio only summer holiay as reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Time perio Flex Flex Flex Flex 4Perios1Saturay ,90% 9,09% 1,55 0,00% ,38% 63,64% 6,45 9,09% 0, ,38% 63,64% 6,45 9,09% 0, ,38% 63,64% 6,45 9,09% 0, Perios1Sunay ,59% 18,18% 1,55 0,00% ,85% 90,91% 13,09 18,18% 1, ,82% 90,91% 12,36 18,18% 1, ,82% 90,91% 12,36 18,18% 1, Perios2Saturay ,15% 14,29% 0,43 0,00% ,54% 85,71% 9,57 0,00% ,22% 71,43% 6,57 0,00% ,22% 71,43% 6,57 0,00% Perios2Sunay ,65% 0,00% - 0,00% ,14% 71,43% 8,86 0,00% ,20% 28,57% 3,00 0,00% ,20% 28,57% 3,00 0,00% Perios3Saturay ,97% 0,00% - 0,00% ,40% 20,00% 1,60 0,00% ,03% 30,00% 2,50 0,00% ,03% 30,00% 2,50 0,00% Perios3Sunay ,38% 0,00% - 0,00% ,34% 20,00% 2,50 0,00% ,62% 20,00% 4,10 10,00% 0, ,62% 20,00% 4,10 10,00% 0, Perios4Saturay ,39% 33,33% 2,33 0,00% ,24% 83,33% 12,67 16,67% 0, ,30% 83,33% 13,50 16,67% 0, ,30% 83,33% 13,50 16,67% 0, Perios4Sunay ,94% 16,67% 0,67 0,00% ,72% 83,33% 11,33 16,67% 0, ,89% 83,33% 11,17 33,33% 3, ,89% 83,33% 11,17 33,33% 3, January ,94% 86,67% 10,13 0,00% ,02% 46,67% 4,20 0,00% ,54% 40,00% 2,87 0,00% ,37% 33,33% 2,47 0,00% February ,98% 85,00% 15,55 5,00% 0, ,39% 75,00% 8,75 5,00% 0, ,33% 40,00% 3,55 0,00% ,33% 40,00% 3,55 0,00% March ,95% 75,00% 18,38 12,50% 0, ,30% 75,00% 12,00 0,00% ,49% 62,50% 5,94 0,00% ,39% 62,50% 5,31 0,00% April ,00% 88,89% 15,72 5,56% 0, ,45% 66,67% 8,78 0,00% ,15% 61,11% 6,83 0,00% ,91% 55,56% 5,67 0,00% May ,79% 23,08% 2,00 0,00% ,70% 15,38% 0,31 0,00% ,02% 23,08% 2,23 0,00% ,25% 23,08% 2,46 0,00% June ,78% 0,00% - 0,00% ,28% 0,00% - 0,00% ,06% 0,00% - 0,00% ,06% 0,00% - 0,00% July ,00% 77,78% 16,78 11,11% 0, ,40% 77,78% 10,22 0,00% ,60% 77,78% 12,11 11,11% 0, ,66% 77,78% 12,78 11,11% 0, August September ,16% 54,55% 5,68 0,00% ,57% 27,27% 2,18 0,00% ,29% 54,55% 6,23 0,00% ,03% 50,00% 5,14 0,00% October ,48% 69,57% 10,61 4,35% 0, ,33% 39,13% 5,70 0,00% ,78% 52,17% 6,96 4,35% 0, ,64% 47,83% 6,43 4,35% 0, November ,00% 100,00% 17,15 10,00% 0, ,79% 80,00% 9,15 0,00% ,60% 75,00% 6,80 0,00% ,67% 75,00% 7,55 0,00% December ,75% 86,67% 13,27 13,33% 1, ,20% 66,67% 6,67 13,33% 0, ,88% 40,00% 4,93 13,33% 0, ,99% 60,00% 5,27 13,33% 0, Carnival holiay ,49% 0,00% - 0,00% ,05% 11,11% 0,44 0,00% ,05% 11,11% 0,44 0,00% ,05% 11,11% 0,44 0,00% Easter / Ascension ,12% 14,29% 0,29 0,00% ,37% 42,86% 11,86 14,29% 0, ,37% 42,86% 11,86 14,29% 0, ,37% 42,86% 11,86 14,29% 0, May holiay ,25% 25,00% 1,13 0,00% ,30% 75,00% 10,75 0,00% ,30% 75,00% 10,75 0,00% ,30% 75,00% 10,75 0,00% Week after may holiay ,90% 0,00% - 0,00% ,40% 57,14% 8,71 0,00% ,40% 57,14% 8,71 0,00% ,40% 57,14% 8,71 0,00% Pentacost ,68% 0,00% - 0,00% ,61% 0,00% - 0,00% ,61% 0,00% - 0,00% ,61% 0,00% - 0,00% Summer holiay W ,81% 57,14% 11,57 14,29% 1, ,81% 57,14% 11,57 14,29% 1, ,81% 57,14% 11,57 14,29% 1, ,81% 57,14% 11,57 14,29% 1, Summer holiay W ,71% 57,14% 7,00 0,00% ,15% 57,14% 4,71 0,00% ,15% 57,14% 4,71 0,00% ,15% 57,14% 4,71 0,00% Summer W3+W ,07% 7,14% 0,21 0,00% ,19% 35,71% 0,93 0,00% ,19% 35,71% 0,93 0,00% ,19% 35,71% 0,93 0,00% Summer W5+W ,52% 14,29% 0,71 0,00% ,64% 7,14% 0,43 0,00% ,64% 7,14% 0,43 0,00% ,64% 7,14% 0,43 0,00% Summer holiay W ,70% 14,29% 0,29 0,00% ,70% 14,29% 0,29 0,00% ,70% 14,29% 0,29 0,00% ,70% 14,29% 0,29 0,00% Christmas / New Year ,24% 0,00% - 0,00% ,36% 33,33% 9,67 33,33% 8, ,36% 33,33% 9,67 33,33% 8, ,36% 33,33% 9,67 33,33% 8, Christmas holiay W ,68% 33,33% 2,33 0,00% ,87% 83,33% 24,00 50,00% 4, ,87% 83,33% 24,00 50,00% 4, ,87% 83,33% 24,00 50,00% 4, Christmas holiay W ,46% 0,00% - 0,00% ,81% 75,00% 16,00 12,50% 1, ,81% 75,00% 16,00 12,50% 1, ,81% 75,00% 16,00 12,50% 1, Week after Christmas ,11% 28,57% 2,86 0,00% ,25% 57,14% 6,00 0,00% ,25% 57,14% 6,00 0,00% ,25% 57,14% 6,00 0,00% Weighte average (year) ,93% 42,47% 7 3,01% 0, ,06% 50,14% 7 4,11% 0, ,32% 47,67% 6 4,93% 0, ,29% 47,40% 6 4,93% 0, Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay 77

90 Table 31: Results valiation for cost scenario 2 Scen 2 1 perio only summer holiay as reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Time perio Flex Flex Flex Flex 4Perios1Saturay ,88% 90,91% 13,55 0,00% ,00% 100,00% 19,64 9,09% 0, ,00% 100,00% 18,64 9,09% 0, ,00% 100,00% 18,64 9,09% 0, Perios1Sunay ,79% 81,82% 12,82 0,00% ,00% 100,00% 27,64 18,18% 1, ,00% 100,00% 25,82 18,18% 1, ,00% 100,00% 25,82 18,18% 1, Perios2Saturay ,91% 85,71% 16,43 0,00% ,00% 100,00% 23,14 0,00% ,95% 85,71% 17,29 0,00% ,95% 85,71% 17,29 0,00% Perios2Sunay ,96% 71,43% 7,43 0,00% ,00% 100,00% 21,29 0,00% ,05% 71,43% 8,14 0,00% ,05% 71,43% 8,14 0,00% Perios3Saturay ,11% 30,00% 4,00 0,00% ,31% 50,00% 7,20 0,00% ,80% 50,00% 8,70 0,00% ,80% 50,00% 8,70 0,00% Perios3Sunay ,86% 20,00% 2,10 0,00% ,22% 20,00% 5,50 0,00% ,38% 60,00% 8,90 10,00% 0, ,38% 60,00% 8,90 10,00% 0, Perios4Saturay ,67% 83,33% 19,83 0,00% ,00% 100,00% 25,50 16,67% 0, ,00% 100,00% 27,50 16,67% 0, ,00% 100,00% 27,50 16,67% 0, Perios4Sunay ,56% 66,67% 10,50 0,00% ,00% 100,00% 25,50 16,67% 0, ,00% 100,00% 23,17 33,33% 3, ,00% 100,00% 23,17 33,33% 3, January ,00% 100,00% 34,93 0,00% ,00% 100,00% 14,93 0,00% ,98% 86,67% 11,00 0,00% ,94% 86,67% 10,13 0,00% February ,00% 100,00% 40,55 5,00% 0, ,00% 100,00% 20,75 5,00% 0, ,53% 75,00% 10,35 0,00% ,68% 75,00% 11,85 0,00% March ,00% 93,75% 40,06 12,50% 0, ,24% 81,25% 22,75 0,00% ,44% 75,00% 13,50 0,00% ,37% 75,00% 12,75 0,00% April ,00% 100,00% 40,78 5,56% 0, ,00% 100,00% 20,94 0,00% ,00% 100,00% 16,94 0,00% ,97% 83,33% 15,06 0,00% May ,92% 84,62% 16,77 0,00% ,92% 30,77% 3,23 0,00% ,26% 61,54% 8,85 0,00% ,48% 69,23% 10,15 0,00% June ,67% 55,00% 5,45 0,00% ,22% 0,00% - 0,00% ,88% 25,00% 1,15 0,00% ,11% 25,00% 1,40 0,00% July ,00% 100,00% 41,89 11,11% 0, ,00% 100,00% 22,22 0,00% ,00% 100,00% 24,89 11,11% 0, ,00% 100,00% 25,78 11,11% 0, August September ,88% 90,91% 25,05 0,00% ,77% 63,64% 8,64 0,00% ,58% 86,36% 16,00 0,00% ,42% 81,82% 13,50 0,00% October ,00% 100,00% 33,96 4,35% 0, ,85% 82,61% 14,57 0,00% ,96% 95,65% 17,09 4,35% 0, ,95% 86,96% 16,13 4,35% 0, November ,00% 100,00% 42,25 10,00% 0, ,00% 100,00% 22,45 0,00% ,00% 100,00% 18,45 0,00% ,00% 100,00% 19,45 0,00% December ,00% 100,00% 37,60 13,33% 1, ,94% 93,33% 18,33 13,33% 0, ,79% 86,67% 14,93 13,33% 0, ,84% 86,67% 15,53 13,33% 0, Carnival holiay ,01% 22,22% 3,00 0,00% ,26% 22,22% 3,22 0,00% ,26% 22,22% 3,22 0,00% ,26% 22,22% 3,22 0,00% Easter / Ascension ,69% 42,86% 8,29 0,00% ,14% 57,14% 20,29 14,29% 0, ,14% 57,14% 20,29 14,29% 0, ,14% 57,14% 20,29 14,29% 0, May holiay ,46% 75,00% 12,25 0,00% ,00% 100,00% 29,63 0,00% ,00% 100,00% 29,63 0,00% ,00% 100,00% 29,63 0,00% Week after may holiay ,53% 57,14% 9,29 0,00% ,00% 71,43% 20,86 0,00% ,00% 71,43% 20,86 0,00% ,00% 71,43% 20,86 0,00% Pentacost ,22% 0,00% - 0,00% ,27% 50,00% 1,00 0,00% ,27% 50,00% 1,00 0,00% ,27% 50,00% 1,00 0,00% Summer holiay W ,24% 71,43% 23,14 14,29% 1, ,24% 71,43% 23,14 14,29% 1, ,24% 71,43% 23,14 14,29% 1, ,24% 71,43% 23,14 14,29% 1, Summer holiay W ,91% 71,43% 17,71 0,00% ,49% 71,43% 14,86 0,00% ,49% 71,43% 14,86 0,00% ,49% 71,43% 14,86 0,00% Summer W3+W ,22% 78,57% 8,14 0,00% ,53% 78,57% 11,29 0,00% ,53% 78,57% 11,29 0,00% ,53% 78,57% 11,29 0,00% Summer W5+W ,83% 42,86% 5,21 0,00% ,41% 42,86% 4,36 0,00% ,41% 42,86% 4,36 0,00% ,41% 42,86% 4,36 0,00% Summer holiay W ,97% 42,86% 7,29 0,00% ,97% 42,86% 7,29 0,00% ,97% 42,86% 7,29 0,00% ,97% 42,86% 7,29 0,00% Christmas / New Year ,83% 0,00% - 0,00% ,00% 100,00% 22,00 33,33% 8, ,00% 100,00% 22,00 33,33% 8, ,00% 100,00% 22,00 33,33% 8, Christmas holiay W ,29% 83,33% 18,17 0,00% ,77% 83,33% 38,67 50,00% 3, ,77% 83,33% 38,67 50,00% 3, ,77% 83,33% 38,67 50,00% 3, Christmas holiay W ,60% 25,00% 3,63 0,00% ,00% 100,00% 32,88 12,50% 1, ,00% 100,00% 32,88 12,50% 1, ,00% 100,00% 32,88 12,50% 1, Week after Christmas ,81% 85,71% 19,00 0,00% ,00% 100,00% 37,43 0,00% ,00% 100,00% 37,43 0,00% ,00% 100,00% 37,43 0,00% Weighte average (year) ,61% 76,44% 22 3,01% 0, ,85% 75,07% 17 4,11% 0, ,06% 77,53% 15 4,93% 0, ,08% 76,16% 15 4,93% 0, Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay 78

91 Table 32: Results valiation for cost scenario 3 Scen 3 1 perio only summer holiay as reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Time perio Flex Flex Flex Flex 4Perios1Saturay ,71% 9,09% 1,82 0,00% ,62% 63,64% 7,27 9,09% 1, ,62% 63,64% 7,27 9,09% 1, ,62% 63,64% 7,27 9,09% 1, Perios1Sunay ,31% 18,18% 2,09 0,00% ,91% 90,91% 13,82 18,18% 2, ,88% 90,91% 13,09 18,18% 2, ,88% 90,91% 13,09 18,18% 2, Perios2Saturay ,83% 42,86% 1,14 0,00% ,63% 85,71% 11,29 0,00% ,54% 85,71% 9,29 14,29% 0, ,54% 85,71% 9,29 14,29% 0, Perios2Sunay ,52% 0,00% - 0,00% ,33% 71,43% 9,86 28,57% 0, ,60% 42,86% 3,71 0,00% ,60% 42,86% 3,71 0,00% Perios3Saturay ,80% 0,00% - 0,00% ,82% 30,00% 2,20 0,00% ,46% 30,00% 3,10 0,00% ,46% 30,00% 3,10 0,00% Perios3Sunay ,18% 0,00% - 0,00% ,84% 20,00% 2,90 0,00% ,15% 20,00% 4,00 10,00% 0, ,15% 20,00% 4,00 10,00% 0, Perios4Saturay ,94% 50,00% 3,50 0,00% ,35% 83,33% 13,50 16,67% 1, ,45% 83,33% 15,00 16,67% 1, ,45% 83,33% 15,00 16,67% 1, Perios4Sunay ,61% 33,33% 1,33 0,00% ,83% 83,33% 11,33 33,33% 2, ,00% 83,33% 11,50 33,33% 4, ,00% 83,33% 11,50 33,33% 4, January ,00% 100,00% 12,67 6,67% 0, ,32% 53,33% 5,20 0,00% ,71% 40,00% 3,27 0,00% ,71% 40,00% 3,27 0,00% February ,00% 100,00% 17,85 20,00% 0, ,53% 75,00% 9,95 10,00% 0, ,48% 45,00% 3,90 5,00% 0, ,61% 55,00% 4,45 5,00% 0, March ,13% 81,25% 19,44 31,25% 1, ,44% 75,00% 12,94 18,75% 0, ,59% 62,50% 6,56 0,00% ,59% 62,50% 6,56 0,00% April ,00% 100,00% 18,44 5,56% 0, ,65% 66,67% 9,83 5,56% 0, ,26% 61,11% 7,22 5,56% 0, ,15% 61,11% 6,78 5,56% 0, May ,48% 23,08% 2,69 0,00% ,17% 15,38% 0,62 0,00% ,48% 23,08% 2,69 0,00% ,71% 23,08% 2,92 0,00% June ,64% 0,00% - 0,00% ,83% 0,00% - 0,00% ,64% 0,00% - 0,00% ,64% 0,00% - 0,00% July ,00% 100,00% 19,11 22,22% 1, ,53% 77,78% 11,22 11,11% 0, ,73% 77,78% 13,00 22,22% 1, ,80% 77,78% 13,56 22,22% 1, August September ,54% 59,09% 7,41 0,00% ,97% 31,82% 2,77 0,00% ,54% 59,09% 7,32 4,55% 0, ,29% 54,55% 6,18 4,55% 0, October ,74% 73,91% 12,17 13,04% 0, ,64% 47,83% 6,35 8,70% 0, ,05% 56,52% 7,48 13,04% 0, ,92% 52,17% 6,91 13,04% 0, November ,00% 100,00% 19,65 10,00% 0, ,88% 85,00% 10,45 10,00% 0, ,67% 75,00% 7,25 10,00% 0, ,79% 80,00% 8,75 10,00% 0, December ,88% 86,67% 15,20 13,33% 2, ,38% 73,33% 7,40 13,33% 1, ,99% 60,00% 4,87 13,33% 1, ,20% 66,67% 5,87 13,33% 1, Carnival holiay ,30% 11,11% 0,11 0,00% ,81% 11,11% 0,78 0,00% ,81% 11,11% 0,78 0,00% ,81% 11,11% 0,78 0,00% Easter / Ascension ,79% 14,29% 0,71 0,00% ,72% 42,86% 11,14 28,57% 2, ,72% 42,86% 11,14 28,57% 2, ,72% 42,86% 11,14 28,57% 2, May holiay ,90% 25,00% 1,88 0,00% ,54% 75,00% 13,00 0,00% ,54% 75,00% 13,00 0,00% ,54% 75,00% 13,00 0,00% Week after may holiay ,76% 0,00% - 0,00% ,80% 57,14% 10,43 0,00% ,80% 57,14% 10,43 0,00% ,80% 57,14% 10,43 0,00% Pentacost ,41% 0,00% - 0,00% ,30% 0,00% - 0,00% ,30% 0,00% - 0,00% ,30% 0,00% - 0,00% Summer holiay W ,98% 71,43% 12,00 28,57% 2, ,98% 71,43% 12,00 28,57% 2, ,98% 71,43% 12,00 28,57% 2, ,98% 71,43% 12,00 28,57% 2, Summer holiay W ,00% 57,14% 8,14 0,00% ,43% 57,14% 5,86 0,00% ,43% 57,14% 5,86 0,00% ,43% 57,14% 5,86 0,00% Summer W3+W ,70% 7,14% 0,36 0,00% ,86% 35,71% 2,00 0,00% ,86% 35,71% 2,00 0,00% ,86% 35,71% 2,00 0,00% Summer W5+W ,09% 14,29% 1,00 0,00% ,52% 14,29% 0,71 0,00% ,52% 14,29% 0,71 0,00% ,52% 14,29% 0,71 0,00% Summer holiay W ,46% 14,29% 0,71 0,00% ,46% 14,29% 0,71 0,00% ,46% 14,29% 0,71 0,00% ,46% 14,29% 0,71 0,00% Christmas / New Year ,98% 0,00% - 0,00% ,62% 66,67% 9,00 33,33% 10, ,62% 66,67% 9,00 33,33% 10, ,62% 66,67% 9,00 33,33% 10, Christmas holiay W ,15% 50,00% 3,67 0,00% ,97% 83,33% 22,33 66,67% 7, ,97% 83,33% 22,33 66,67% 7, ,97% 83,33% 22,33 66,67% 7, Christmas holiay W ,28% 0,00% - 0,00% ,08% 75,00% 16,75 25,00% 3, ,08% 75,00% 16,75 25,00% 3, ,08% 75,00% 16,75 25,00% 3, Week after Christmas ,70% 42,86% 3,86 0,00% ,64% 57,14% 7,71 0,00% ,64% 57,14% 7,71 0,00% ,64% 57,14% 7,71 0,00% Weighte average (year) ,38% 47,95% 8 6,03% 0, ,38% 52,88% 7 8,77% 0, ,63% 50,68% 7 8,49% 0, ,63% 51,23% 7 8,49% 0, Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay 79

92 Table 33: Results valiation for cost scenario 4 Scen 4 1 perio only summer holiay as reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Time perio Flex Flex Flex Flex 4Perios1Saturay ,57% 9,09% 0,73 0,00% ,50% 45,45% 3,18 9,09% 0, ,33% 45,45% 2,73 9,09% 0, ,33% 45,45% 2,73 9,09% 0, Perios1Sunay ,35% 9,09% 0,45 0,00% ,37% 63,64% 8,36 18,18% 1, ,26% 63,64% 7,91 18,18% 1, ,26% 63,64% 7,91 18,18% 1, Perios2Saturay ,67% 0,00% - 0,00% ,05% 57,14% 5,14 0,00% ,52% 42,86% 2,86 0,00% ,52% 42,86% 2,86 0,00% Perios2Sunay ,13% 0,00% - 0,00% ,31% 42,86% 5,43 0,00% ,33% 28,57% 1,86 0,00% ,33% 28,57% 1,86 0,00% Perios3Saturay ,55% 0,00% - 0,00% ,92% 10,00% 0,60 0,00% ,69% 20,00% 1,00 0,00% ,69% 20,00% 1,00 0,00% Perios3Sunay ,06% 0,00% - 0,00% ,90% 20,00% 1,30 0,00% ,34% 20,00% 3,00 10,00% 0, ,34% 20,00% 3,00 10,00% 0, Perios4Saturay ,27% 16,67% 0,67 0,00% ,94% 83,33% 7,50 16,67% 0, ,99% 83,33% 8,33 16,67% 0, ,99% 83,33% 8,33 16,67% 0, Perios4Sunay ,59% 0,00% - 0,00% ,07% 50,00% 7,17 16,67% 0, ,56% 66,67% 7,17 33,33% 3, ,56% 66,67% 7,17 33,33% 3, January ,02% 46,67% 4,20 0,00% ,99% 33,33% 1,80 0,00% ,34% 13,33% 1,07 0,00% ,10% 13,33% 0,93 0,00% February ,39% 75,00% 8,45 10,00% 0, ,74% 55,00% 4,95 5,00% 0, ,38% 25,00% 1,95 0,00% ,38% 25,00% 1,95 0,00% March ,30% 75,00% 11,44 18,75% 0, ,80% 62,50% 7,81 0,00% ,92% 43,75% 3,06 0,00% ,77% 31,25% 2,63 0,00% April ,45% 66,67% 8,50 5,56% 0, ,78% 55,56% 5,06 5,56% 0, ,35% 44,44% 3,61 0,00% ,04% 38,89% 2,72 0,00% May ,70% 15,38% 0,31 0,00% ,12% 0,00% - 0,00% ,65% 15,38% 0,92 0,00% ,90% 15,38% 1,08 0,00% June ,28% 0,00% - 0,00% ,70% 0,00% - 0,00% ,37% 0,00% - 0,00% ,37% 0,00% - 0,00% July ,40% 77,78% 9,67 11,11% 0, ,92% 55,56% 5,78 11,11% 0, ,21% 66,67% 7,33 11,11% 0, ,27% 77,78% 8,00 11,11% 0, August September ,57% 27,27% 2,18 0,00% ,28% 22,73% 0,77 0,00% ,35% 36,36% 3,45 0,00% ,97% 31,82% 2,77 0,00% October ,33% 39,13% 5,43 8,70% 0, ,22% 34,78% 3,52 4,35% 0, ,77% 34,78% 4,35 8,70% 0, ,59% 34,78% 4,09 4,35% 0, November ,79% 80,00% 8,75 10,00% 0, ,31% 60,00% 4,75 5,00% 0, ,95% 50,00% 3,05 0,00% ,08% 55,00% 3,55 5,00% 0, December ,20% 66,67% 6,00 13,33% 1, ,32% 26,67% 3,60 13,33% 0, ,67% 20,00% 3,00 13,33% 0, ,90% 20,00% 2,93 13,33% 1, Carnival holiay ,06% 0,00% - 0,00% ,94% 0,00% - 0,00% ,94% 0,00% - 0,00% ,94% 0,00% - 0,00% Easter / Ascension ,86% 0,00% - 0,00% ,02% 42,86% 8,29 14,29% 0, ,02% 42,86% 8,29 14,29% 0, ,02% 42,86% 8,29 14,29% 0, May holiay ,02% 0,00% - 0,00% ,84% 50,00% 5,38 0,00% ,84% 50,00% 5,38 0,00% ,84% 50,00% 5,38 0,00% Week after may holiay ,41% 0,00% - 0,00% ,23% 57,14% 3,57 0,00% ,23% 57,14% 3,57 0,00% ,23% 57,14% 3,57 0,00% Pentacost ,57% 0,00% - 0,00% ,61% 0,00% - 0,00% ,61% 0,00% - 0,00% ,61% 0,00% - 0,00% Summer holiay W ,63% 42,86% 8,29 14,29% 1, ,63% 42,86% 8,29 14,29% 1, ,63% 42,86% 8,29 14,29% 1, ,63% 42,86% 8,29 14,29% 1, Summer holiay W ,45% 42,86% 2,86 0,00% ,63% 28,57% 1,43 0,00% ,63% 28,57% 1,43 0,00% ,63% 28,57% 1,43 0,00% Summer W3+W ,48% 0,00% - 0,00% ,13% 0,00% - 0,00% ,13% 0,00% - 0,00% ,13% 0,00% - 0,00% Summer W5+W ,16% 7,14% 0,07 0,00% ,56% 0,00% - 0,00% ,56% 0,00% - 0,00% ,56% 0,00% - 0,00% Summer holiay W ,20% 0,00% - 0,00% ,20% 0,00% - 0,00% ,20% 0,00% - 0,00% ,20% 0,00% - 0,00% Christmas / New Year ,11% 0,00% - 0,00% ,55% 33,33% 7,00 33,33% 9, ,55% 33,33% 7,00 33,33% 9, ,55% 33,33% 7,00 33,33% 9, Christmas holiay W ,79% 16,67% 0,17 0,00% ,47% 83,33% 16,83 50,00% 4, ,47% 83,33% 16,83 50,00% 4, ,47% 83,33% 16,83 50,00% 4, Christmas holiay W ,08% 0,00% - 0,00% ,14% 75,00% 9,88 12,50% 1, ,14% 75,00% 9,88 12,50% 1, ,14% 75,00% 9,88 12,50% 1, Week after Christmas ,18% 14,29% 0,57 0,00% ,69% 28,57% 2,29 0,00% ,69% 28,57% 2,29 0,00% ,69% 28,57% 2,29 0,00% Weighte average (year) ,31% 29,59% 3 3,84% 0, ,93% 35,62% 4 5,21% 0, ,17% 32,60% 3 5,21% 0, ,13% 32,05% 3 5,21% 0, Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay 80

93 Table 34: Results valiation for cost scenario 5 Scen 5 1 perio only summer holiay as reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Time perio Flex Flex Flex Flex 4Perios1Saturay ,90% 9,09% 1,55 0,00% ,38% 63,64% 7,09 0,00% ,38% 63,64% 7,09 0,00% ,38% 63,64% 7,09 0,00% Perios1Sunay ,59% 18,18% 1,55 0,00% ,85% 90,91% 14,55 9,09% 0, ,82% 90,91% 13,73 0,00% ,82% 90,91% 13,73 0,00% Perios2Saturay ,15% 14,29% 0,43 0,00% ,54% 85,71% 9,57 0,00% ,22% 71,43% 6,57 0,00% ,22% 71,43% 6,57 0,00% Perios2Sunay ,65% 0,00% - 0,00% ,14% 71,43% 8,86 0,00% ,20% 28,57% 3,00 0,00% ,20% 28,57% 3,00 0,00% Perios3Saturay ,97% 0,00% - 0,00% ,40% 20,00% 1,60 0,00% ,03% 30,00% 2,50 0,00% ,03% 30,00% 2,50 0,00% Perios3Sunay ,38% 0,00% - 0,00% ,34% 20,00% 2,50 0,00% ,62% 20,00% 4,30 0,00% ,62% 20,00% 4,30 0,00% Perios4Saturay ,39% 33,33% 2,33 0,00% ,24% 83,33% 13,17 0,00% ,30% 83,33% 14,00 0,00% ,30% 83,33% 14,00 0,00% Perios4Sunay ,94% 16,67% 0,67 0,00% ,72% 83,33% 12,00 0,00% ,89% 83,33% 14,17 16,67% 0, ,89% 83,33% 14,17 16,67% 0, January ,94% 86,67% 10,13 0,00% ,02% 46,67% 4,20 0,00% ,54% 40,00% 2,87 0,00% ,37% 33,33% 2,47 0,00% February ,98% 85,00% 15,85 0,00% ,39% 75,00% 8,85 0,00% ,33% 40,00% 3,55 0,00% ,33% 40,00% 3,55 0,00% March ,95% 75,00% 18,75 0,00% ,30% 75,00% 12,00 0,00% ,49% 62,50% 5,94 0,00% ,39% 62,50% 5,31 0,00% April ,00% 88,89% 15,94 0,00% ,45% 66,67% 8,78 0,00% ,15% 61,11% 6,83 0,00% ,91% 55,56% 5,67 0,00% May ,79% 23,08% 2,00 0,00% ,70% 15,38% 0,31 0,00% ,02% 23,08% 2,23 0,00% ,25% 23,08% 2,46 0,00% June ,78% 0,00% - 0,00% ,28% 0,00% - 0,00% ,06% 0,00% - 0,00% ,06% 0,00% - 0,00% July ,00% 77,78% 17,22 0,00% ,40% 77,78% 10,22 0,00% ,60% 77,78% 12,56 0,00% ,66% 77,78% 13,33 0,00% August September ,16% 54,55% 5,68 0,00% ,57% 27,27% 2,18 0,00% ,29% 54,55% 6,23 0,00% ,03% 50,00% 5,14 0,00% October ,48% 69,57% 10,78 0,00% ,33% 39,13% 5,70 0,00% ,78% 52,17% 7,13 0,00% ,64% 47,83% 6,61 0,00% November ,00% 100,00% 17,45 0,00% ,79% 80,00% 9,15 0,00% ,60% 75,00% 6,80 0,00% ,67% 75,00% 7,55 0,00% December ,75% 86,67% 14,53 6,67% 0, ,20% 66,67% 7,47 0,00% ,88% 40,00% 5,60 0,00% ,99% 60,00% 6,20 0,00% Carnival holiay ,49% 0,00% - 0,00% ,05% 11,11% 0,44 0,00% ,05% 11,11% 0,44 0,00% ,05% 11,11% 0,44 0,00% Easter / Ascension ,12% 14,29% 0,29 0,00% ,37% 42,86% 12,57 0,00% ,37% 42,86% 12,57 0,00% ,37% 42,86% 12,57 0,00% May holiay ,25% 25,00% 1,13 0,00% ,30% 75,00% 10,75 0,00% ,30% 75,00% 10,75 0,00% ,30% 75,00% 10,75 0,00% Week after may holiay ,90% 0,00% - 0,00% ,40% 57,14% 8,71 0,00% ,40% 57,14% 8,71 0,00% ,40% 57,14% 8,71 0,00% Pentacost ,68% 0,00% - 0,00% ,61% 0,00% - 0,00% ,61% 0,00% - 0,00% ,61% 0,00% - 0,00% Summer holiay W ,81% 57,14% 13,14 0,00% ,81% 57,14% 13,14 0,00% ,81% 57,14% 13,14 0,00% ,81% 57,14% 13,14 0,00% Summer holiay W ,71% 57,14% 7,00 0,00% ,15% 57,14% 4,71 0,00% ,15% 57,14% 4,71 0,00% ,15% 57,14% 4,71 0,00% Summer W3+W ,07% 7,14% 0,21 0,00% ,19% 35,71% 0,93 0,00% ,19% 35,71% 0,93 0,00% ,19% 35,71% 0,93 0,00% Summer W5+W ,52% 14,29% 0,71 0,00% ,64% 7,14% 0,43 0,00% ,64% 7,14% 0,43 0,00% ,64% 7,14% 0,43 0,00% Summer holiay W ,70% 14,29% 0,29 0,00% ,70% 14,29% 0,29 0,00% ,70% 14,29% 0,29 0,00% ,70% 14,29% 0,29 0,00% Christmas / New Year ,24% 0,00% - 0,00% ,36% 33,33% 14,33 33,33% 4, ,36% 33,33% 14,33 33,33% 4, ,36% 33,33% 14,33 33,33% 4, Christmas holiay W ,68% 33,33% 2,33 0,00% ,87% 83,33% 28,17 0,00% ,87% 83,33% 28,17 0,00% ,87% 83,33% 28,17 0,00% Christmas holiay W ,46% 0,00% - 0,00% ,81% 75,00% 17,63 0,00% ,81% 75,00% 17,63 0,00% ,81% 75,00% 17,63 0,00% Week after Christmas ,11% 28,57% 2,86 0,00% ,25% 57,14% 6,00 0,00% ,25% 57,14% 6,00 0,00% ,25% 57,14% 6,00 0,00% Weighte average (year) ,93% 42,47% 7 0,27% 0, ,06% 50,14% 7 0,55% 0, ,32% 47,67% 6 0,55% 0, ,29% 47,40% 6 0,55% 0, Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay Regul ar Occupanc y rate regular bes % of time flexbes #flexb es % of ays a Amissi on stop occur Refuse / elaye patient s per ay Costs per ay 81

94 APPENDIX X VALIDATION GRAPHS 370 Scenario 2 Regular Bes Realization 1 perio no reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Figure 26: Realization versus the regular bes for cost scenario 2 incluing all ifferent perios 370 Scenario 2 Regular + Flex Bes Realization 1 perio no reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Figure 27: Realization versus the regular bes + flex-bes for cost scenario 2 incluing all ifferent perios 82

95 370 Scenario 3 Regular Bes Realization 1 perio no reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Figure 28: Realization versus the regular bes for cost scenario 3 incluing all ifferent perios 370 Scenario 3 Regular + Flex Bes Realization 1 perio no reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Figure 29: Realization versus the regular bes + flex-bes for cost scenario 3 incluing all ifferent perios 83

96 370 Scenario 4 Regular Bes Realization 1 perio no reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Figure 30: Realization versus the regular bes for cost scenario 4 incluing all ifferent perios 370 Scenario 4 Regular + Flex Bes Realization 1 perio no reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Figure 31: Realization versus the regular bes + flex-bes for cost scenario 4 incluing all ifferent perios 84

97 370 Scenario 4 Regular Bes Realization 1 perio no reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Figure 32: Realization versus the regular bes for cost scenario 5 incluing all ifferent perios Scenario 5 Regular + Flex Bes Realization 1 perio no reuction 1 perio with reuction 4 perios with reuction 12 perios with reuction Figure 33: Realization versus the regular bes + flex-bes for cost scenario 5 incluing all ifferent perios 85

98 APPENDIX XI: CRITICAL VALUES FOR THE KOLMOGOROV-SMIRNOV TEST FOR GOODNESS OF FIT Table 35: Critical values for the Kolmogorov-Smirnov Test for gooness of fit 86