IOP Conference Series: Materials Science an Engineering OPEN ACCESS Multi-Criteria Knapsack Problem for Disease Selection in an Observation War To cite this article: N Lurkittikul an O Kittithreerapronchai 2014 IOP Conf. Ser.: Mater. Sci. Eng. 58 012017 Vie the article online for upates an enhancements. Relate content - Designing an appointment system for an outpatient epartment Chalita Panaviat, Haruetai Lohasiriat an Wipaee Tharmmaphornphilas - Improvement of Project Portfolio Management in an Information Technology Consulting Company S Kaeta an P Chutima - 3D Machine Vision an Aitive Manufacturing: Concurrent Prouct an Process Development Ismet P Ilyas This content as onloae from IP aress 148.251.232.83 on 28/09/2018 at 17:22
Multi-Criteria Knapsack Problem for Disease Selection in an Observation War N Lurkittikul 1 an O Kittithreerapronchai 1 1 Department of Inustrial Engineering, Chulalongkorn University, Bangkok, Thailan 10330 E-mail: nopparuth.l.ty127@gmail.com Abstract. The aging population an the introuction of Thailan universal healthcare have increase inpatients an outpatients to public hospitals, particularly to a hospital that provies special an comprehensive health services. Many inpatient ars have experience large influx of inpatients as the hospitals have to amit all patients regarless their conitions. These overcroing ars cause stress to meical staffs, block access beteen meical epartments, hospital-acquire infections, an ineffective uses of resources. One ay to manage such inunate inpatient is to select some patients hose conitions require less clinical attention or hose lengths of stay are preictable an short an, then, place them at an observation ar. This intermeiate ar increases turnover of bes an reuces unnecessary paperork as patients are consiere to be outpatients. In this article, e stuie inpatient ata of a tertiary care hospital in hich an observation ar as consiere to alleviate the overcroing problem at Internal Meicine Department. The analysis of ata shoe that the hospital can balance inpatient flo by managing a group of patients ho is amitte because of treatments orere by its special clinics. Having explore several alternatives, e suggeste patient selection criteria an propose a layout at an observation ar. The hospital shoul increase meical bes in a ne builing ar because the current observation ar can hanle 27.3% of total short stay patients, hile the observation ar is projecte to hanle 80% of total short stay patients. 1. Introuction The aging population an the introuction of Thailan universal healthcare have increase numbers of inpatients an outpatients in public hospitals for the last ecae. Accoring to Bureau of Policy an Strategy Ministry of Health, the numbers of inpatients an outpatients have approximately ouble from five millions inpatients an 90 million outpatients in 2001 to telve millions inpatients an 170 million outpatients in 2011, respectively. In particular, public tertiary-care hospitals that operate by the government an provie comprehensive health services have experience large influx of inpatients as the hospitals are equippe ith sufficient resources an have to amit all patients regarless their conitions. These overcroing ars cause stress to meical staffs, access block beteen meical epartments, hospital-acquire infections, an ineffective uses of resources. All of hich unermines the public health quality in terms of prevention an treatment. Many researchers an health offices have aresse this patient overcroe problem an propose recommenations, such as shortening patient s length of stay by streamlining non-meical processes, reucing aiting time by scheuling an preparing key resources, an managing the flo of Content from this ork may be use uner the terms of the Creative Commons Attribution 3.0 licence. Any further istribution of this ork must maintain attribution to the author(s) an the title of the ork, journal citation an DOI. Publishe uner licence by Lt 1
patients by grouping inpatients by their conitions an/or symptoms. One ay to manage such inunate inpatients hile accomplishes these three recommenations is to select some patients hose conitions require less clinical attention or hose lengths of stay are preictable an short an, then, place them at a special area, calle an observation ar. The observation ar can be viee a buffer ar beteen Outpatient Department an Inpatient Department as targete patients usually stay in the ar uring 8-48 hours. This intermeiate ar increases turnover of bes as it promotes the rapi flo of inpatients an reuces unnecessary paperork as patients are consiere to be outpatients. In some case, an observer ar coul reuce the aiting time of patients an the cost of treatments. The concept of an observation ar proviing specialize services to selecte patients so that the patients receive better services in terms of treatment an prevention is a rational one. In fact, many suggestions an case stuies have been reporte in the area of Emergency Meicine. 2. Literature revie The relevant researches to this article can be groupe into to categories: observation ar an analytic moel in health service. 2.1. Observation ar An observation ar also referre to as an observation unit or an observation room is a health facility locate outsie inpatient ars that consists of bes an meical equipment esigne for proviing a short term therapy an/or observing an evaluating symptoms of selecte patients [2]. Establishing an observation ar benefits three stakeholers: Patient aspect: Recuperating at an observation ar improves the patient s quality of life an satisfaction. Patients ho recover in an observation ar usually stay in a hospital shorter than those ho stay in a general ar because the patients experience less hospital-acquire infection an receive prompt treatments [2, 5]. Some researchers reporte that an observation ar helps reuce the patient mortality [7]. Meical staff aspect: As patients ho recover in an observation ar usually have mil symptoms or minor injuries, the comprehensive investigations of patients, e.g. full triage cross examination, an patient relative intervie, are not require [2, 4, 5]. As a result, meical staffs, particularly nurses, spen more time tening patient s nees that, in turn, helps etecting any complications. Hospital aspect: A hospital coul reuce overall expeniture as patients recover faster ith less infection [5, 6]. Nevertheless, an observation ar has rabacks such as increasing of re-amission rate [6, 7] an emaning aitional space an staffs if it is poorly manage. Researchers reporte the abuses of an observation ar on ifference purposes, such as to prolong length of stay of inpatients, to bill emergency visits, an to hanle post-operation patients. Therefore, it is important to establish the clear goals. Accoring to Brillman et al. [1], the goals of observation ar are usually intertine ith a meical epartment that is irectly responsible for an observation ar an can be groupe into three types as follos: Emergency Department: Majority of observation ars are locate in Emergency Department an leae by emergency physicians to assist patients ho require further treatments or evaluations. The main objectives are to improve quality of treatments an to assess conitions of patients. The efficient treatment an effective assessment shoul reuce amitte patients, aiting times, an cost of treatments. Outpatient Department: Some observation ar aims at patients ho ait for amission or transferring. This ar is generally operate by non-emergency physicians. Locate in 2
Outpatient Department, its main goal is to manage patients ho are meically stable or reay for isposition. Inpatient Department: Aime at cost reuction an alleviate croe amitte patients, the observation ar locate in Inpatient Department targets short stay patients. A group of inpatient physicians an emergency physician are usually in charges of these units to ensure uninterrupte flos of patients. In some cases, an observation ar coul use to observe an to iagnose patients hose causes of isease are unknon or as a temporary ar for treating short stay patients or evaluating the patient s psychosocial nees. Besie the irect responsible epartment that usually contributes to the location of an observation ar, the other important parts of establishing the clear goals are the targete patients an the appropriate time limit. The targete patients shoul exhibit clinical conitions easy to observe an treat [1-3] e.g., patient s consciousness, strong vital signs, exact goal of treatment, an mil symptom. An observation ar has to operate ithin an appropriate time limit to ensure the constant an uninterrupte flo of patients. As a result, many stuies suggeste ifferent urations in hich patients shoul stay in an observation ar ranging from 8-48 hours an epening on the goals. Nevertheless, the previous stuies agree that patients ho stay more than 72 hours shoul be amitte into an inpatient ar [5] because their presence increases the orkloa an iminishes the effectiveness of an observation ar. The effectiveness of an observation ar epens largely on sufficient resources, such as basic equipment an versatile meical staffs, as patients share similar non-chronic symptoms an an observation ar has to hanle patients as a one-stop service. 2.2. Analytic moel in health service A health system is a eicate an complex system that usually involves the life of human beings. As a result, any initiative faces challenges an securities from stakeholers resulting strong resistance. One ay to unerstan the ramifications of an initiative before the actual implementation is to use an analytic moel, such as simulation moels an mathematical moels. Simulation moels have been iely applie to the health system for ifferent purposes. To narro the scope of this revie, e focus on the simulation moels to etermine numbers of resources an allocation policy. One of the most competing resources in hospital is an operation room as a surgery may be critical to a patient s life an requires many resources, for example surgeons, anesthesiologists, scrub nurses, an instrument. As a result, the maximum numbers of patients ho can be preppe for surgeries as propose by Ballar et al [9] to improve the patient flo hile maintain the hospital stanars. The simulation leae to significant numbers of patients ho receive surgeries before the original planne. Besies the resources, the orkloa balancing an bottleneck elimination are important issues in an operation room. Therefore, Zheng et al [13] propose a simulation moel to improve process an utilization of key resources, incluing manpoer an facilities. All these stuies iscover that a simulation moel is funamental for re-engineering an unerstaning hat-if scenario. Since the simulation moel requires enormous ata an statistics, one of sensible approaches is a mathematical moel embee ith historical ata. The inspiration of this approach erives from engineering isciplines, particularly factory an plant esign. For example, Caputo et al [10] stuie the environmental situation at an inustrial plant that emits many hazar materials an the ecisions by a safety manager to reuce overall hazar release in orer to comply ith environmental regulations. Therefore, the portfolio of safety measures ith buget constraints is moele as multicriteria knapsack moel. The sensitivity analysis of the moel ith respecte to bugets reveals the useful information for further analytic ecision. Another example is the stuy of founry inustry by 3
Camargo et al [11]. As one of the important Brazilian inustries, the key to sustain groth an to maintain competitiveness is the efficient prouction planning as prouction sequence an quantities highly affect operation costs. To solve this generalize lot-sizing problem, the to-step heuristic metho that combines a genetic algorithm an a knapsack algorithm is propose an compare ith the optimal solution. The result is applicable to the inustry as the quality of solution an the computation time are both ithin reasonable range. This article aims to illustrate the analysis an proceures necessary for esign an observation ar. Having aresse the contribution, the remaining sections are organize as follos. Section 3 overvies the backgroun of the case stuy hospital along ith the analysis of ata that lea to the hospital ecision to consier an observation ar. Section 4 escribes the mathematical moel that enables the selection of iseases for an observation ar an the esign of an observation room base on available space. Section 5 iscusses the conclusion an guielines to the future research. 3. Case Stuy Hospital The case stuy hospital is the 855-be tertiary care hospital locate in the estern region of Thailan. The hospital covers 14 meical specialties for outpatients an 10 meical specialties for inpatients an is capable to hanle 600,000 outpatients an 44,000 inpatients annually as shon in figure 1. Figure 1. Numbers of patients amitte into specialty ars at the case stuy hospital in 2011 an 2012. The figure shos numbers of inpatients in each specialty ar in 2011 an 2012. With exceptions of Peiatrics ars, numbers of patients amitte into major specialty ars increase in 2012. This aligns ith the high aging population an lo birthrate in the estern region. Figure 1 also suggests that 30% of total inpatients are amitte into Internal Meicine Department. This epartment can be further ivie into nine ars as shon in figure 2. 4
Figure 2. Number of hospital bes at each ar is responsible by Internal Meicine Department. Figure 2 epicts numbers of registere bes at each ar responsible by Internal Meicine Department hich can be classifie by expeniture into to types: private be an general be. Private bes are eicate bes locate in separate rooms esigne to serve patients ho prioritize privacy an capable to affor aitional expense, hereas general bes are economic bes locate in common area an easy to access by nurses. Wars 1, 2, 3 an 4 are main ars of the epartment as their targete patients are those ho recuperate from incentive care units or have chronic iseases, such as Cancel, Pneumonia, an Leukemia. As the tertiary health facility an the central hospital in the region, the hospital has to amit all patients regarless their conitions, incluing a large numbers of non-chronic patients. As a result, the numbers of inpatients in these main ars excee the numbers of registere bes, an the hospital has to use stretchers as temporary meical bes an place non-chronic patients alongsie corriors. To investigate this observation, e analyze the length of stay of inpatient in Internal Meical Wars 1, 2, 3, an 4 in 2011 an 2012, as shon in figure 3. Figure 3. Length of stay of inpatient in Internal Meical Wars 1, 2, 3, an 4 in 2011 an 2012. Figure 3 confirms our observation. That is, a large portion of inpatients stays in the ars less than to ays or 48 hours. In aition, numbers of inpatients ho recuperate more than to ay graually ecrease. Eviently, these meical ars serve more non-chronic patients than their originally 5
esigne, an reucing number of short-stay inpatients shoul alleviate the overcroe ars an improve the quality of treatments. Hoever, it is orth to unerstan arrival patterns of these shortstay inpatients before suggest any solutions, as shon in figure 4. Figure 4. Arrival patterns of inpatients istributions of short stay patient eman on each ay of eek. Figure 4 illustrates the arrival patterns an frequencies of the short-stay inpatients on each ay of the eek. Despite relatively high variations, numbers of the patients ho arrive on eeken are less than those ho arrive on eekay. The figure shos that the inpatients ten to arrive on Monay or ith average of 16.6 an stanar eviation of 6.5 patients. The similar pattern can be observe on Wenesay an Friay. The further investigation an the intervie ith stakeholers reveal that the pattern is influence by special clinics that require specific treatments such as bloo transfusion an bone marro extractions. Moreover, these patients visit the hospital at fixe an preictable time intervals. Having contemplate these eviences an organize series of meetings, the hospital suggests that establishing an observation ar shoul help to alleviate numbers of short-stay patients in these ars an to streamline meical ocuments require for these inpatients. 4. Designing an observation ar After revieing the purpose an resources require, an observation ar is ecie to be locate in Emergency Department as shon in figure 5. Figure 5. Layout an numbers of meical bes of the propose observation ar in Emergency Department. 6
Because of the limite space in Emergency Department, this observation ar contains only three meical bes an serves as a temporary faculty until a ne builing is constructe an fully functione. During the meetings, some topics such as availability of nurses, information flos, an supporting activities are raise. Nevertheless, the to biggest concerns are: utilization of meical bes in an observation ar an selection of patients. The ansers to these concerns are important an paramount to the success of an observation ar. Before applying an analytical moel to anser these concerns, it is important to unerstan the nature of length of stay. Unlike the processing time in manufacturing machines, to ientical patients ho are amitte an iagnose ith the same isease may have ifferent length of stay as illustrate in figure 6. Figure 6. Length of stay of Essential hypertension isease (ICD10:I10). Figure 6 epicts hours in hich patients ho are amitte ith Essential (primary) hypertension isease spen in the ars. The figure suggests that the length of stay epens on an iniviual patient. To narro iseases before using an analytical moel, e applie Pareto principle or 80/20 rule to the 2011-2012 meical recors. Among 793 iseases that patient spen less than 48 hours in the ars, 114 iseases account for 80% of total short stay patients. These iseases become caniates to an observation ar, an theirs ata are embee in the folloing mathematical moel. 4.1. Mathematical Moel = set of iseases = set of ay in eek p l n H b x = = impact in isease = average length of stay of isease = average numbers of patient of isease on ay = available hours of each meical be on ay = number of meical bes in an observation ar 1, if isease is selecte in the observation ar 0, otherise. 7
max z p x (1) l n x b H (2) s.t. x {0,1} (3) Expression 1 is the objective function that maximizes the total impacts of the selecte iseases. The hospital is intereste in impacts as many criteria such as numbers of patent in each isease, possibility to evelop serious symptom, nature of treatment, available equipment an skille of staff. These criteria are ifferent from one hospital to others an require serious iscussion among physicals an meical staffs. The constraints of this Integer Programming are liste in Expressions 2 an 3. Expression 2 ensures that the average uration require by patients ho are serve by an observation ar on each ay of the eek oes not excess the meical-be capacities. This expression reflects the fact that meical bes are allocate irectly to each epartment an cannot be easily borroe or transferre. Expression 3 assures that the ecision variable or the selection of isease is binary as an initial triage unable to preict the length of stay of each patient. Mathematically, Expressions 1 3 can be viee as the multi-criteria knapsack problem a generalization of classical knapsack problem in hich a person must select a set of items to maximize total benefits hile satisfy the limitations of all resources. Using the analogy of the multi-criteria knapsack problem, parameters p, l n, an b H can be viee as the benefit of each item, resources require of each item, an total limite resources, respectively. 4.2. Numerical Experience We embee the ata of the case stuy hospital into our moel an solve it ith Microsoft Excel/ Solver [12]. Since the available hours of each meical be is a ifficult parameter to be estimate, e varie the parameter from 14 hours to 24 hours ith to-hour interval, i.e., {14,16,18,20,22,24} an reporte the result an numerical experience as shon in table 1. Table 1. Numbers of isease an percentage of serve inpatient ith ifferent available hours of each meical be ( H ). H numbers of iseases x ) ( % of serve patients a Daily average utilization (%) Daily stanar eviation of utilization (%) 24 42 27.3 93.1 10.4 22 39 25.1 93.4 9.1 20 36 23.3 93.8 9.1 18 29 21.2 93.9 8.9 16 31 19.2 93.5 10.0 14 28 17.1 94.6 8.0 a percentage form 80% of total short stay patient (targete patient) As the available hours of each meical be ecrease, table 1 suggests that number of patients ho are serve by an observation ar graually ecreases. Decreasing H results in changing the set of iseases. Interestingly, the number of iseases at H 16 H 18 is 31 iseases hich is larger than or 29 iseases because many iseases are introuce into an observation ar ath 16. In particular, the moel selects iseases to maintain high utilization of an observation 8
ar. It is orth to mention that the moel fails to reach 100% utilization as average numbers of patients on Saturay an Sunay are significant less than that on eekay, resulting to 93% utilization of meial bes. 4.3. Greenfiel Design Because of the limite space, the propose observation ar can hanle 17.1-27.3% of potential inpatients. This raises a question: ho many meical bes oes the hospital require if there is no spatial constraint? As a result, e moifie Expression 2 by assuming x 1 to etermine the number of meical bes require ith Expression 4. l n b max H (4) Number of bes in an observation ar (b ) is the maximum roun-up value of total hours all shortstay patients spen in an observation ar each ay over available hours of be. The result of this calculation, average utilization, an stanar eviation are shon in table 2. Table 2. Number of bes in an observation ar ith ifferent available hours of each meical be ( H ). H number of bes (b ) % of serve patients a Daily average utilization (%) Daily stanar eviation of utilization (%) 24 17 100 69.4 18.4 22 18 100 71.5 18.9 20 20 100 70.8 18.7 18 22 100 71.5 18.9 16 25 100 70.8 18.7 14 28 100 72.3 19.1 a percentage form 80% of total short stay patients As the available hours ecrease, table 2 shos that the numbers of bes graually increase. The result reveals that the utilization of bes epens on number of patients on Monay. This reflects the fact that majority of patients sho up on Monay resulting to the uner-utilization in other ays. If numbers of inpatients ere similar to other ays, the observation ar oul require only 15 bes instea of 20 bes in case of H 20 or 25% less capacity. This observation leas to the iscussion on patient flos. The imbalance of patient flos affects to utilization of bes. The average of utilization in Greenfiel Design obviously loer than Numerical Experience because the moel in Numerical Experience attempt to maximum impact an it affects high utilization simultaneously. 5. Conclusion an future orks We analyze the ata of a Thailan tertiary care hospital an foun that the hospital has face the overcroe inpatient in the major ars responsible by Internal Meicine Department as the inpatients spens less than 48 hours in the ars. The aitional investigation reveale that some of these short-stay patients are cause by special treatments. As a result, the hospital consiers an observation ar to alleviate this problem an to streamline proceures. Furthermore, the meeting beteen Internal Meicine Department an Emergency Department conclue a temporary site of an observation ar. Because of a limite space, e propose a mathematical moel to select the set of 9
iseases an etermine numbers of meical bes if there is no spatial constraint. The moel suggests that three meical bes available at Emergency Department can ieally hanle approximately 27.3% of targete patients that consists of 42 iseases. Depening on the meical be turnover, 17-28 meical bes are recommene if the hospital plans to setup a ne observation ar in a ne builing. The result also implies that Internal Meicine Department shoul revie special clinics scheule to balance the patient flos an to reuce a number of bes require in an observation ar. The propose mathematical moel serves as a primary esign tool as the eterministic arrival time an recuperate time are assume. The further stuies an comprehensive esign using a iscrete event simulation that accounts for the stochastic events are require. In aition, the esign of an observation ar shoul incorporate ith the proceure an information flo to ensure smooth an successful implementation. Acknolegement We are forever inebte to Thai Health Promotion Founation for financial supports an personal connection to the case stuy hospital. The authors oul like to thank Thira Woratanara, M.D.,Wut Dulyachai, M.D., Supachai Paiboonpol, M.D., an the staffs at the case stuy hospital for their valuable time, useful comments, an various supports throughout this project. References [1] Brillman J et al 1995 Management of observation units Annals of Emergency Meicine 25 823-830. [2] Bran C et al 2004 Short Stay an Observation Units, Meical Assessment an Planning Units an Emergency Meical Units. Clinical Epiemiology an Health Service Evaluation Unit (Australia: Melbourne Health), Retrive from http://.mh.org.au/. [3] Dallos V an Mouzas GL 1981 An evaluation of the functions of the short-stay observationar in the accient an emergency epartment British Meical Journal 282 37. [4] Jones A, O'Driscoll K an Luke LC 1995 Hea injuries an the observation ar Journal of Accient an Emergency Meicine 12 160. [5] Cooke MW, Higgins J an Ki P 2003 Use of emergency observation an assessment ars: a systematic literature revie Emerg Me J 20 138-142. [6] Daly S, Campbell DA an Cameron PA 2003 Short-stay units an observation meicine: a systematic revie The Meical Journal of Australia (MJA) 178 559-563. [7] Juan A, Salazar A, Alvarez A, Perez JR, Garcia L an Corbella X 2006 Effectiveness an safety of an emergency epartment shortstay unit as an alternative to stanar inpatient hospitalization Emerg Me J 23 833-837. [8] Ballar SM an Kuhl ME 2006 Winter Simulation Conference (WSC). [9] Zheng Q, Shen J, Liu Z, Fang K an Xiang W 2011 International Conference on Inustrial Engineering an Engineering Management (IE&EM). [10] Caputo AC, Pelagagge PM an Salini P 2013 A multicriteria knapsack approach to economic optimization of inustrial safety measures Safety Science 51 534-360 [11] Camargo VCB, Mattiolli L an Toleo F 2012 A knapsack problem as a tool to solve the prouction planning problem in small founries Computers an Operations Research 39 86-92 [12] Fylstra D, Lason L, Watson J an Waren A 1998 Design an use of the microsoft excel solver Interfaces 28 29-55. 10