The construction of new hospitals is an opportunity

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1 ECONOMICS, EDUCATION, AND HEALTH SYSTEMS RESEARCH SECTION EDITOR RONALD D. MILLER Determining the Number of Beds in the Postanesthesia Care Unit: A Computer Simulation Flow Approach Eric Marcon, PhD*, Saïd Kharraja*, Nicole Smolski, MD, Brigitte Luquet, and Jean Paul Viale, MD, PhD *Department of Industrial Maintenance, Jean Monnet University, Saint Etienne; and Departments of Anesthesiology and Surgery, Hospital Croix-Rousse, Lyon, France Designing a new operating room (OR) suite is a difficult process owing to the number of caregivers involved and because decision-making managers try to minimize the direct and indirect costs of operating the OR suite. In this study, we devised a computer simulation flow model to calculate, first, the minimum number of beds required in the postanesthesia care unit (PACU). In a second step, we evaluated the relationship between the global performance of the OR suite in terms of OR scheduling and number of staffed PACU beds and porters. We designed a mathematical model of OR scheduling. We then developed a computer simulation flow model of the OR suite. Both models were connected; the first one performed the input flows, and the second simulated the OR suite running. The simulations performed examined the number of beds in the PACU in an ideal situation or in the case of reduction in the number of porters. We then analyzed the variation of number of beds occupied per hour in the PACU when the time spent by patients in the PACU or the number of porters varied. The results highlighted the strong impact of the number of porters on the OR suite performance and particularly on PACU performances. (Anesth Analg 2003;96: ) The construction of new hospitals is an opportunity for managers and all participants of the operating room (OR) suite to be involved in the design of the surgical facilities, to question the organization and the construction of their OR scheduling, and moreover, to determine the labor and material resources required for OR efficiency. However, it is difficult to appropriately allocate health care resources. Hospital centers that are confronted with the problem of provisioning physical space, appropriate staffing, and equipment of new surgical facilities cannot use their own previous experience or that of other institutions because of the continuous evolution of medical practice and organization. There are no worldwide-accepted rules concerning the conditions of practice of anesthesia, but a number of recommendations are available, coming from different societies of anesthesiology around the world (1 3). However, precise indications regarding the design of the postanesthesia care unit (PACU) are still lacking. In particular, the ratio of PACU beds to the number of Accepted for publication December 13, Address correspondence and reprint requests to Eric Marcon, Laboratoire d Analyze des Signaux et des Processus Industriels (LASPI), IUT de Roanne, 20 Ave de Paris, Roanne Cedex. Address to marcon@univ-st-etienne.fr. DOI: /01.ANE B9 surgical rooms is not clearly defined. In this context, our study deals with using a discrete event simulation for determining the number of PACU beds required. In addition, we used simulation to analyze the impact of the decrease in the number of porters in the OR with respect to the number of PACU bed requirements. We performed a study of sensitivity of the evolution of the hourly number of beds occupied in the PACU when the PACU length of stay varied or when the number of porters was reduced. Methods The computer simulation to analyze and test the dynamic running of OR suites has been performed in sequential steps. First, a data set was selected, and then a mathematical model of planning was used on this data set; finally, computer flow simulations were performed allowing us to test several strategies (Fig. 1). All the procedural times and time periods used in this paper are in accordance, when available, with the Association of Anesthesia Clinical Directors Glossary of Terms (4). The data used in this study came from the historical collection of the current OR suite and from the specifications for a future OR suite planned in our institution. The average of the surgical cases and range of case were calculated from 2003 by the International Anesthesia Research Society /03 Anesth Analg 2003;96:

2 1416 ECONOMICS, EDUCATION, AND HEALTH SYSTEMS RESEARCH MARCON ET AL. ANESTH ANALG DETERMINING POSTANESTHESIA CARE UNIT BEDS WITH FLOW SIMULATION 2003;96: Figure 1. Functional layout of the operating room (OR) suite simulation model. historical data collection over the previous months. The number of cases per day to be performed was in accordance with the previsions of the new OR suite. The of the surgical case is the time between patient in room and patient out of room. In our institution, each surgical team had its own surgical program and dedicated rooms. The scientific literature regarding the statistical distribution of surgical case models suggests unanimously the use of log-normal distribution. Therefore, we modeled the set of elective surgical cases of a same surgical specialty by a random variable using a log-normal distribution law (5) whose variables are presented in Table 1. We used a random variable to simulate the set of surgical case s rather than actual data because this procedure allowed us to perform flow simulations that were independent of the sample of data chosen. The model used the statistical data of surgical activity by specialty and per day to elaborate the elective OR schedule that was performed every day in the surgical suite. The elective OR-schedule strategy is based on open planning (open scheduling). For the open-scheduling strategy, an OR is open to every surgical specialty. Every surgeon can schedule his or her surgical cases for any workday. Every week the OR manager and one surgeon, by specialty, schedule the demands of the surgeons for an OR suite for the following week. The mathematical model must determine, for all elective surgical cases, the earliest start time and OR location. Therefore, it must be able to consider the constraints of OR running and to provide an OR schedule that maximizes the efficiency of ORsuite use. This OR schedule was developed using the Constrain Satisfaction Programming (CSP) model (6).

3 ANESTH ANALG ECONOMICS, EDUCATION, AND HEALTH SYSTEMS RESEARCH MARCON ET AL ;96: DETERMINING POSTANESTHESIA CARE UNIT BEDS WITH FLOW SIMULATION Table 1. Forecast Activity Information of the Different Surgical Specialties of OR Suite Number of rooms Number of surgeons per day Mean of surgical case sd a Range Number of surgical cases Surgical specialty Ophthalmology [30 120] 8 Orthopedics [45 200] 7 General surgery [30 420] 12 Otorhinolaryngology [20 180] 14 Endoscopy and radiology [20 120] 15 Ambulatory surgery Ambulatory ophthalmology [10 60] 7 Ambulatory orthopedics [10 60] 5 Ambulatory otorhinolaryngology and general surgery [10 60] 6 a All s are given in minutes. The purpose of the CSP model is to solve a scheduling problem by minimizing and balancing the time of OR close. The constraints taken into account in the model were the following: A surgeon performed the set of his or her surgical cases in a sequential manner. All the OR staff (i.e., anesthesiologists, physicians, and nurses) were assigned to the OR just as the surgeon was. We suppose, for the OR-scheduling model as well as the computer simulation model, that the number of OR staff was always sufficient to perform a surgical case when this one is scheduled. The details of the mathematical model are given in Appendix 1. The computer simulation model of OR suite was performed with ARENA 5 simulation language. This model included all facilities of the OR suite: ORs, PACU, and OR staff (surgeons, anesthesiologists, physicians, nurses, nurse aides, and porters). This model allowed us to simulate the overall patient perioperative process. The different management rules of resources and staffs and the different pathways of the patient (i.e., ambulatory surgery or hospitalization) were taken into account. The different steps of the perioperative process were the following: transportation of the patient from his or her surgical ward bed or ambulatory unit to the OR suite, the surgical procedure including the anesthesia induction, the surgical preparation, the surgical procedure, the patient s PACU stay, and the transportation of the patient to his or her surgical ward bed or ambulatory unit. As for the surgical case s, all these procedural times were calculated from the historical collection of data of the current OR over the previous 6 mo. The preparation time depends on the surgical case, the surgical specialty. A statistical analysis for each specialty over the previous 6 mo allowed us to calculate their average. We observed that the average s of surgical preparation varied from 5 to 30 min. Clean-up depends on many factors, including surgical cases, the new equipment for the next surgical case, and the turnover of the surgical team. As for the preparation time, we have performed average per specialty. These mean s per specialty are displayed in Table 2. The mean of transport of patients was 15 min for 20% of surgical cases and for ambulatory surgical cases and 30 min otherwise. PACU lengths of stay are given in Table 3. Situation 0 corresponded to the required length of stay in PACU estimated by the anesthesiologists and the OR manager. These estimations are in accordance with the results of a statistical analysis obtained from a 2-yr database of a French public hospital (9). The authors concluded that the PACU length of stay was 46% of the total length of anesthesia (9). Situations 1 and 2 corresponded to an increase of PACU length of stay caused by medical complications or nonmedical causes (no ward bed available or PACU nurses admitting another patient). Additional assumptions included the absence of untoward events during the surgical procedures, a patient stay in the OR when no PACU bed was available, and a rule of priority for bed transport allowing the porter to anticipate the transfer of the next patient when half the time of the current case had elapsed. Three scenarios were simulated on the number of PACU beds and the number of porters occupied. The first one considered an infinite number of porters and a large capacity of 30 PACU beds. The second examined the effect of a progressive limited number of available porters. The number of porters varied from 10, the average number found in the first scenario, to 6, the theoretical average number required if all the transports were evenly distributed over the day. Finally, the effect of an increasing PACU length of stay was tested on the number of PACU beds to be staffed. The different lengths of tested PACU stay are listed in

4 1418 ECONOMICS, EDUCATION, AND HEALTH SYSTEMS RESEARCH MARCON ET AL. ANESTH ANALG DETERMINING POSTANESTHESIA CARE UNIT BEDS WITH FLOW SIMULATION 2003;96: Table 2. Average Duration ( sd) of Surgical Preparation and Clean-Up Procedure Calculated from the Last 6 Mo Historical Collection Surgical specialty Surgical preparation a Clean-up Ophthalmology Orthopedics General surgery Otorhinolaryngology Endoscopy and radiology Ambulatory surgery a All s are given in minutes. Table 3. The Different Postanesthesia Care Unit Lengths of Stay Depending on Surgical Case Duration and Situation Surgical case (SCD) Situation 0 Situation 1 Situation 2 SCD 60 min 30 min 60 min 60 min 60 SCD 90 min 60 min 90 min 120 min SCD 90 min 120 min 120 min 180 min Table 3. For the first two scenarios tested, only the Situation 0 of Table 3 was used. In addition, interactions between the two factors, namely the number of available porters and the of PACU stay, were examined. For all of these simulations, the daily resource hours of OR and PACU were 600 min (10 h 00 min) and 690 min (11 h 30 min), respectively. To accurately investigate the hourly evolution of the number of beds occupied in the PACU and the number of porters required, we simulated 100 different OR working days. The surgical cases for each day were different from all other days, and every assumption described in the previous section was considered. Results Simulations performed in this ideal context permitted 608 min (10 h 08 min) for OR suite and 702 min (11 h 12 min) for PACU. These results show the similarity between scheduled and simulated results. The difference between the two results was 2%. The number of PACU beds required increased regularly from 8:00 am to 12:00 am, and then it decreased until 4:00 pm and remained fairly stable over the next hours (Fig. 2). For porters, the number required was very large for the first hour of the workday because all ORs opened at 8:00 am and all patients were present in the surgical care unit or ambulatory unit. During the workday, the number of porters required decreased steadily, except for a slight peak at 1:00 pm. Reducing the number of porters caused an increase in the number of PACU beds required, and an overuse of the PACU and sometimes the ORs (Table 4). For a staff of eight porters, the average impact on the OR suite and on the PACU was a delay ranging from 20 to 40 min. The impact of decreasing the number of porters was mainly on the hourly number of PACU beds (Fig. 3). Indeed, compared with infinite capacity results (Fig. 2), 10 additional beds were required during a critical period ranging from 10:00 am to 1:00 pm. In addition, the eight porters were overloaded during the first 4 h of their workday. Simulating a strategy including only six porters for the workday (Fig. 4) led to an increased dysfunction of the OR suite. The average impact on the OR suite and on the PACU was approximately a 1-hr delay. In this configuration, the porter staff was overloaded from 8:00 am until 3:00 pm. The overload of the PACU beds required was the consequence of the nonavailability of porters for patients discharging from the PACU. The PACU was therefore transformed into a storage area for the patients who needed to be transferred to their surgical care units. Consequently, a larger number of PACU beds were used during a greater part of the workday, and a saturation of all PACU beds occurred for the period ranging from 12:00 am until 1:00 pm. Table 5 displays only the results obtained for the two new situations (i.e., Situation 1 and Situation 2) because the results of Situation 0 have been displayed in Table 4. An increase in PACU length of stay had only a slight effect on the OR suite, even if the number of porters was decreased. Nevertheless, this behavior changed when all beds in the PACU were occupied. Indeed, in this situation, the patient waking was spent in the OR, and all surgical cases scheduled in this room were delayed. Moreover, the effect on the PACU was considerable. Figure 5 shows that increasing PACU length of stay had an impact on hourly bed requirement in the PACU. Finally, for the last two situations, the evolution of the hourly use of the number of the PACU beds and porters was studied, whereas the number of porters was decreased, respectively. The simulation results for Situations 1 and 2 were very close to those obtained for Situation 0. The increase in the PACU bed requirement was proportional to the increase in the patients length of stay in the PACU. Conversely, when the number of porters decreased, the beds required in PACU increased dramatically (the total capacity of the PACU required reached 20 beds and 30 beds for eight and six porters, respectively). If we compare Situation 0 with six porters and Situation 2 with an ideal number of porters, we note that the average length of stay in PACU for Situation 0 and Situation 2 is approximately 135 min.

5 ANESTH ANALG ECONOMICS, EDUCATION, AND HEALTH SYSTEMS RESEARCH MARCON ET AL ;96: DETERMINING POSTANESTHESIA CARE UNIT BEDS WITH FLOW SIMULATION Figure 2. Hourly use of number of postanesthesia care unit (PACU) beds and porters for an infinite capacity of PACU beds and porters. Discussion The major finding of this study was the significant impact of the number of porters on the hourly use of number of PACU beds. Indeed, decreasing the number of porters brought about an increase in the number of PACU beds to be staffed. Moreover, according to our simulation, the porters seemed to play the role of bottleneck in the flow of patients in the operating process. The interest of using computer flow simulation for understanding and evaluating OR suite performance is two-fold (7,10,11). First, flow simulation is based on a flow process model. The flow model should include all the main determinants of the simulated process, namely in the case of surgical process, the functioning of the OR suite, the most common decisions, activities and rules of management, and sharing resources. Second, the model we used was built on the basis of the specifications provided by all the participants of the OR suite. It is noteworthy that the model was developed using a number of assumptions that were supposed to be confirmed at all the times. In particular, in the model we used, some resources were considered unlimited (nurse staffing for example), and moreover, no unexpected event took place such as emergency surgery or unexpected delay in a surgical case. Table 4. Simulation Results on the Evolution of the Operating Room Suite Duration and Postanesthesia Care Unit Duration When the Number of Porters Decreases for the Situation 0 Number of porters available Average of OR suite Average of PACU h 08 min 11 h 42 min 9 10h5min 11h49min 8 10h20min 12h12min 6 10h42min 12h14min In our study, simulation flow permits one to invalidate the theoretical static calculation of porters required in the OR suite. The simple division of the total of transports of all the patients in a day by the number of hours a porter works in a day gives a minimal number of porters required. This calculation does not take into account the dynamic behavior of the patient flow. The simulation is a way to include the effect of sharing resources, simultaneous need, and effect of random length of surgical case on the number of porters required. The simulation with an infinite number of resources gave us quantitative information on the hourly number of beds occupied in the PACU and number of porters required. The hourly number of beds occupied in the PACU was 12 beds for 18 working ORs. Consequently,

6 1420 ECONOMICS, EDUCATION, AND HEALTH SYSTEMS RESEARCH MARCON ET AL. ANESTH ANALG DETERMINING POSTANESTHESIA CARE UNIT BEDS WITH FLOW SIMULATION 2003;96: Figure 3. Hourly use of number of postanesthesia care unit (PACU) beds and porters with a staff of eight porters. the ratio of PACU beds to OR rooms was less than one. This simulation result is not in line with the often accepted PACU beds-to-or ratio, ranging from 1.5:1 to 2:1, provided in the scientific literature or by the various societies of anesthesiology (2,3,12). Several explanations may account for this discrepancy. The first could be the running resource assumptions we used in the model. For example, transport assistance was available at once when requested in the PACU, or no unexpected event occurred during the surgical procedures. A second explanation could be the of the surgical cases we selected. Indeed, the shorter the surgical procedure was, the larger the PACU beds-to-or ratio. The simulation confirms that the ratio is smaller when dealing with long surgical cases instead of dealing with short cases of ambulatory surgery. Moreover, our simulations were performed using absolute numbers of OR and PACU beds and not PACU beds-to-or ratio. Extension of the results to facilities having different numbers of OR and PACU beds could require using the ratio instead of actual number. Recent studies present the nonmedical causes as the main causes of delay in patient discharge from PACU (13,14). Among them, the most common are: no assigned bed, busy PACU nurses, and no available porters. In our analysis, we have only considered the porters availability effect. Concerning the delays caused by medical and nonmedical reasons for discharge into the PACU, we modeled them by increasing PACU length of stay in Situations 1 and 2. With these assumptions, the simulation with a decreasing number of porters showed a major effect on the number of PACU beds occupied per hour. Decreasing the number of porters generated a delay in the patient s discharge and caused an increase in the number of PACU beds required. In this context, the PACU was used as an area where all patients to be transferred are stored. When the number of porters was insufficient, all the PACU beds were occupied, and therefore, some patients had to stay in the OR while recovering. In this case, the transport assistance limitation generated a bottleneck effect between the OR suite and medical floor wards causing a major dysfunction of the OR suite. Such lengthening of stay in the PACU has already been described in an observational study emphasizing

7 ANESTH ANALG ECONOMICS, EDUCATION, AND HEALTH SYSTEMS RESEARCH MARCON ET AL ;96: DETERMINING POSTANESTHESIA CARE UNIT BEDS WITH FLOW SIMULATION Figure 4. Hourly use of number of postanesthesia care unit (PACU) beds and porters with a staff of six porters. Table 5. Simulation Results on the Evolution of the Operating Room Suite Duration and Postanesthesia Care Unit Duration When the Number of Porters Decreases for the Situations 1 and 2 Number of porters Average OR suite Situation 1 Situation 2 Average PACU Average OR suite Average PACU Infinite 10 h 11 min 11 h 46 min 10 h 11 min 12 h 45 min h 11 min 11 h 46 min 10 h 11 min 12 h 45 min 8 10h18min 11h53min 10h15min 12h50min 6 10h39min 12h14min 10h39min 13h9min that physical transport could be the main limiting factor of a PACU efficiency (9). In the third group of simulations (Figs. 2 and 5), we observed that the hourly number of beds in the PACU was more sensitive to the variation of the number of porters than to the variation of PACU length of stay. Indeed, the total number of beds required in the PACU was much more dependent on the number of porters than on the length of stay in the PACU. This points up the impact of number of porters on the resources required in the operating process. From a practical point of view, these findings suggest that when designing staff resources and organization, taking the number of PACU beds into consideration, it would be more relevant to search for an appropriate number of porters than to decrease the PACU length of stay. From an economical point of view, the reasoning could be at variance. Indeed, the economical balance consists of the PACU beds that need to be built, the monitors to be purchased, and the beds to be staffed with the appropriate PACU bed-to-nurse ratio on one hand and the number of porters on the other. To conclude, this study highlights the interest of using computer flow simulation for determining the number of PACU beds in an OR multidisciplinary suite. It is a powerful tool when we design a new OR suite because it validates or invalidates estimates or recommendations. In our case, it allowed us to settle the choice between increasing the number of porters (six to eight) and decreasing the number of PACU

8 1422 ECONOMICS, EDUCATION, AND HEALTH SYSTEMS RESEARCH MARCON ET AL. ANESTH ANALG DETERMINING POSTANESTHESIA CARE UNIT BEDS WITH FLOW SIMULATION 2003;96: Figure 5. Simulation results of hourly use number of postanesthesia care unit (PACU) beds and porters for Situations 1 and 2 for an infinite capacity of PACU beds and porters. beds (30 to 14). This analysis tool will be even more relevant when many resources are shared and a large number of tasks must be performed. Appendix 1 The mathematical program used for planning and scheduling is described as follows: Data i surgical case index, [1, n] j OR index, [1, m] l surgeon index, [1, p] D_Bloc i OR for the i th surgical case Conta i contamination level of the i th surgical case [1, 5] Ouv OR suite. This value is also used as a large constant in a constraints model. C i,j 1 if the i th surgical case is performed by the j th surgeon 0 else Decision Variables O i,j 1 if the i th surgical case is performed in the j th OR 0 else t i the time at which the i th surgical case can start (t i 0) y i,j 1ift i t j 0 else Z the cost variable of the objective function n O i,j D_Bloc i Ouv j [1 to m] (1) i 1 m O i,j 1 i 1ton (2) j 1 y i,j y j,i 1 i,j) [1 to n], i j, i j (3) t j t i Ouv y i,j (i,j) [1 to n], i j (4) Equation (1) means that the sum of the surgical case scheduled on every OR is lower or equal to the OR opening time. Equations (2), (3), and (4) are integrity constraints on the decision variables of the model. t j t i D_bloc i Ouv 3 O i,k O j,k y i,j (i,j) [1 to n], i jet k [1 to m] (5)

9 ANESTH ANALG ECONOMICS, EDUCATION, AND HEALTH SYSTEMS RESEARCH MARCON ET AL ;96: DETERMINING POSTANESTHESIA CARE UNIT BEDS WITH FLOW SIMULATION Equation (5) represents the disjunctive constraint of the OR scheduling, whereas equation (6) represents the disjunctive constraint of the surgeon scheduling. t j t i D_bloc i Ouv 3 C i,l C j,l y i,j (i,j) [1 to n], i jet l [1 to p] (6) Equation (7) means that the OR scheduling for each operating room satisfies contamination constraints. y i,j conta i conta j (i,j) [1 to n], i j (7) From these constraints, we perform an OR scheduling that minimizes either the time wasted by the surgeons (7) or the gap of OR end time to balance the workload on all the ORs (8). The minimization of the unused time between every surgical case consists in reducing the OR attendance of the surgeon so that he can dedicate more time to other tasks such as inpatient or outpatient clinics. If we want to minimize the surgeon time wasted, we can define: Mi l Min t i C i,l /i [1 to n] /1 [1 to p] Ma l Max t i D_bloc i C i,l /i [1 to n] /1 [1 to p] (8) p Minimize n Ma l Mi l D_bloc i C i,l l 1 If we want to minimize OR end time to balance the workload, we can define: i 1 t i D_bloc i Z i [1 to n] aiming at : Minimizing {Z} (9) We modeled this planning and scheduling problem as a linear program in binary variables. We built this model with a CSP approach (6) with ILOG scheduler C library. References 1. Ministère des Affaires Sociales. Décret n du 5 décembre 1994 relatif aux conditions techniques de fonctionnement des établissements de santé en ce qui concerne la pratique de l anesthésie et modifiant le code de la santé publique. JO de la République 8 décembre 1994 article D and Recommandation de la SFAR. Concernant la surveillance et les soins postanesthésiques, chapitre 3 [froq] personnel de la salle de réveil [frcq], chapitre 4 [froq] salle de réveil [frcq]. 2ème ed American Society of Anesthesiologists. ASA Standards, guidelines and statements. ASA Publications and Services Catalogue, Procedural Times Glossary of the AACD Association of Anesthesia Clinical Directors, Glossary.html. 5. Strum DP, May JH, Vargas LG. Modeling the uncertainty of surgical procedure time: comparison of log-normal and normal models. Anesthesiology 2000;92: Tsang EPK. Foundations of constraint satisfaction. London and San Diego: Academic Press, Lowery JC, Davis JA. Determination of operating room requirements using simulation. Proceedings of the 1999 Winter Simulation Conference (WSC 99), Phoenix, AZ, December 5 8, Tessler MJ, Mitmaker L, Wabba RM, Covert CR. Patient flow in the post anesthesia care unit: an observational study. Can J Anaesth 1999;46: Velay H, Boutouatou M, Auroy Y, et al. Recueil et analyse de l activité anesthésique dans un service d anesthésie. Bibliothèque des infirmières et infirmiers anesthésistes 1999; Centeno MA, López E, Lee MA, et al. Challenges of simulating hospital facilities. Proceedings of the Twelfth Annual Conference of the Production and Operations Management Society, POM-2001, Orlando, FL, March 30 April 2, Yang Y, Sullivan K, Wang P, et al. Applications of computer simulation in medical scheduling. Proceedings of the Joint Conference on Information Sciences (JCIS 2000), February 27 March 3, Dexter F, Tinker JH. Analysis of strategies to decrease postanesthesia care unit costs. Anesthesiology 1995;82: Deepika K, Kenaan CA, Deresz G, et al. Causes of delayed discharge and prolonged stay in PACU. 76th IARS Clinical and Scientific Congress, San Diego, CA, March 16 20,h Gan TJ, Hopkins M, Sloan B, et al. Main causes of delay in in-patient discharge from PACU in a major teaching hospital. American Society of Anesthesiologists Annual Meeting, Orlando, FL, October 14, 2002.