Policies and decision models for solving elective case Operating Room scheduling

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an conference paper published by IEEE in: J. M. M. Pariente, J. M. F. Torres and T. G. Cia, "Policies and decision models for solving elective case Operating Room scheduling," 2009 International Conference on Computers & Industrial Engineering, Troyes, France, 2009, pp. 112-117, doi: 10.1109/ICCIE.2009.5223538. “© 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other Works” Policies and Decision Models for Solving Elective Case Operating Room Scheduling*. Jose Manuel Molina Pariente1, Jose Manuel Framinan Torres1, Tomas Gomez Cia2 1 Industrial Management, School of Engineering. University of Seville. Camino de los Descubrimientos s/n. 41092, Spain. (jmo[email protected].es, [email protected]s) 2 Head of Plastic Surgery Unit. University Hospital Virgen del Rocio. Av. Manuel Siurot s/n. 41013, Spain. ([email protected]) ABSTRACT Surgical cases constitute one of the most important activities in a hospital both from social and economics point of view. The most expensive facility involved in the surgical process is the Operating Room (OR), as it consumes between 10-15% of the budget in a hospital. Therefore, adequate decision-making for planning and scheduling ORs is of vital importance. This process can be decomposed in three phases: session panning problem (SPP), master surgical schedule (MSS) and elective case scheduling (ECS). In this paper, we focus on the ECS which serves to assign dates for surgery to all patients in the surgical unit’s waiting list. In our model, patients must be operated before an exogenous deadline, while taking into account the different availability of surgeons. For this problem, we have developed a mixed integer programming model. We analyse two different allocation policies, which correspond to different surgical service models. In the P-S-OR policy, patients are first assigned to a surgeon and subsequently the set “patient-surgeon” is allocated to an OR shift. In the P-OR-S policy, patients are first assigned to an OR shift, and later a surgeon is assigned to each OR shift in the planning horizon. These two policies are tested using real surgical data from a surgical unit in a Spanish hospital. The results yielded by the P-OR-S policy suggest the latter to be more flexible than P-S-OR, as the patient doesn’t have assigned a surgeon and therefore he/she does not depend on the surgeon’s availability. Keywords: operating room, scheduling, mixed integer programming. † * Preprint submitted to International Conference on Computers and Industrial Engineering, CIE 2009, DOI: 10.1109/ICCIE.2009.5223538. 1. INTRODUCTION Surgical processes are amongst the most important activities in hospitals, not only from a medical and social perspective, but also from an economic viewpoint, as they generate around 70% of revenues and represent 40% of costs in a hospital. More specifically, the Operating Room -OR-, is the facility that consumes more budget (10-15%) in the hospital. Therefore, adequate decision-making for planning and scheduling ORs is of vital importance. Surgical process scheduling may be decomposed in three phases [10]: Phase I. Session planning problem (SPP): available OR’s hours are assigned to the different surgical units in a hospital. Phase II. Master Surgical Schedule (MSS): OR shifts are allocated to surgical units in the hospital. Obviously, the total length of the OR shifts allocated to each surgery unit should not exceed the number of hours obtained by the previous phase. Phase III. Elective case scheduling (ECS): The patients waiting in each surgery unit are assigned to the OR shifts assigned in the previous phase. FIGURE 1. Surgical scheduling decisions problems In general, elective case scheduling is solved into two steps. A first step (Advance Scheduling) refers to the allocation of operations to ORs for a certain date. The second step (Allocation Scheduling) schedules operations assigned to each OR for a particular day in order to improve the use of OR while taking into account the constraints on related resources. This work focuses on the advance scheduling phase. Our objectives are to develop decision models and to test different policies of OR scheduling. The OR scheduler has to simultaneously take into account a number of issues related to patients and surgical resources. In our case, patients must to be operated before a deadline which depends on patient’s degree of clinical priority. Besides, an OR manager has to take into account the availability of surgeons to perform surgical cases in an OR shift. While there are many contributions in the literature dealing with OR scheduling, we are not aware of references dealing with the constraints described above. Table 1 summarises the main hypotheses in related literature, and compare them with those in our models. Model Hypothesis 1 2 3 4 5 6 7 8 9 [10] X Det [4] X X Det X [3] X X Det X X [6] X X Sto [7] X Det [11] Sto [8] X X Det [1] X Det X X [2] Det [9] X Sto [5] Det X P - S - OR X X X Det X X X X X P - OR - S X X Det X X X TABLE 1. Comparison of models Hypothesis in Table 1, are: (1) continuity of care, (2) use of clinical weights for patients, (3) forbidden ORs, (4) consideration of surgical times (Deterministic or Stochastic), (5) surgeons’ availability, (6) constraints on the number of ORs that can be assigned to a surgeon, (7) constraints on the Block Time (BT) assigned to a surgeon, (8) consideration of special surgical cases and (9) patient deadline. The resolution of the problem is tackled by using the following policies.  P-S-OR, first, patients are assigned to a surgeon. Subsequently, the set “patient-surgeon” is allocated to an OR where the surgical case can be performed. This policy guarantees the continuity of care, i.e. patient is operated by the surgeon who treated him/her from his/her arrival to the hospital.  P-OR-S, first, patients are assigned to an OR, and then surgeons are allocated to the set “patients-operating room”. This policy is more flexible than P-S-OR since the patient doesn’t depend on surgeon’s availability to be operated, but it presents problems both from social and professional points of view. On one hand, it is possible that a patient doesn’t want to be operated by a surgeon who didn’t treat him/her before. On other hand, it may happen that a surgeon doesn’t want operate a patient who has been initially treated to another surgeon. 2. ELECTIVE CASE SCHEDULING MODELS First, we describe the assumptions taken into account in order to develop the models to solve the advance scheduling phase for each proposed policy. Patients’ weights are parameters crucial for the model. These are defined by the degree of medical priority and by the number of the days that the patient is in the waiting list. The medical priority can be normal (1) or preferential (2-5), where 5 is the highest priority. We assume that the objective is to maximize the number of surgical cases performed before patients’ deadline. We can consider different objectives: one may be to perform as many surgical cases as possible within the planning horizon by maximizing the sum of patients’ weights scheduled in the planning horizon. Other may be to operate the maximum number of patients with greater weight as soon as possible in the planning horizon. These objectives are incrorporated in the objective function by means of a parameter “n” which is the exponent of the patient’s weight, so that if n = 1, we consider the first objective, while n > 1 indicates the second one. From the objectives described above, the compliance with deadlines’ constraints is the most difficult, since, on one hand, the surgical unit’s demand is usually bigger than the surgical unit’s capacity available in the planning horizon and, on the other hand, surgeons are not available to perform surgical cases in all OR shift in the planning horizon. Therefore, other objective could be to operate the maximum number of patients so the difference between the date and the deadline of surgical cases is minimized, as long as patient doesn’t suffer health complications. The previously described problems are modeled as a Linear Programming models, which are not detailed in this abstract due to the lack of space. Instead, we will describe the main results in the next section. 3. EXPERIMENTS In order to evaluate and compare the proposed policies, real data of surgical cases performed in a Plastic Surgery unit in the Spanish university hospital “Virgen del Rocio” over a 4-period from March to June in 2008 are used. Plastic surgery unit is made up of 16 surgeons who can perform any kind of surgical case, so there is not a constraint in the assignment of patients to surgeons. The surgical unit has 4 ORs, three in the morning shift (Q51T, Q52T, Q55T) and one (QTT) in the afternoon shift. We compare the policies over a week and a month planning horizon, excluding outpatient surgery and emergencies. The software PARALLEL CPLEX is used to solve the problems. In the first test (problem P1), we make a comparison between the real (manual) schedule performed in the surgical unit during a certain planning horizon and the schedule proposed by the models developed. In the second test (problem P2), we introduce as input a waiting list constituted for patient was operated in the planning horizon Hi plus patients who were operated in the consecutive planning horizon Hi+1. TABLE 2. OR Schedules TABLE 3. OR schedules Problem P2 Surgeon OR Available surgeon’s OR Shift ( during planning horizon) 1 3 S1 Q51T 130 0 Q52T 0 0 Q55T 110 0 QTT - - TABLE 4. BTs (minute) assigned to a surgeon Table 2 and 3 show the schedules proposed by the models, indicating the number of waiting list’s patients who are scheduled in the planning horizon. Table 4 shows the BT which is assigned into each OR in the available surgeon’s OR shifts. 4. CONCLUSIONS The two models give better results than the manual schedules manually performed by the OR scheduler. The P-OR-S policy yield the best results, as it is more flexible than P-S-OR. In view of the results, a future line of research would be to evaluate the impact on the waiting list of a hybrid policy between P-S-OR and P-OR-S. In this policy, there will be patients who will be scheduled with P-S-OR and others with P-OR-S, depending of patient’s disease. In addition, other future lines might be to introduce preoperative and postoperative aspects in the models and to study techniques to forecast the times of surgical case REFERENCES [1] Chaabane, S., Meskens, N., Guinet, A., Laurent, M., "Comparison of Two Methods of Operating Theatre Planning: Application in Belgian Hospital", International Conference on Service Systems and Service Management, Vol. 1, pp386-392, 2006. [2] Fei, H., Chu, C., Meskens, N., Artiba, A., "Solving surgical cases assignment problem by a branch-and-price approach", International Journal of Production Economics, In Press, Corrected Proof. 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Problem P1 Horizon Real schedule Schedule proposed P-S-OR (n=1) P-S-OR (n=2) P-OR-S 01 - 07 49 77 77 83 08 - 14 45 55 55 59 15 - 21 14 30 30 37 22 - 31 55 76 76 84 01 - 31 163 226 225 228 Problem 2 Horizon Real schedule Schedule proposed P-S-OR (n=1) P-S-OR (n=2) P-S-OR (n=3) P-OR-S 01 - 07 49 77 77 77 83 08 - 14 45 55 55 55 59 15 - 21 14 30 30 26 37 22 - 31 55 76 76 74 84 01 - 31 163 226 225 226 228