Elsevier

Computers & Operations Research

Volume 54, February 2015, Pages 21-34
Computers & Operations Research

A two level metaheuristic for the operating room scheduling and assignment problem

https://doi.org/10.1016/j.cor.2014.08.014Get rights and content

Abstract

Given a surgery department comprising several specialties that share a fixed number of operating rooms and post-surgery beds, we study the joint operating room (OR) planning and advanced scheduling problem. More specifically, we consider the problem of determining, over a one week planning horizon, the allocation of OR time blocks to specialties together with the subsets of patients to be scheduled within each time block. The aim of this paper is to extend and generalize existing approaches for the joint OR planning and scheduling problem. First, by allowing schedules that include patients requiring weekend stay beds which was not the case previously. Second, by tackling simultaneously both the OR planning and patient scheduling decision levels, instead of taking them into account in successive phases. To achieve this, we exploit the inherent hierarchy between the two decision levels, i.e., the fact that the assignment decisions of OR time blocks to surgical specialties directly affect those regarding the scheduling of patients, but not the reverse. The objective function used in this study is an extension of an existing one. It seeks to optimize both patient utility (by reducing waiting time costs) and hospital utility (by reducing production costs measured in terms of the number of weekend stay beds required by the surgery planning). 0–1 linear programming formulations exploiting the stated hierarchy are proposed and used to derive a formal proof that the problem is NP-hard. A two level metaheuristic is then developed for solving the problem and its effectiveness is demonstrated through extensive numerical experiments carried out on a large set of instances based on real data.

Section snippets

Introduction and literature review

Operating Rooms (ORs) planning is a critical activity with important financial impacts for most hospital setting. In addition, demand for surgery very often overwhelms supply therefore causing long waiting times for patients and reducing their quality of life [1]. This is particularly true in publicly funded health care systems such as those found in Italy, in the province of Québec in Canada and many other settings. One of the main questions health care system planners and administrators are

Problem definition and notation

Given a set of surgical specialties, a list of patients waiting to be operated on for each specialty and a number of OR time blocks to be assigned to each specialty, we face the problem of determining for a given planning horizon of one week: (1) the cyclic timetable that gives for each day of the planning horizon the assignment of specific OR time blocks to specialties, referred to as the Master Surgical Schedule Problem (MSSP); and (2) the surgery date and operating room assigned to each

0–1 linear programming formulations

In this section, we introduce 01 linear programming formulations for both the SCAP and the ORPP in order to clearly highlight the hierarchy between the two decision levels present in the ORPP. These models are then used to derive a formal proof of the complexity of ORPP.

To formulate the SCAP, we assume as input data the cyclic timetable that gives, for each day of the planning horizon, the assignment of surgical specialties to OR time blocks (i.e., the master surgical schedule). Therefore, the

A two level metaheuristic

The proposed solution algorithm specifically exploits the hierarchy between the two scheduling levels composing the ORPP. The main idea of the approach is to iterate the search process between the two decision levels in such a way as to address each one while trying to globally improve the current solution. The solution procedure is based on the tabu search methodology. It uses a greedy constructive heuristic to build an initial solution from which a basic search procedure is launched. This

Computational results

In this section we report and analyze the computational results obtained when testing algorithms AORPP and ASCAP. First, we describe the computational environment and the benchmark instances in Section 5.1. In Section 5.2 we briefly discuss some remarks regarding the objective function (1). The two-level approach, that is the idea of using the concept of local optimum and the use of s-swap(in,in) as intensification strategy is numerically tested and validated in Section 5.3 while Section 5.4

Conclusion

In this paper we have presented a two level metaheuristic algorithm that solves the joint master surgical schedule and advance scheduling problem taking into account many resource and operative constraints while minimizing the total social cost of the resulting surgery schedule.

The proposed solution approach exploits the inherent hierarchy between the two decision levels present within the problem, i.e., the assignment of OR time blocks to surgical specialties and the assignment of patients to

Acknowledgments

All the authors acknowledge support from the Italian Ministry of Education, University and Research (MIUR), under the Grant no. RBFR08IKSB, “Firb – Futuro in Ricerca 2008”. Patrick Soriano׳s research on this project was also supported by the Natural Sciences and Engineering Research Council of Canada and the Fonds québécois de la recherche sur la nature et les technologies under Grants OGP0218028, OGP0184121, and 01-ER-3254. This support is hereby gratefully acknowledged. The authors wish to

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