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