An ant colony optimization approach for solving an operating room surgery scheduling problem☆
Introduction
One of the main challenges in health care systems in recent years is to deliver high quality service under limited available resources. With the increase of aging population, social demands for surgical service have been constantly increased (Etzioni, Liu, Maggard, & Ko, 2003). As a vital hospital component, the operating room (OR) division accounts for approximately more than 40% of a hospital’s total revenues and expenses (Denton, Viapiano, & Vogl, 2007). Hence, it is essential to improve patient flow and optimize OR management in order to provide timely treatments for the patients and to maximize utilization of the available resources. As a required step, surgery scheduling plays a crucial role in the OR management.
OR surgery scheduling determines the operation start time of every surgery to be performed in different surgical groups, as well as the resources assigned to each surgery over a schedule period. The overall surgery process involves several activities before (pre-operative/surgery), during (peri-operative/surgery) and after (post-operative/surgery) an actual surgical procedure. Fig. 1 illustrates these three stages as well as the required resources. The resources required to perform a surgery comprises of personnel (surgeons, anesthetists, nurses, etc.), facilities (specialized equipment, pre-operative holding units (PHUs), multiple operating rooms, post anesthesia care units (PACUs), and intensive care units (ICUs)). Other factors such as personnel shifts and qualifications, different surgical specialties (SSs) and priorities for services also need to be taken into account. Furthermore, many hospitals utilize open scheduling and the ORs are no longer assigned to specific departments, which makes the surgery scheduling problem even more complex. Therefore, researchers made attempts to develop decision support systems for efficient surgery scheduling so as (1) to maximize the operating room efficiency, (2) to increase the number of daily performed operations, and (3) to realize an appropriate resource allocation using various optimization approaches (Blake and Carter, 1997, Guerriero and Guido, 2011, Przasnyski, 1986).
A number of reviews on OR surgery scheduling have been reported in the past (Blake and Carter, 1997, Przasnyski, 1986, Cardoen et al., 2010, Erdogan and Denton, 2010, Guerriero and Guido, 2011, May et al., 2011). Cardoen et al. (2010) surveyed the related manuscripts published since year 2000, and provided detailed classifications based on surgery durations (deterministic or stochastic), patient arrivals (elective and non-elective), and operations research methodology. Erdogan and Denton (2010) further limited the review scope on the type of Operational Research methodology used for daily scheduling and categorized the literature in Queuing models, Simulation, Optimization and Heuristic Methods. Guerriero and Guido (2011) underlined the major developments which emerged throughout the years of Operational Research in management of operating room and grouped the research contributions based on different decision levels, such as strategic, tactical, operational and mixed decision level. According to the classification by Guerriero and Guido (2011), our research article belongs to the mixed decision level (integrating planning and scheduling) because we consider the open scheduling strategy. A typical surgical case scheduling problem in the operational level or the mixed decision level generally covers two sub-problems: advanced scheduling (patients are assigned to operating rooms, also known as OR planning) and allocation scheduling (surgeries are sequenced adequately). It is evident that the two sub-problems are generally formulated as separate combinatorial optimization models. The problem becomes even more difficult when several different surgery specialties are considered in the models and all types of available resources for all three surgery stages. Unlike most published papers in this field, our approach handles both the advanced and allocation scheduling problems simultaneously and provides an ACO approach to solve such a computationally challenging problem. Based on our knowledge, there has been little to no research on ACO applications in healthcare field, especially in surgery scheduling.
The rest of the paper is organized as follows. In Section 2, we provide a sum of the recent surgery scheduling literatures that are most relevant to our work. In Section 3, the scheduling environment we consider is outlined and a formal problem statement is given. Section 4 introduces an ACO algorithm for solving the surgery scheduling problem, and presents the details of our approach. Section 5 provides the computational experiments to validate and evaluate our approach. We close our paper in Section 6 with summary and suggestions for future research.
Section snippets
Literature review
Given the ever increasing demand in the healthcare industry and the fact that the OR management accounts for approximately 40% of a hospital’s budget, a great deal of efforts have been made to improve surgery scheduling. Because literature on OR surgery is vast, we intend to focus this section on literature that is most relevant to our problem, i.e. surgery scheduling dealing with both advanced and allocation scheduling and/or adopting the open scheduling strategy. Furthermore, we limit the
Surgery scheduling problem statement
Surgery cases in a hospital can be classified as elective or emergent surgery. Here we focus on elective surgery.
Ant colony algorithm for surgery scheduling
As job shop scheduling problem is a well-known NP-complete problem, the combinatorial nature of the surgery scheduling problem makes obtaining an optimal scheduling result challenging. Instead, we aimed at a meta-heuristic approach for sub-optimal solution and developed an ACO algorithm to solve the surgery scheduling problem. Since ACO is originally designed to solve the well known Travelling Salesman Problem (TSP), to tailor it for surgery scheduling problem, several modifications and
Five illustrative test cases
The performance of the proposed ACO algorithm is evaluated using five test surgery cases that are different in surgery duration and their required OR resources. The surgeries are classified into five types, small, medium, large, extra-large, and special, according to surgery duration regardless of which surgery group they belong to. These five surgery cases with their respective surgery durations are shown in Table 1. Table 1 also shows the duration for the pre-surgery stage and the
Conclusion and ongoing work
We have developed an ACO approach with a hierarchical ant graph for solving the surgery scheduling problem that arises in large operating suites. The problem is complicated by the need to account for the entire three stages associated with a surgery, open scheduling strategy, as well as multiple resource constraints. We considered both the surgery sequencing problem and the resource allocation problem at the same time. It is described as a multi-resource constrained flexible job-shop scheduling
Acknowledgements
The project is supported by Zhejiang Provincial Natural Science Foundation of China (LY12G01007), Ningbo Natural Science Foundation (2013A610109), and K.C. Wong Magna Fund in Ningbo University.
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