Jeroen Belien

Operating room planning and scheduling: A literature review

This paper provides a review of recent operational research on operating room planning and scheduling. We evaluate the literature on multiple fields that are related to either the problem setting (e.g., performance measures or patient classes) or the technical features (e.g., solution technique or uncertainty incorporation). Since papers are pooled and evaluated in various ways, a diversified and detailed overview is obtained that facilitates the identification of manuscripts related to the readers specific interests. Throughout the literature review, we summarize the significant trends in research on operating room planning and scheduling, and we identify areas that need to be addressed in the future.

Personnel scheduling: A literature review

This paper presents a review of the literature on personnel scheduling problems. Firstly, we discuss the classification methods in former review papers. Secondly, we evaluate the literature in the many fields that are related to either the problem setting or the technical features. Each perspective is presented as a table in which the classification is displayed. This method facilitates the identification of manuscripts related to the reader’s specific interests. Throughout the literature review, we identify trends in research on personnel staffing and scheduling, and we indicate which areas should be subject to future research.

A branch-and-price approach for integrating nurse and surgery scheduling

A common problem at hospitals is the extreme variation in daily (even hourly) workload pressure for nurses. The operating room is considered to be the main engine and hence the main generator of variance in the hospital. The purpose of this paper is threefold. First of all, we present a concrete model that integrates both the nurse and the operating room scheduling process. Second, we show how the column generation technique approach, one of the most employed exact methods for solving nurse scheduling problems, can easily cope with this model extension. Third, by means of a large number of computational experiments we provide an idea of the cost saving opportunities and required solution times.

Operating Room Planning and Scheduling

Operating room (OR) planning and scheduling decisions involve the coordination of patients, medical staff, and hospital facilities. The patients arriving to the hospital are assigned to a surgery date and a surgery time slot. At the time of surgery, a suitable OR, the attending surgeon, supporting anesthesiologists, nurses, and, after the surgery, rooms in secondary facilities such as post-anesthesia care unit (PACU), intensive care unit (ICU), and ward need to be available. In order to deal with the complexity and the variety of problems faced in OR scheduling, it is useful to involve methods from operations research. In this chapter, we review the recent literature on the application of operations research to OR planning and scheduling. We start by discussing the impact of planning and scheduling of the ORs on the overall performance of a hospital. Next, we discuss the criteria for included publications and summarize the structure of Cardoen et al. (Eur J Oper Res 201:921–932, 2010) that served as the guideline for organization of this chapter. In the remainder of the chapter, we describe the evolution of the literature over the last 10 years with regard to the patient type, the different performance measures, the decision that has to be made, the incorporation of uncertainty, the operations research methodology, and the applicability of the research. Moreover, each of these evolutions will be demonstrated with a short review of some relevant papers. This chapter ends with conclusions and a discussion of interesting topics for further research.

Integrated staffing and scheduling for an aircraft line maintenance problem

This paper studies the problem of constructing the workforce schedules of an aircraft maintenance company. The problem involves both a staffing and a scheduling decision. We propose an enumerative algorithm with bounding in which each node of the enumeration tree represents a mixed integer linear problem (MILP). We reformulate the MILP such that it becomes tractable for commercial MILP solvers. Extensive computational tests on 40 instances that are derived from a real-life setting indicate that the algorithm is capable of finding close-to-optimal solutions.

Integrating Nurse and Surgery Scheduling

One common problem at hospitals is the extreme variation in daily (even hourly) workload pressure for nurses. The operating room is considered to be the main engine and hence the main generator of variance in the hospital. It is our believe that integrating the operation room scheduling process with the nurse scheduling process is a simple, yet effective way to achieve considerable savings in staffing costs. The purpose of this paper is threefold. First of all, we present a concrete model that integrates both the nurse and the operating room scheduling process. Secondly, we show how the column generation technique, often employed for nurse scheduling problems, can easily cope with this model extension. Thirdly, by means of a large number of computational experiments we provide an idea of the cost saving opportunities and required solution times.

Solving the Case Mix Problem Optimally by Using Branch-and-Price Algorithms

This paper describes a methodology for the case mix problem in the health care sector. Aiming at maximizing the overall financial contribution of the given resource capacity within a hospital, the case mix problem is formulated as an integer linear programming model to produce the optimal patient mix pattern together with its associated resource allocation scheme. In order to solve the huge integer program optimally, an efficient solution approach, branch-and-price, is proposed, developed and implemented in this research. When studied from the column generation perspective, the integer linear programming model can be formulated differently. According to different decomposition units, namely wards, surgeon groups and patient groups, three decomposition based reformulations are built respectively. Among them, the first two reformulations are suitable to be solved within the framework of branch-and-price, while this is not the case for the last one. Numerical experiments are carried out, and the computational results are presented and compared, which demonstrate that the branch-and-price approach outperforms the integer linear programming method significantly and that decomposition on wards performs much better than decomposition on surgeon groups both with respect to the solution quality and the computation speed.

Scheduling Surgical Cases in a Day-Care Environment: A Branch-and-Price Approach

In this paper we will investigate how to sequence surgical cases in a day-care facility so that multiple objectives are simultaneously optimized. The limited availability of resources and the occurrence of medical precautions, such as an additional cleaning of the operating room after the surgery of an infected patient, are taken into account. A branch-and-price methodology will be introduced in order to develop both exact and heuristic algorithms. In this methodology, column generation is used to optimize the linear programming formulation of the scheduling problem. Both a dynamic programming approach and an integer programming approach will be specified in order to solve the pricing problem. The column generation procedure will be combined with various branching schemes in order to guarantee the integrality of the solutions. The resulting solution procedures will be thoroughly tested and evaluated using real-life data of the surgical day-care center at the university hospital Gasthuisberg in Leuven (Belgium). Computational results will be summarized and conclusions will eventually be formulated.

A Two-Stage Mixed Integer Programming Approach for Optimizing the Skill Mix and Training Schedules for Aircraft Maintenance

This paper presents a two-stage mixed integer programming approach for optimizing the skill mix and training schedule at the aircraft maintenance company Sabena Technics. Of course, when all workers are trained for all skills, cheaper workforce schedules are possible. However, the training that is required to acquire all those skills can become very expensive. In the first stage of our two-staged approach, we therefore make a trade-off between the training costs and the resulting cheaper workforce schedule. As we assume that workers are unavailable to work during their training, the obtained result is only applicable in practice if the required training can be performed without endangering the current maintenance operations. In the second stage, we therefore want to find an optimal and feasible training schedule in order to obtain the desired skill mix with minimal costs. We illustrate our models with a computational experiment based on real-life data of Sabena Technics.

Optimizing the Workforce Schedule and Collection Routes for Glass Containers

This paper presents and compares two different solution approaches to optimize the glass collection process at a single intermunicipal authority in Belgium. First, a model enhancement approach is proposed to solve a shift scheduling optimization problem integrating the construction of glass collection routes. Second, a simulation based rolling horizon procedure is designed to determine the possible benefits of providing the glass containers with fill level sensors. The performance of both solution approaches is evaluated and compared using real-life data.