We provide a comprehensive overview of the typical decisions to be made in resource capacity planning and control in health care, and a structured review of relevant articles from the field of Operations Research and Management Sciences (OR/MS) for each planning decision. The contribution of this paper is twofold. First, to position the planning decisions, a taxonomy is presented. This taxonomy provides health care managers and OR/MS researchers with a method to identify, break down and classify planning and control decisions. Second, following the taxonomy, for six health care services, we provide an exhaustive specification of planning and control decisions in resource capacity planning and control. For each planning and control decision, we structurally review the key OR/MS articles and the OR/MS methods and techniques that are applied in the literature to support decision making.

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Taxonomic classification of planning decisions in health care: a structured review of the state of the art in OR/MS

Operating room (OR) scheduling is an important operational problem for most hospitals. In this study, we present a novel two-stage stochastic mixed-integer programming model to minimize total expected operating cost given that scheduling decisions are made before the resolution of uncertainty in surgery durations. We use this model to quantify the benefit of pooling ORs as a shared resource and to illustrate the impact of parallel surgery processing on surgery schedules. Decisions in our model include the number of ORs to open each day, the allocation of surgeries to ORs, the sequence of surgeries within each OR, and the start time for each surgeon. Realistic-sized instances of our model are difficult or impossible to solve with standard stochastic programming techniques. Therefore, we exploit several structural properties of the model to achieve computational advantages. Furthermore, we describe a novel set of widely applicable valid inequalities that make it possible to solve practical instances. Based on our results for different resource usage schemes, we conclude that the impact of parallel surgery processing and the benefit of OR pooling are significant. The latter may lead to total cost reductions between 21% and 59% on average.

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Operating Room Pooling and Parallel Surgery Processing Under Uncertainty

In hospitals, the operating room (OR) is a particularly expensive facility and thus efficient scheduling is imperative. This can be greatly supported by using advanced methods that are discussed in the academic literature. In order to help researchers and practitioners to select new relevant articles, we classify the recent OR planning and scheduling literature into tables regarding patient type, used performance measures, decisions made, OR up- and downstream facilities, uncertainty, research methodology and testing phase. Based on these classifications, we identify trends and promising topics. Additionally, we recognize three common pitfalls that hamper the adoption of research results by stakeholders: the lack of a clear choice of authors on whether to target researchers (contributing advanced methods) or practitioners (providing managerial insights), the use of ill-fitted performance measures in models and the failure to understandably report on the hospital setting and method-related assumptions. We provide specific guidelines that help to avoid these pitfalls. First, we show how to build up an article based on the choice of the target group (i.e., researchers or practitioners). Making a clear distinction between target groups impacts the problem setting, the research task, the reported findings, and the conclusions. Second, we discuss points that need to be considered by researchers when deciding on the used performance measures. Third, we list the assumptions that need to be included in articles in order to enable readers to decide whether the presented research is relevant to them.

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Scheduling operating rooms: achievements, challenges and pitfalls

Uncertainty in the duration of surgical procedures can cause long patient wait times, poor utilization of resources, and high overtime costs. We compare several heuristics for scheduling an Outpatient Procedure Center. First, a discrete event simulation model is used to evaluate how 12 different sequencing and patient appointment time-setting heuristics perform with respect to the competing criteria of expected patient waiting time and expected surgical suite overtime for a single day compared with current practice. Second, a bi-criteria genetic algorithm (GA) is used to determine if better solutions can be obtained for this single day scheduling problem. Third, we investigate the efficacy of the bi-criteria GA when surgeries are allowed to be moved to other days. We present numerical experiments based on real data from a large health care provider. Our analysis provides insight into the best scheduling heuristics, and the trade-off between patient and health care provider-based criteria. Finally, we summarize several important managerial insights based on our findings.

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Bi-Criteria Scheduling of Surgical Services for an Outpatient Procedure Center

This paper provides a comprehensive survey of research on operating room planning and scheduling problems. Aiming to give a comprehensive classification on the studied problems, we review the literature from the perspectives of decision level, scheduling strategy, patient characteristics, problem setting, uncertainty, mathematical models, and solutions and methods. The papers are reviewed in diversified ways so as to obtain a detailed overview in this area, and the fields that need to be focused on are summarized. It shows that mathematical programming and heuristics are frequently applied in the complex linear and combinatorial optimization problems. Furthermore, future research trends and directions on operating room planning and scheduling are also identified.

Operating room planning and surgical case scheduling: a review of literature

We propose a multistage stochastic mixed-integer programming formulation for the assignment of surgeries to operating rooms over a finite planning horizon. We consider the demand for and the duration of surgery to be random variables. The objective is to minimize three competing criteria: expected cost of surgery cancellations, patient waiting time, and operating room overtime. We discuss properties of the model and an implementation of the progressive hedging algorithm to find near-optimal surgery schedules. We conduct numerical experiments using data from a large hospital to identify managerial insights related to surgery planning and the avoidance of surgery cancellations. We compare the progressive hedging algorithm to an easy-to-implement heuristic for practical problem instances to estimate the value of the stochastic solution. Finally, we discuss an implementation of the progressive hedging algorithm within a rolling horizon framework for extended planning periods.

A progressive hedging approach for surgery planning under uncertainty

Surgical services require the coordination of many activities, including patient check-in and surgical preparation, surgery, and recovery after surgery. Each of these activities requires the availability of resources including staff, operating rooms, and intake and recovery beds. Furthermore, each of these activities has substantial uncertainty in their duration. The combination of a complex resource constrained environment, and uncertainty in the duration of activities, creates challenging scheduling problems. In this study we report on a discrete event simulation model of an outpatient surgical suite, and investigate the impact of several sequencing and scheduling heuristics on competing performance criteria.

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Bi-criteria evaluation of an outpatient procedure center via simulation

Chemotherapy appointment scheduling is a challenging problem due to the uncertainty in pre-medication and infusion durations. In this paper, we formulate a two-stage stochastic mixed integer programming model for the chemotherapy appointment scheduling problem under limited availability and number of nurses and infusion chairs. The objective is to minimize the expected weighted sum of nurse overtime, chair idle time, and patient waiting time. The computational burden to solve real-life instances of this problem to optimality is significantly high, even in the deterministic case. To overcome this burden, we incorporate valid bounds and symmetry breaking constraints. Progressive hedging algorithm is implemented in order to solve the improved formulation heuristically. We enhance the algorithm through a penalty update method, cycle detection and variable fixing mechanisms, and a linear approximation of the objective function. Using numerical experiments based on real data from a major oncology hospital, we compare our solution approach with several scheduling heuristics from the relevant literature, generate managerial insights related to the impact of the number of nurses and chairs on appointment schedules, and estimate the value of stochastic solution to assess the significance of considering uncertainty.

A Stochastic Programming Approach for Chemotherapy Appointment Scheduling

The number and availability of turnover teams may significantly affect the performance of a surgery schedule. We propose a two-stage stochastic integer programming formulation for setting the patient appointment times for surgeries under limited availability of turnover teams. We assume that a surgery schedule has already been created, and study how the schedule may be refined. We consider the durations of surgical operation and turnover to be random variables. The objective is to minimize the competing criteria of expected patient waiting time and operating room idle time. We discuss an implementation of a heuristic to generate near-optimal surgery schedules. We conduct numerical experiments using data from a large hospital. We compare the heuristic with a well-known and practical procedure used in earlier studies for setting patient appointment times for surgeries. Finally, we evaluate the impact of the number of turnover teams into the surgery schedules with respect to performance criteria of interest.

Serhat Gul

Papers

Bi-Criteria Scheduling of Surgical Services for an Outpatient Procedure Center

A progressive hedging approach for surgery planning under uncertainty

Bi-criteria evaluation of an outpatient procedure center via simulation

A Stochastic Programming Approach for Chemotherapy Appointment Scheduling

A Stochastic Programming Approach for Appointment Scheduling Under Limited Availability of Surgery Turnover Teams