Robust Optimization Framework to Operating Room Planning and Scheduling in Stochastic Environment

Arrangement of surgical activities can be classified as a three-level process that directly impacts the overall performance of a healthcare system. The goal of this dissertation is to study hierarchical planning and scheduling problems of operating room (OR) departments that arise in a publicly funded hospital. Uncertainty in surgery durations and patient arrivals, the existence of multiple resources and competing performance measures are among the important aspect of OR problems in practice. While planning can be viewed as the compromise of supply and demand within the strategic and tactical stages, scheduling is referred to the development of a detailed timetable that determines operational daily assignment of individual cases. Therefore, it is worthwhile to put effort in optimization of OR planning and surgical scheduling. We have considered several extensions of previous models and described several real-world applications. Firstly, we have developed a novel transformation framework for the robust optimization (RO) method to be used as a generalized approach to overcome the drawback of conventional RO approach owing to its difficulty in obtaining information regarding numerous control variable terms as well as added extra variables and constraints into the model in transforming deterministic models into the robust form. We have determined an optimal case mix planning for a given set of specialties for a single operating room department using the proposed standard RO framework. In this case-mix planning problem, demands for elective and emergency surgery are considered to be random variables realized over a set of probabilistic scenarios. A deterministic and a two-stage stochastic recourse programming model is also developed for the uncertain surgery case mix planning to demonstrate the applicability of the proposed RO models. The objective is to minimize the expected total loss incurred due to postponed and unmet demand as well as the underutilization costs. We have shown that the optimum solution can be found in polynomial time. Secondly, the tactical and operational level decision of OR block scheduling and advance scheduling problems are considered simultaneously to overcome the drawback of current literature in addressing these problems in isolation. We have focused on a hybrid master surgery scheduling (MSS) and surgical case assignment (SCA) problem under the assumption that both surgery durations and emergency arrivals follow probability distributions defined over a discrete set of scenarios. We have developed an integrated robust MSS and SCA model using the proposed standard transformation framework and determined the allocation of surgical specialties to the ORs as well as the assignment of surgeries within each specialty to the corresponding ORs in a coordinated way to minimize the costs associated with patients waiting time and hospital resource utilization. To demonstrate the usefulness and applicability of the two proposed models, a simulation study is carried utilizing data provided by Windsor Regional Hospital (WRH). The simulation results demonstrate that the two proposed models can mitigate the existing variability in parameter uncertainty. This provides a more reliable decision tool for the OR managers while limiting the negative impact of waiting time to the patients as well as welfare loss to the hospital

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

We provide a structured overview of the typical decisions to be made in resource capacity planning and control in health care, and a review of relevant OR/MS articles 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

Minimizing bed occupancy variance by scheduling patients under uncertainty

International audienceIn this paper we consider the problem of scheduling patients in allocated surgery blocks in a Master Surgical Schedule. We pay attention to both the available surgery blocks and the bed occupancy in the hospital wards. More specifically, large probabilities of overtime in each surgery block are undesirable and costly, while large fluctuations in the number of used beds requires extra buffer capacity and makes the staff planning more challenging. The stochastic nature of surgery durations and length of stay on a ward hinders the use of classical techniques. Transforming the stochastic problem into a deterministic problem does not result into practically feasible solutions. In this paper we develop a technique to solve the stochastic scheduling problem, whose primary objective it to minimize variation in the necessary bed capacity, while maximizing the number of patients operated, and minimizing the maximum waiting time, and guaranteeing a small probability of overtime in surgery blocks. The method starts with solving an Integer Linear Programming (ILP) formulation of the problem, and then simulation and local search techniques are applied to guarantee small probabilities of overtime and to improve upon the ILP solution. Numerical experiments applied to a Dutch hospital show promising results

A survey of health care models that encompass multiple departments

In this survey we review quantitative health care models to illustrate the extent to which they encompass multiple hospital departments. The paper provides general overviews of the relationships that exists between major hospital departments and describes how these relationships are accounted for by researchers. We find the atomistic view of hospitals often taken by researchers is partially due to the ambiguity of patient care trajectories. To this end clinical pathways literature is reviewed to illustrate its potential for clarifying patient flows and for providing a holistic hospital perspective

An Optimization Model for Operating Room Scheduling to Reduce Blocking Across the Perioperative Process

Operating room (OR) scheduling is important. Because of increasing demand for surgical services, hospitals must provide high quality care more efficiently with limited resources. When constructing the OR schedule, it is necessary to consider the availability of downstream resources, such as intensive care unit (ICU) and post anaesthesia care unit (PACU). The unavailability of downstream resources causes blockings between every two consecutive stages. In this paper we address the master surgical schedule (MSS) problem in order to minimize blockings between two consecutive stages. First, we present a blocking minimization (BM) model for the MSS by using integer programming, based on deterministic data. The BM model determines the OR block schedule for the next day by considering the current stage occupancy (number of patients) in order to minimize the number of blockings between intraop and postop stages. Second, we test the effectiveness of our model under variations in case times and patient arrivals, by using simulation. The simulation results show that our BM model can significantly reduce the number of blockings by 94% improvement over the base model. Scheduling patient flow across the 3-stage periop process can be applied to work flow scheduling for the s-stage flow shop shop production in manufacutirng, and also Smoothing patient flow in periop process can be applied to no-wait flow shop production

Integrated Planning in Hospitals: A Review

Efficient planning of scarce resources in hospitals is a challenging task for which a large variety of Operations Research and Management Science approaches have been developed since the 1950s. While efficient planning of single resources such as operating rooms, beds, or specific types of staff can already lead to enormous efficiency gains, integrated planning of several resources has been shown to hold even greater potential, and a large number of integrated planning approaches have been presented in the literature over the past decades. This paper provides the first literature review that focuses specifically on the Operations Research and Management Science literature related to integrated planning of different resources in hospitals. We collect the relevant literature and analyze it regarding different aspects such as uncertainty modeling and the use of real-life data. Several cross comparisons reveal interesting insights concerning, e.g., relations between the modeling and solution methods used and the practical implementation of the approaches developed. Moreover, we provide a high-level taxonomy for classifying different resource-focused integration approaches and point out gaps in the literature as well as promising directions for future research

Simulation-Based Optimization for the Scheduling of Elective Surgery Under Uncertainty And Downstream Capacity Constraints

The generation of an optimal schedule of elective surgery cases for a hospital surgery services unit is a well-known problem in the operations research field. The complexity of the problem is greatly compounded when uncertainties in the parameters are considered and is an issue that has been addressed in few works in the literature. Uncertainties appear in surgery durations and the availability of downstream resources such as surgical intensive care units (SICU), presenting large deviations from their expected value and impacting in the performance of the scheduling process. The technique presented here addresses the uncertainties in the optimal scheduling of a given set of elective surgery cases by means of simulated-based optimization. The main advantage of this approach over previous works is that detailed systems? simulations can be constructed without losing computational performance, thus improving the robustness of the scheduling solution.Fil: Durand, Guillermo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Química; ArgentinaFil: Bandoni, Jose Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Química; Argentin

Balancing control and autonomy in master surgery scheduling: benefits of ICU quotas for recovery units

When scheduling surgeries in the operating theater, not only the resources within the operating theater have to be considered but also those in downstream units, e.g., the intensive care unit and regular bed wards of each medical specialty. We present an extension to the master surgery schedule, where the capacity for surgeries on ICU patients is controlled by introducing downstream-dependent block types – one for both ICU and ward patients and one where surgeries on ICU patients must not be performed. The goal is to provide better control over post-surgery patient flows through the hospital while preserving each medical specialty’s autonomy over its operational surgery scheduling. We propose a mixed-integer program to determine the allocation of the new block types within either a given or a new master surgery schedule to minimize the maximum workload in downstream units. Using a simulation model supported by seven years of data from the University Hospital Augsburg, we show that the maximum workload in the intensive care unit can be reduced by up to 11.22% with our approach while maintaining the existing master surgery schedule. We also show that our approach can achieve up to 79.85% of the maximum workload reduction in the intensive care unit that would result from a fully centralized approach. We analyze various hospital setting instances to show the generalizability of our results. Furthermore, we provide insights and data analysis from the implementation of a quota system at the University Hospital Augsburg. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10729-021-09588-8