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Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes.

Motivated by the operational problems in click and collect systems, such as curbside pickup programs, we study a joint admission control and capacity allocation problem. We consider a system where arriving customers have preferred service delivery times and gauge the service quality based on the service provider's ability to complete the service as close as possible to the preferred time. Customers can be of different priority classes, and their priority may increase as they wait longer in the queue. The service provider can reject customers upon their arrival if the system is overloaded or outsource the service (alternatively work overtime) when the capacity is not enough. The service provider's goal is to find the minimum-cost admission and capacity allocation policy to dynamically decide when to serve and whom to serve. We model this problem as a Markov Decision Process. Our structural results partially characterize a set of suboptimal solutions, and we develop solution methods using these results. We also develop a problem-specific approximation method that is based on state aggregation to overcome the computational challenges. We present extensive computational results and discuss the impact of problem parameters on the optimal policy.

Regular tuberculosis (TB) screening is required for healthcare employees since they can come into contact with infected patients. TB is a serious, contagious, and potentially deadly disease. Early detection of the disease, even when it is in latent form, prevents the spread of the disease and helps with treatment. Currently, there are two types of TB diagnostic tests on the market: skin test and blood test. The cost of the blood test is much higher than the skin test. However, the possibility of getting a false positive or false negative result in skin test is higher especially for persons with specific characteristics, which can increase costs. In this study, we categorize healthcare employees into multiple risk groups based on the department they work in, the specific job they do, and their birth country. We create a Markov decision process (MDP) model to decide which TB test should be taken by each employee group to minimize the total costs related to testing, undetected infections, employees' time lost. Due to the curse of dimensionality, we use approximate dynamic programming (ADP) to obtain a near-optimal solution. By analyzing this solution to the ADP we specify not only the type but the frequency with which each test should be taken. Based on this analysis, we propose a simple policy that can be used by healthcare facilities since such facilities may not have the expertise or the resources to develop and solve sophisticated optimization models.

Automated material handling systems are used in healthcare facilities to optimize material flow, minimize workforce requirements, reduce the risk of contamination, and reduce injuries. This study proposes a framework that integrates data analysis with system simulation and optimization to address the following research questions: (i) What are the implications of redesigning a hospital's material handling system? (ii) What are the implications of improving a hospital's material handling process? This paper develops a case study using data from the Greenville Memorial Hospital (GMH) in South Carolina, USA. The case study is focused on the delivery of surgical cases to operating rooms at GMH via Automated Guided Vehicles (AGVs). The data analysis provides distributions of travel times, AGV utilization, and AGV movement patterns in the current system. The results of data analysis are integrated in a simulation-optimization model that incorporates the size of AGV fleet and the corresponding routes to improve system efficiency, increase AGV utilization, and reduce congestion. To address research question (i), a redesign of AGV pathways is evaluated to determine whether congestion is reduced. For research question (ii), the implementation of a Kanban system is proposed to improve AGV utilization by controlling the number of AGVs used daily, based on the volume of surgical cases. An extensive sensitivity analysis, simulation-optimization experiments, and a pilot study are conducted and indicate that the proposed Kanban system leads to significant reductions in congestion and travel times and increased utilization of AGVs.

For operating rooms (ORs) and hospitals, inventory management of surgical instruments and material handling decisions of perioperative services are critical to hospitals' service levels and costs. However, efficiently integrating these decisions is challenging due to hospitals' interdependence and the uncertainties they face. These challenges motivated the development of this study to answer the following research questions: (R1) How does the inventory level of surgical instruments, including owned, borrowed and consigned, impact the efficiency of ORs? (R2) How do material handling activities impact the efficiency of ORs? (R3) How do integrating decisions about inventory and material handling impact the efficiency of ORs? Three discrete event simulation models are developed here to address these questions. Model 1, Current, assumes no coordination of material handling and inventory decisions. Model 2, Two Batch, assumes partial coordination, and Model 3, Just-In-Time (JIT), assumes full coordination. These models are verified and validated using real life-data from a partnering hospital. A thorough numerical analysis indicates that, in general, coordination of inventory management of surgical instruments and material handling decisions has the potential to improve the efficiency and reduce OR costs. More specifically, a JIT delivery of instruments used in short-duration surgeries leads to lower inventory levels without jeopardizing the service level provided.

Retailers use a variety of mechanisms to enable sales and delivery. A relatively new offering by companies is curbside pickup where customers purchase goods online, schedule a pickup time, and come to a pickup facility to receive their orders. To model this new service structure, we consider a queuing system where each arriving job has a preferred service completion time. Unlike most queuing systems, we make a strategic decision for when to serve each job based on their requested times and the associated costs. We assume that all jobs must be served before or on their requested time period, and the jobs are outsourced when the capacity is insufficient. Costs are incurred for jobs that are outsourced or served early. For small systems, we show that optimal capacity allocation policies are of threshold type. For general systems, we devise heuristic policies based on similar threshold structures. Our numerical study investigates the performance of the heuristics developed and shows the robustness of them with respect to several service parameters. Our results provide insights on how the optimal long-run average costs change based on the capacity of the system, the length of the planning horizon, cost parameters and the order pattern., Comment: 25 pages, 6 tables, 1 figure

Diagnostic clinics are among healthcare facilities that suffer from long waiting times which can cause medical issues and lead to increases in patient no-shows. Reducing waiting times without significant capital investments is a challenging task. We tackle this challenge by proposing a new appointment scheduling policy for such clinics that does not require significant investments. The clinic in our study serves outpatients, inpatients, and emergency patients. Emergency patients must be seen on arrival, and inpatients must be given next day appointments. Outpatients, however, can be given later appointments. The proposed policy takes advantage of this by allowing the postponement of the acceptance of appointment requests from outpatients. The appointment scheduling process is modeled as a two-stage stochastic programming problem where a portion of the clinic capacity is allocated to inpatients and emergency patients in the first stage. In the second stage, outpatients are scheduled based on their priority classes. After a detailed analysis of the solutions obtained from the two-stage stochastic model, we develop a simple, non-anticipative policy for patient scheduling. We evaluate the performance of this proposed, easy-to-implement policy in a simulation study which shows significant improvements in outpatient indirect waiting times.