A queueing theoretic approach to set staffing levels in time-dependent dual-class service systems

This article addresses the optimal staffing problem for a nonpreemptive priority queue with two customer classes and a time-dependent arrival rate. The problem is related to several important service settings such as call centers and emergency departments where the customers are grouped into two classes of “high priority” and “low priority,” and the services are typically evaluated according to the proportion of customers who are responded to within targeted response times. To date, only approximation methods have been explored to generate staffing requirements for time-dependent dual-class services, but we propose a tractable numerical approach to evaluate system behavior and generate safe minimum staffing levels using mixed discrete-continuous time Markov chains (MDCTMCs). Our approach is delicate in that it accounts for the behavior of the system under a number of different rules that may be imposed on staff if they are busy when due to leave and involves explicitly calculating delay distributions for two customer classes. Ultimately, we embed our methodology in a proposed extension of the Euler method, coined Euler Pri, that can cope with two customer classes, and use it to recommend staffing levels for the Welsh Ambulance Service Trust (WAST)

Sharing delay information in service systems: a literature survey

Service providers routinely share information about upcoming waiting times with their customers, through delay announcements. The need to effectively manage the provision of these announcements has led to a substantial growth in the body of literature which is devoted to that topic. In this survey paper, we systematically review the relevant literature, summarize some of its key ideas and findings, describe the main challenges that the different approaches to the problem entail, and formulate research directions that would be interesting to consider in future work

Serial production line performance under random variation:Dealing with the ‘Law of Variability’

Many Queueing Theory and Production Management studies have investigated specific effects of variability on the performance of serial lines since variability has a significant impact on performance. To date, there has been no single summary source of the most relevant research results concerned with variability, particularly as they relate to the need to better understand the ‘Law of Variability’. This paper fills this gap and provides readers the foundational knowledge needed to develop intuition and insights on the complexities of stochastic simple serial lines, and serves as a guide to better understand and manage the effects of variability and design factors related to improving serial production line performance, i.e. throughput, inter-departure time and flow time, under random variation

Operational Research: Methods and Applications

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