Strategic Decision Making Using Waiting Line Models

Introduction

The use of strategic decision sciences in management has been well documented, with a vast array of applications, including all-important moral considerations (Byford, 2018) and (Lichtenstein et al., 2017). There is an endless supply of business models that are based on effective use of available information (Rascão, 2018), the determination of a framework for shipbuilding (John and Kumar, 2018) and the efficiency and effectiveness of the aviation sector (Kumar et al., 2018). There is also a continuous flow of books on strategic decision-making, such as Reed (2015) and Peltonen (2019), the latter outlining some of the best and worst management decisions that have been made. More recently, Wang (2019) suggests a socially optimal queue length while Teimoury and Fathi (2019) use a queueing-game model in problems of supply chain management. An interesting problem (Wang et al., 2019) considers various methods of finding the optimal order to serve agents in a queueing situation where waiting costs are an issue.

Of particular interest in this research is the use of queueing models to improve the efficiency of business and to optimise operations. The use of self-service technology has led to customers having to make a decision on how they would like to be served (Kokkinou and Cranage, 2015), how waiting times affects purchasing behaviour (Lu et al., 2013) and the way in which patients abandon a queue in an emergency room (Batt and Terwiesch, 2015). There are several applications of waiting line models in the health industry, including the improvement in performance of hospitals dealing with increasing demands for their services (Bittencourt et al., 2018). Among the more prominent books written are those by Chun (2016) who discusses the fairness of queues, and Keblis (2012) on queueing quality and capacity.

The practical value of waiting line models to business and their use by management has been subject of lengthy debate over many years, initially resulting from an early paper by Byrd (1978) suggesting that real-life applications were essentially non-existent. Part of this criticism included the assertion that the assumptions simply do not hold in practice. This was despite a previous study by Ledbetter and Cox (1977) that had already revealed queueing theory did indeed cover a wide range of applications, although there was unfortunately a low percentage of utilization.

There was also an immediate deluge of rebuttals to Byrd’s claims including those by Bhat (1978), Kolesar (1979) and Vazsonyi (1979). An early summary of these arguments was given by Croucher (1985) and a paper by Croucher (1983) provided a further application of queueing theory to server scheduling. There are numerous other instances in the literature of the practical applications of waiting line models, typical examples including those by Foote (1976), Quinn (1991), Tavakoli and Grove (1996) and Khoo (2002), Fu (2002), Carmichael (2006), Lee (2016), Cho et al. (2017) and Falokunde et al. (2018).

In more recent times, queueing models have been successfully applied to networking situations, including radio (Paluncic et al., 2018), telecommunication (Melikov and Ponomarenko, 2014) and (Geng et al., 2017), along with single server finite population queueing networks (Argon and Deng, 2017). Other practical applications involve labour and delivery (Gombolay et al., 2019), certain types of manufacturing systems (Askin and Hanumantha, 2017), replacement models (Ghasemi and Esmaelli, 2015) and the formulation of a workload conservation law in queueing systems (El-Taha, 2017). A queueing-inventory system has been analysed (Krishnamoorthy and Benny, 2017) and a queueing method to handle shared spaces in buildings (Jia and Spanos, 2017).