Optimal control of service for facilities holding inventory

Abstract

This paper addresses the problem of optimally controlling service rates for an inventory system of service facilities. We consider a finite capacity system with Poisson arrivals and exponentially distributed leadtimes and service times. For given values of maximum inventory and reorder levels, we determine the service rates to be employed at each instant of time so that the long-run expected cost rate is minimized. The problem is modelled as a semi-Markov decision problem. We establish the existence of a stationary optimal policy and we solve it by employing linear programming. Several instances of a numerical example, which provide insight into the behaviour of the system, are presented. Scope and purpose In this article we discuss the problem of inventory control of service parts at a service facility where there is only a limited waiting space for customers. If a customer enters the service facility and sees all the waiting spaces occupied he/she will leave the facility, which results in both intangible losses (loss of goodwill) and tangible losses (loss in profit). Hence, the service provider aims at obtaining an optimal rate at which service is to be provided by balancing costs due to waiting time and limited waiting spaces against costs due to ordering and overheads due to storing items. We develop an algorithm that controls the service rate as a function of the number of customers waiting for service.