Optimal Control of Service Rates of Discrete-Time (s, Q) Queueing-Inventory Systems with Finite Buffer

Abstract

This article, we develop an optimal policy to control the service rate of a discrete time queueing-inventory system with finite buffer. The customers arrive according to a Bernoulli process and the service time for the customers are geometric. Whenever the buffer size attains its maximum, any arriving new customers are considered to be lost. The customers are served one by one according to FCFS rule and each customers request random number of items. The inventory is replenished according to a (s, Q) inventory policy with geometric lead time. The main objectives of this article are to determine the service rates to be employed at each slot so that the long run expected cost rate is minimized for fixed inventory level and fixed buffer size and to minimize the expected waiting time for a fixed inventory level and fixed buffer size. The problems are modelled as Markov decision problem. We establish the existence of a stationary policy and employ linear programming method to find the optimal service rates. We provide some numerical examples to illustrate the behaviour of the model.

Keywords

Queueing-inventory system / discrete time / batch demand-Markov decision process

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