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

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. One item is used to serve a customer and the inventory is replenished according to a (s, S) inventory policy with geometric lead time. To minimize long run expected costs for a fixed inventory level and a fixed waiting hall capacity, we determine the service rates for each slot. Using Markov decision theory, the problem is modeled. The optimal service rates are determined by linear programming using the stationary policy. To illustrate the model's behavior, we provide a numerical example.