An inventory and order admission control policy for production systems with two customer classes

In this paper we examine a Markovian single‐stage system producing a single item to satisfy demand of two different customer classes. A simple threshold type heuristic policy is proposed for the joint control of inventories and backorders. Explicit forms of the steady‐state probabilities under this policy are derived and used to assess the average profit rate of the system and determine the optimal control parameters. Certain properties of the average profit rate are established and used to develop computationally efficient algorithms for finding the optimal control parameter values. Numerical results show that the proposed policy is a very good approximation of the optimal policy and outperforms other commonly used policies.