Flexible service policies for a Markov inventory system with two demand classes

This paper explores flexible service policies for an (r, Q) Markov inventory system with two classes of customers, ordinary and prioritized customers. When the on-hand inventory drops to pre-determined safety level r, arrival ordinary customers receive service at probability p. Firstly, the inventory level state transitions equation is set up. The steady-state probability distribution and the system's performance measures which are used for the inventory control are derived. Next, a long-run average inventory cost function is established and a mixed integer optimization model is set up. And, an improved genetic algorithm for the optimum control policies is presented. Finally, the optimal inventory control polices and the sensitivities are investigated through numerical experiments.