Discrete MDP problem in service facility systems with inventory management

In this article, we consider a discrete time (equally spaced) service facility system in which arrival of customers to the system is controlled by taking decision at the beginning of each period. Customers arrive for service are placed in a specified queue called potential queue. Controller observes the number of customers in the system (eligible queue + server), the number of items in inventory and decides the quantity of customers to be admitted from the potential queue, others are rejected. Demands arrive throughout the period, but they are satisfied (service completion) only at the end of the period. Inventory is maintained in the server to satisfy the customers at the service completion time. Inventory is replenished instantaneously when the level become zero. The system is formulated as a Markov decision process. A stationary cost structure is imposed at each decision epoch and optimal policy is obtained by using policy iteration algorithm. A numerical example is provided to illustrate the problem.