On a production-inventory system with defective items and lost sales

Abstract

A production-inventory system with the item produced being admitted (added to the inventory) with probability δ as well as an item from the inventory supplied to the customer with probability γ at the end of a service, is considered in this paper. The (s, S) control policy is followed. We obtain the joint distribution of the number of customers and the number of items in the inventory as the product of their marginals under the assumption that customers do not join when the inventory level is zero. Performance measures that impact the system are obtained. A few level-crossing results are derived. In particular optimal pairs (s, S) are obtained through numerical procedures for values of (γ, δ) on the set {0.1, 0.2, . . . , 1} × {0.1, 0.2, . . . , 1} . A comparison of the performance measures for a few (γ, δ) pair values is provided. Finally, we discuss the first emptiness time distribution for the M/M/1/1 production-inventory system.