A Sharp Bound for the Ergodic Distribution of an Inventory Control Model Under the Assumption That Demands and Inter-Arrival Times Are Dependent

Abstract

In this study, a stochastic process which represents a single-item inventory control model with (s, S)-type policy is constructed when the demands of a costumer are dependent on the inter-arrival times between consecutive arrivals. Under the assumption that the demands can be expressed as a monotone convex function of the inter-arrival times, it is proved that this process is ergodic, and closed form of the ergodic distribution is given. Moreover, a sharp lower bound for this distribution is obtained. © 2014 Hanalioǧlu (Khaniyev) and Aksop.