In the study of stochastic inventory systems it is generally assumed that the demand epochs are renewable in nature. The present paper deals with a single-item (s, S) inventory model with a finite number of different types of demands, in which the demand epochs form a Markov renewal process. The lead times are exponentially distributed and the demands that occur during stockout periods are not backordered. For this model the transient and limiting inventory level distributions are computed. Also the theory of point processes is used to obtain the mean reorder and shortage rates and their limiting values. For the special case of renewal demands, the problem of minimizing the long-run expected cost rate is analysed. © 1989.
Kalpakam, S., & Arivarignan, G. (1989). (s, S) Inventory systems with lost sales and Markov renewal demands. Mathematical and Computer Modelling, 12(12), 1511–1520. https://doi.org/10.1016/0895-7177(89)90328-2