(s, S) Inventory Systems with Correlated Demands

Most inventory models in the literature assume that demands are independent among different time periods. However, a number of recent studies suggest that demands are often correlated over different time periods, which motivates our work here. In this paper, we study a class of periodic review (s, S) inventory systems in which demands are correlated and modeled as a Markov-modulated process. Using a Maclaurin series analysis and a Pade approximation, as well as an infinite system of linear equations, we develop algorithms to calculate the moments of the inventory level based on which various performance measures of the system can also be evaluated. Numerical experiments show that our approach is quite efficient and provides accurate estimates for the moments of the inventory level and other related performance measures.