Eoq Analysis under Stochastic Production and Demand Rates

In this paper we study a type of production-inventory system in which the production and demand rates are modulated by a background state process modeled as a finite state Continuous Time Markov Chain (CTMC). When the production rate exceeds the demand rate, the inventory level increases, and when the demand rate exceeds the production rate, it decreases. When the inventory level reaches zero, an order is placed from an external supplier, and it arrives instantaneously. We model this system as a bivariate Markovian stochastic process and derive the limiting distribution of the inventory level. Assuming linear holding costs and fixed ordering costs, we show that the classical deterministic Economic Order Quantity (EOQ) policy minimizes the long-run average cost if one replaces the deterministic demand rate by the expected demand production rate in steady state. Finally, we extend the model to allow backlogging.