Inventory models of future supply uncertainty with single and multiple suppliers

The authors consider order-quantity/reorder-point inventory models where the availability of supply is subject to random fluctuations. They use concepts from renewal reward processes to develop average cost objective function models for single, two, and multiple suppliers. Identifying the regenerative cycle for each problem aids the development of the cost function. In the case of two suppliers, spectral theory is used to derive explicit expressions for the transient probabilities of a four-state continuous-time Markov chain representing the status of the system. These probabilities are used to compute the exact form of the average cost expression. For the multiple-supplier problem, assuming that all the suppliers have similar availability characteristics, the authors develop a simple model and show that as the number of suppliers becomes large, the model reduces to the classical EOQ model.