A Markovian Dual-Source Production-Inventory Model with Order Bands

We present a Markovian model of a single rm engaging in a periodic review inventory policy to procure goods from two alternate suppliers. Each supplier quotes a state-dependent minimum order quantity, maximum order quantity, and unit price. The purchasing rm faces state-dependent unit inventory holding costs, as well as backorder/penalty costs if they are unable to immediately satisfy their customer demand. We show that a modi ed base-stock policy is optimal in the situation where the suppliers have lead times which di er by one time unit. This policy is de ned by a vector of pairs of numbers { one for each lead time { indexed by the states of the Markov chain. In each state the rm will place orders as close to these two indices as possible, while satisfying the stipulated minimum and maximum order sizes. In addition, we demonstrate that use of In nitesimal Perturbation Analysis, or IPA, to compute the optimal vector of inventory levels is valid for arbitrary lead times, which subsumes the case of lead times di ering by one unit. For general lead times it is known that the structure of the optimal policy can be extremely complex; therefore for problems of this type solutions are usually restricted to the class of order-up-to policies. GSIA Working Paper # 1998-E200