Myopic policy for a two-product and multi-period supply contract with different delivery lead times and storage limitation

This paper considers a two-product and multi-period supply contract in which a buyer orders two products in each period from a supplier with two possible delivery lead times to satisfy multi-period random demands. The expedited one delivers the products immediately and the regular one requires a one-period delivery lead time. The supplier has two production modes. The expensive one produces the products immediately and the regular one requires a one-period production lead time. Unsatisfied demands at the buyer in a period are backordered and the demands must be satisfied in the next period. The two products at the buyer share storage space and there is a limitation on the storage space in each period. The buyer chooses an ordering policy in each period to minimize his expected cost during the planning horizon and the supplier chooses unit expedited ordering costs at the beginning of the planning horizon and a production policy in each period to maximize her expected profit during the planning horizon. We provide conditions under which the buyer's myopic ordering policy and the supplier's myopic production policy are optimal. Our simulation shows that the expedited delivery could benefit both the buyer and the supplier.