A seller-buyer supply chain model with exponential distribution lead time

Supply chain is an accepted way of remaining in the competition in today's rapidly changing market. This paper presents a coordinated seller-buyer supply chain model in two stages, which is called Joint Economic Lot Sizing (JELS) in literature. The delivery activities in the supply chain consist of a single raw material. We assume that the delivery lead time is stochastic and follows an exponential distribution. Also, the shortage during the lead time is permitted and completely back-ordered for the buyer. With these assumptions, the annual cost function of JELS is minimized. At the end, a numerical example is presented to show that the integrated approach considerably improves the costs in comparison with the independent decisions by seller and buyer.