Developing a coordinated vendor–buyer model in two-stage supply chains with stochastic lead-times

This paper develops an approach to determine the optimal production and shipment policy for an integrated vendor–buyer problem. The vendor manufactures the product in batches at a finite rate and ships the output to the buyer. All shipments to the buyer are equal-sized batches. Despite previous papers in the literature, we assume that the supply lead-time between vendor and buyer is stochastic and shortage is also allowed. The objective is to minimize the expected total cost of both buyer and vendor. We derive the expected annual integrated total cost function and propose an analytic solution procedure to determine the optimal policy. To illustrate the significance of cost-reduction of the integrated approach in comparison with independent decisions by buyer or vendor, some numerical examples are also presented.