Two-echelon supply chain inventory model with shortage, optimal reorder point, and controllable lead time

This paper considers a two-echelon supply chain inventory problem consisting of a single-supplier and a single-buyer. In the system under discussion, the supplier produces a product and supplies it to the buyer facing a stochastic demand condition. Buyer's lead time is controllable that can be shortened at an added cost. In addition, all shortages are backordered. A model is formulated for an integrated supplier-buyer problem to simultaneously determine the optimal order quantity, reorder point, lead time, and the number of shipments from the supplier to the buyer during a production cycle. The objective function is to minimize the total expected cost of the system. An algorithm is developed to obtain the optimal solution and a numerical example is also included to show the results of the proposed model.