Two-echelon inventory model with controllable reorder point and lead time subject to service level constraint

This paper considers a two-echelon supply chain inventory problem consisting of single-supplier and 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 number of shipments from the supplier to the buyer during a production cycle. Instead of having the shortage cost in the objective function, a service level constraint is included in the model. 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. The results show that for k* = 0.65, the convexity behavior of the joint total expected cost (JTEC) with respect to m is stopped to confirm the value of JTEC at a higher values of m. Therefore, the optimal solution is known as the number of shipments m* = 3, lead time L* = 4 weeks, order quantity Q* = 145.07 units, and the JTEC = $6323.67/year. Finally, we then find out that the optimal reorder point R* = 55.25 units using the last step of the algorithm.