A Coordinated Supply Chain Model for Imperfect Items under Power Function Lead Time Crashing Cost and Investment with a Service Level Constraint

This paper presents a coordinated vendor-buyer supply chain model in two stages with imperfect quality items, lead time and ordering cost reduction, and service level constraint. It is assumed that each arrival lot received by the buyer contains a percentage of imperfect quality items which follows a uniform distribution. A 100% screening process for detecting the defective items is conducted. Lead time crashing cost and investment for ordering cost reduction follow power function distribution. The shortage during the lead time is permitted and backordered partially for the buyer. However, the level of shortage is limited by service level constraint policy. The optimal order quantity, reorder point, lead time, ordering cost, and the number of delivery are determined by the Lagrange method such that joint total cost of the system is minimized and the service level constraint is satisfied. An iterative procedure is developed to determine the optimal solution and a numerical example is presented to illustrate the result of the proposed model.