Setup cost reduction in an integrated production inventory system for defective items with service level constraint and delay in payments

In this article, we have developed a two level supply chain model for defective items with controllable lead time in an imperfect production process. Trade credit offered by the supplier to the retailer is considered. The lead time demand follows a normal distribution and the lead time is crashed. The vendor's setup cost is reduced by an extra added cost. A mathematical model is derived to obtain the optimal number of shipments delivered from vendor to buyer in a production cycle, the order quantity, lead time and setup cost with the objective of minimizing the total expected cost. The theory developed in this article is illustrated using a numerical example. Managerial insights and the effect of key parameters are studied through sensitivity analysis to analyze the behavior of model.