A supply chain model with defective items and disposal cost in a just-in-time (JIT) environment

Previous studies in the issue of supply chain models with imperfect quality assumed the defectives could be sold at lower unit price by the end of the inspection process and the lot-for-lot delivery policy was employed. However, in practice, defective items may have no salvage value but may need additional disposal cost to process them. The beginning of the printed circuit board (PCB) industry in Taiwan provides a good example of such a situation. Besides, in a just-in-time (JIT) environment, the supplier splits the order quantity into small lot size and delivers them over multiple periods to response the buyerʹs need. Therefore, in this paper, a new mathematical model were developed, in which defective items are processed with disposal cost and lot-splitting (single setup, multiple delivers) policy is employed, to determine an optimal single-supplier- single-buyer inventory policy. The objective is to minimize the total joint annual cost incurred by the vendor and buyer in a JIT environment. A procedure free of employing convexity is developed to determine the order quantity, the number of deliveries and the shipping quantity. Numerical example was provided to illustrate the effectiveness of the proposed model. Based on the numerical example, sensitivity analysis was given to investigate the effects of the defective percentage on the optimal solution.