Optimum profit model considering single sampling inspection plan and quality loss of product

In 2007, Chen and Liu's model presented the optimum profit model between the producers and the purchasers for the supply chain system. However, their model with simple manufacturing cost did not consider the used cost of customers in pure procurement policy. Hence, the modified Chen and Liu's model should be addressed for determining the optimum product and process parameters. In this study, the author proposes a modified Chen and Liu's model considering single sampling inspection plan and quality loss of product. Assume that the demand quantity of the customer is independent with the quality characteristic of product. Taguchi's (1986) symmetric quadratic quality loss function will be applied in evaluating the product quality. The optimum purchaser's order quantity and the producer's wholesale price and process quality level will be jointly determined by maximizing the expected profit between the producers and the purchasers.