Optimum profit model considering production, quality and sale problem

Chen and Liu [‘Procurement Strategies in the Presence of the Spot Market-an Analytical Framework’, Production Planning and Control, 18, 297–309] presented the optimum profit model between the producers and the purchasers for the supply chain system with a pure procurement policy. However, their model with a simple manufacturing cost did not consider the used cost of the customer. In this study, the modified Chen and Liu's model will be addressed for determining the optimum product and process parameters. The authors propose a modified Chen and Liu's model under the two-stage screening procedure. The surrogate variable having a high correlation with the measurable quality characteristic will be directly measured in the first stage. The measurable quality characteristic will be directly measured in the second stage when the product decision cannot be determined in the first stage. The used cost of the customer will be measured by adopting Taguchi's quadratic quality loss function. The optimum purchaser's order quantity, the producer's product price and the process quality level will be jointly determined by maximising the expected profit between them.