A two-echelon supply chain management with setup time and cost reduction, quality improvement and variable production rate

This model investigates the variable production cost for a production house; under a two-echelon supply chain management where a single vendor and multi-retailers are involved. This production system goes through a long run system and generates an out-of-control state due to different issues and produces defective items. This model considers the reduction of the defective rate and setup cost through investment. A discrete investment for setup cost reduction and a continuous investment is considered to reduce the defective rate and to increase the quality of products. Setup and processing time are dependent on lead time in this model. The model is solved analytically to find the optimal values of the production rate, safety factors, optimum quantity, lead time length, investment for setup cost reduction, and the probability of the production process going out-of-control. An efficient algorithm is constructed to find the optimal solution numerically and sensitivity analysis is given to show the impact of different parameters. A case study and different cases are also given to validate the model.