An integrated production-distribution inventory system for deteriorating products involving fuzzy deterioration and variable setup cost

An integrated two-stage supply chain system with one supplier and one buyer for deteriorating products is considered in this study to face growing setup cost and fuzzy random deterioration rate in the real-life inventory management. This study offers strategic decision-making to produce and supplies products in order to minimize total system cost under fuzzy deterioration rate and variable setup cost environment. We consider the cases where the deterioration rate is treated as the triangular fuzzy number and the setup cost is a function of capital expenditure. We then determine the optimal policy for the proposed model using the differential calculus optimization technique after the defuzzification of the total cost function with the signed distance method. Numerical example and sensitivity analysis are given to demonstrate the application and the performance of the proposed methodology. Some managerial implications are also included.