Optimal inventory modeling of supply chain system involving quality inspection errors and fuzzy defective rate

Abstract

In this paper an integrated vendor–buyer supply chain model is designed for a defective inventory product. We provide a simple mathematical model for determining an optimal vendor–buyer inventory policy by accounting for fuzzy defective rate and quality inspection errors at the buyer’s end. In this study we fuzzify the defective rate to the triangular fuzzy number in the expected total cost of the entire supply chain. We then used the signed distance method to defuzzify the fuzzy total cost of the system and a methodology has been proposed to minimize this cost. We frame an iterative algorithm procedure to achieve the optimal solution of delivery lot-size, the total number of deliveries from the vendor to the buyer in one production batch, and it has been illustrated by way of a numerical example. Also sensitivity analysis are given to demonstrate the performance of the proposed methodology. Our results indicate that the optimal solutions of the fuzzy case slightly fluctuate from the solutions of the crisp case.