Fuzzy integrated production-distribution planning problem with the maximum NPV of cash flows in a closed-loop supply chain network

The environmental coefficients and parameters are normally indefinite or inexact due to incomplete and imperfect or unavailable information, in the real-world production-distribution decision planning problems in closed-loop supply chains. This work presents an integrated production-distribution planning linear model with the aim of maximizing the net present value of cash flows under a fuzzy environment. The proposed model for a network of closed-loop supply chain (CLSC), including suppliers, manufacturing plants and customers is presented. Also, the objective function coefficients and customer demand are assumed to be triangular fuzzy numbers. The proposed approach attempts to minimize the total production-distribution costs by considering the cost model includes the cost of raw material procurement, production, warehousing, transportation, and are reworking. We present a fuzzy developed method for the proposed fuzzy model, that the fuzzy problem into a linear programming model. The main advantage of the proposed model is that it presents a systematic framework that production/distribution fuzzy decision-making for solving the production-distribution planning problems with net present value of cash flows and multi-time period in three-echelon closed-loop supply chains under an uncertain environment. At the end, the performance of the developed approach is illustrated by using a hypothetical numerical example and the results of the proposed model are discussed.