A new vendor-managed inventory four-tier model based on reducing environmental impacts and optimal suppliers selection under uncertainty

. For the best implementation of (vendor-managed inventory) VMI, a vendor must choose the optimal combination of suppliers that can better meet the criteria of environmental problems. In VMI, a vendor controls some retailers' inventory decisions. This study aims to select the best suppliers in the green VMI and assign orders to them. In this study, the vendor selects suppliers by accounting for various factors, including quality factors, delivery reliability, and the reduction of the return percentage of raw materials in the developed mathematical model. For this purpose, this paper applies the Bayesian best worst approach (BWM), as one of the multi criteria decision making (MCDM) techniques, for ranking these criteria and the fuzzy technique for order of preference by similarity to ideal solution (FTOPSIS) for prioritizing the suppliers. Then, the obtained weights are plugged into the model as the inputs of the proposed model. Since the developed model is a non-differentiable, non-convex, and mixed-integer function, genetic algorithm (GA) and particle swarm optimization (PSO) are leveraged to solve the formulated model. Finally, the efficiency of the presented method is verified through a case study with actual data collected from the electronic supply chain.