A Green Vendor Managed Inventory of a Multi-item Multi-retailer EPQ model under Fuzzy Environment with Stochastic Constraints: A Geometric Programming Approach

The purpose of this paper is to develop a multi-item multi-constraint EPQ model with shortage in the form of backorder for a single-vendor multi-retailer supply chain under vendor managed inventory (VMI) policy. Due to the rising concern in environmental conservation, green supply chain is considered in this paper. To include an extended applicability in real-world situations, three constraints are assumed in stochastic form. In addition, demands are considered imprecise. Since the model is developed in multi-product form, for the vendor's fixed ordering cost different conditions are considered. Geometric programming (GP) approach is employed to find the optimal solution of the model with the objective of minimizing the total cost of the system. Since the model contains signomial terms, an algorithm is utilized to convert the model into the standard form of GP. To evaluate the performance of the model and the solving method, computational experiments are presented.