Providing Sustainable Inventory Management Model with Stochastic Free Distribution Demand in Single-Level Supply Chain

Today, in supply chain, we are faced with new approaches that address environmental, social and economic considerations, which complicates most of its issues, and in particular the field of inventory management. One of these approaches is a sustainability approach. The current research considers a sustainable inventory problem in which lead time demand is a random variable. Also, distribution function is unknown and its mean and Variance is defined. This research applies min-max approach to solve this problem and uses Scarf’s bound to optimize the problem function for the worst case (worst demand distribution function). The results of optimization for considered problem showed that sustainability dimensions has an important role in determination of EOQ, also, suitable transportation equipment for transferring orders and ultimately total costs of a system. So, because of attaining to environmental costs, in the farther distances, as the distance between ordering point and order supply increases, the transportation equipment selects one in which consumes lower energy and it increases ordering size.