A Mathematical Location-Inventory Model for Designing a Forward /Backward Logistic Network under Demand and Return Uncertainty with Multiple Capacity Levels

Today, the competitive business environment has led to increasing cooperation among companies as the members of supply chain networks. In this area, the supply chain logistics network design is an important subject due to its effect on the responsiveness and efficiency. Over the past few years, due to environmental issues, their legal requirements and economic benefits, great attention has been paid to inverse logistics. In this paper, a mixed integer stochastic location-inventory model has been proposed for the integrated design of the network of a multi-period multi-product closed loop supply chain considering multiple capacity levels for facilities. The market demand and correspondingly the return value are considered to be uncertain in order to make the model close to the real-life conditions. Since the capacitated facility location problem considered in this research is an NP-hard type problem, we have used two meta-heuristic algorithms including the genetic algorithm (GA) and the Bees algorithms (BA) for solving this problem. Some numerical problems are designed and solved to assess the performance of the model and solution heuristics. From the viewpoint of solution quality, the BA outperforms the GA (by an average of 11.6%) whilst from the viewpoint of solution time, the GA is five times faster than the BA on average.