Closed-loop Inventory Routing Problem for returnable transport items

Increasing concerns on supply chain sustainability have given birth to the concept of closed-loop supply chain. Closed-loop supply chains include the return processes besides forward flows to recover the value from the customers or end-users. Vendor Managed Inventory (VMI) systems ensure collaborative relationships between a vendor and a set of customers. In such systems, the vendor takes on the responsibility of product deliveries and inventory management at customers. Product deliveries also include reverse flows of returnable transport items. The execution of the VMI policy requires vendor to deal with a Closed-loop Inventory Routing Problem (CIRP) consisting of its own forward and backward routing decisions, and inventory decisions of customers. In CIRP literature, traditional assumptions of disregarding reverse logistic operations, knowing beforehand distribution costs between nodes and customers demand, and managing single product restrict the usage of the proposed models in current food logistics systems. From this point of view, the aim of this research is to enhance the traditional models for the CIRP to make them more useful for the decision makers in closed-loop supply chains. Therefore, we propose a probabilistic mixed-integer linear programming model for the CIRP that accounts for forward and reverse logistics operations, explicit fuel consumption, demand uncertainty and multiple products. A case study on the distribution operations of a soft drink company shows the applicability of the model to a real-life problem. The results suggest that the proposed model can achieve significant savings in total cost and thus offers better support to decision makers.