Incorporating a Reverse Logistics Scheme in a Vehicle Routing Problem with Cross-Docking Network: A Modelling Approach

Reverse logistics has been implemented by various companies because of its ability to gain more profit and maintain the competitiveness of the company. However, extensive studies on the vehicle routing problem with cross-docking (VRPCD) only considered the forward flow instead of the reverse flow. Motivated by the ability of a VRPCD network to minimize the distribution cost in the forward flow, this research incorporates the reverse logistics scheme in a VRPCD network, namely the VRP with reverse cross-docking (VRPRCD). We propose a VRPRCD mathematical model for a four-level supply chain network that involves suppliers, cross-dock, customers, and outlets. The main objective is to minimize vehicle operational and transportation costs. Experimental results show that only small instances of newly generated VRPRCD instances can be optimally solved by CPLEX. Furthermore, we present sensitivity analysis towards the cost structure.