An Optimization Model for the Hard Time Windows Vehicle Routing Problem with Moving Shipments at the Cross Dock Center

Abstract

Cross-Docking (CD) technique was initiated in the 1930s to make a cost-effective supply chain. Vehicle Routing Problem (VRP) is one of the widely discussed optimization problems. The research on integration of VRP with CD (VRPCD) was initiated at the beginning of 2000s. Moving Shipments (MS) from receiving doors to shipping doors is an activity inside a Cross-Dock Centre (CDC). This study mainly considers MS as an additional aspect in the literature of VRPCD. In this study, not only loading or unloading shipments at all the nodes including CDC and homogenous fleets of vehicles within pickup or delivery process are considered, but also aspects of heterogeneous fleets of vehicles between pickup and delivery processes are considered. Furthermore, Time Windows (TW) characteristics are also considered here. A mixed integer nonlinear programming model is developed to obtain the optimal solutions to hard time windows vehicle routing problem with moving shipments at the cross-dock centre (TW-VRPCD-MS). The compatibility of the proposed model is tested using sixteen randomly generated small scale instances. Since the average computational time is reasonably less for the tested instances, it can be concluded that this proposed model can be used for last time planning for similar small-scale problems. Further analysis revealed that the convergence rate to reach the optimal solution rises exponentially with the scale of the problem. Therefore, this study recommends in applying heuristic or metaheuristic techniques to solve large scale instances of TW-VRPCD-MS to obtain a near optimal solution in a reasonable computational time.