Open vehicle routing problem with moving shipments at the cross-docking terminal

Abstract

In this study, one of the internal operations at the Cross-docking Terminal (CDT), moving shipments (MS) from receiving doors to shipping doors of CDT is integrated with Open Vehicle Routing Problem (OVRP) and the problem is indicated here as OVRPCD-MS. As an additional feature, asymmetric distance between any two customers is assigned by incorporating a characteristic of one-way routes between cities in real-life transportation. The objective is to minimize the total transportation cost which incurs travelling cost between customers, service cost at customer points, service cost at the receiving and shipping doors of CDT, cost of moving shipments inside the CDT and finally the cost of hiring fleets of vehicles. To solve the OVRPCD-MS problem, a Mixed Integer Linear Programming (MILP) model is developed. The programming models are implemented in LINGO (version 18) optimization software. Branch and Bound algorithm is employed to solve ten small-scale instances generated randomly. The applicability of the proposed MILP model is observed. The required fleets of vehicles to be hired and run time to reach the optimal solution are determined. The study revealed that the average run time is exponential for small-scale instances. Thus, it can be concluded that this proposed model can be used for last time planning for small-scale instances. Also, the combinatorial nature of the vehicle routing problem makes OVRPCD-MS as NP-hard. Therefore, this study recommends that heuristic or meta-heuristic methods are more appropriate for the large-scale instances of OVRPCD-MS to reach near-optimum solutions.