Two phase genetic algorithm for vehicle routing and scheduling problem with cross-docking and time windows considering customer satisfaction

Cross-docking is a new warehousing policy in logistics which is widely used all over the world and attracts many researchers attention to study about in last decade. In the literature, economic aspects has been often studied, while one of the most significant factors for being successful in the competitive global market is improving quality of customer servicing and focusing on customer satisfaction. In this paper, we introduce a vehicle routing and scheduling problem with cross-docking and time windows in a three-echelon supply chain that considers customer satisfaction. A set of homogeneous vehicles collect products from suppliers and after consolidation process in the cross-dock, immediately deliver them to customers. A mixed integer linear programming model is presented for this problem to minimize transportation cost and early/tardy deliveries with scheduling of inbound and outbound vehicles to increase customer satisfaction. A two phase genetic algorithm (GA) is developed for the problem. For investigating the performance of the algorithm, it was compared with exact and lower bound solutions in small and large-size instances, respectively. Results show that there are at least 86.6% customer satisfaction by the proposed method, whereas customer satisfaction in the classical model is at most 33.3%. Numerical examples results show that the proposed two phase algorithm could achieve optimal solutions in small-size instances. Also in large-size instances, the proposed two phase algorithm could achieve better solutions with less gap from the lower bound in less computational time in comparison with the classic GA.