A simulated annealing algorithm for solving two-echelon vehicle routing problem with locker facilities

We consider the problem of utilizing the parcel locker network for the logistics solution in the metropolitan area. Two-echelon distribution systems are attractive from an economic standpoint, whereas the product from the depot can be distributed from or to intermediate facilities. In this case, the intermediate facilities are considered as locker facilities present in an accessible location in the vicinity of the final customers. In addition, the utilization of locker facilities can reduce the cost caused by the unattended deliveries. The problem is addressed as an optimization model that formulated into an integer linear programming model denoted as the two-echelon vehicle routing problem with locker facilities (2EVRP-LF). The objective is to minimize the cost of transportation with regards to the vehicle travelling cost, the intermediate facilities renting cost, and the additional cost to compensate the customer that needs to travel to access the intermediate facilities. Because of its complexity, a simulated annealing algorithm is proposed to solve the problem. On the other hand, the modelling approach can be conducted by generating two-phase optimization model approaches, which are the p-median problem and the capacitated vehicle routing problem. The results from both methods are compared in numerical experiments. The results show the effectiveness of 2EVRP-LF compared to the two-phase optimization. Furthermore, the simulated annealing algorithm showed an effective performance in solving 2EVRP-LF.