Robust Periodic Vehicle Routing Problem with Time Windows under Uncertainty: An Efficient Algorithm

Abstract

In a competitive environment, distributors engage in intense rivalry to meet the customers’ demands and accordingly earn maximum profits. Due to changes in customers’ demands, changes in a planned combination of customers to be visited in various days, traffic changes, etc., a sequence of visiting customers by competitors will be changed. So, planning for serving customers ahead of competitors will be uncertain. On the other hand, total transportation costs are also of high importance in distribution of goods. By keeping this issue in mind, we develop a bi-objective mathematical model to evaluate a Periodic Vehicle Routing Problem (PVRP) with time windows under uncertainty for companies competing to provide services to customers. The model is established using an improved scenario-based robust optimization approach. Given that the PVRP is an NP-hard problem, an Improved Differential Evolution (IDE) algorithm is used to identify efficient solutions for the model. The results on small-scale problems were compared with those obtained using the CPLEX solver. To evaluate the performance of the proposed IDE algorithm, a few sample tests on large-scale problems are conducted, and the results are compared with those derived using two other differential evolution algorithms. The findings show that the IDE algorithm exhibits suitable accuracy and performance in solving the presented model.