A Scenario-based Robust Optimization Model for a Periodic Vehicle Routing Problem with Time Windows under Uncertainty by Using a Differential Evolution Algorithm

A vehicle routing problem is an important problem that has attracted great attention of researchers in recent years. This paper presents a model for evaluating the efficiency of a periodic vehicle routing problem (PVRP) to get the short routes with maximum sale by providing suitable services to customers before delivering the goods by other competitor distributors. In the goods distribution with short lifetime that customers need a special device for keeping them, the arriving time to customers influence on the sales amount, in which classical VRPs are unable to calculate this kind of assumptions. According to real world applications, the arriving time of the competitors is uncertain because of customer demands, traffic, weather conditions, and the like. A scenario approach is used to handle the uncertainty of the arriving time of rivals. The purpose of this paper is to solve this problem by optimizing the sale of products to customers before delivering the products to other competitor distributors in an uncertain condition by robust optimization. To evaluate the presented model, a number of test problems are solved by two strategies of a differential evolution (DE) algorithm and the results are compared with the results obtained by the CPLEX method in GAMS in small and medium sizes. To evaluate the proposed algorithm for solving large-scale problems, some problems are carried out and the results are compared in term of their accuracy. The computational results represent the capability of the proposed DE strategies in solving large-scale problems in a reasonable time.