A new mathematical model for a competitive vehicle routing problem with time windows solved by simulated annealing

This paper presents an extension of a competitive vehicle routing problem with time windows (VRPTW) to find short routes with the minimum travel cost and maximum sale by providing good services to customers before delivering the products by other rival distributors. In distribution of the products with short life time that customers need special device for keeping them, reaching time to customers influences on the sales amount which the classical VRPs are unable to handle these kinds of assumptions. Hence, a new mathematical model is developed for the proposed problem and for solving the problem, a simulated annealing (SA) approach is used. Then some small test problems are solved by the SA and the results are compared with obtained results from Lingo 8.0. For large-scale problems, the, Solomon's benchmark instances with additional assumption are used. The results show that the proposed SA algorithm can find good solutions in reasonable time.