Evaluating of the particle swarm optimization in a periodic vehicle routing problem

•Presenting a new mathematical approach for measuring and evaluating the performance of the vehicle routing problem.•Introducing a new class of PVRP with competitive time windows.•Measuring efficiency of improved particle swarm optimization.•The performance of the proposed method, is measured using an exact algorithm.•The problem takes into account both efficiency and practical.

This paper presents a new mathematical model for measuring and evaluating efficiency of periodic vehicle routing problem (PVRP) that arises in a competitive environment. In the competitive environment several distributors are in competition and arriving to the customers earlier than other competitors affect amount of the sale. The main objectives are to minimize the travel cost and maximize the sale to serve customers before other rival distributors. To measuring the efficiency of the problem an improved particle swarm optimization (IPSO) algorithm is proposed and it compared with an original PSO algorithm in terms of accuracy. Computational results indicate that the improved PSO algorithm performs well in terms of accuracy but the original PSO performs better in computational time.