This paper presents a novel multi-objective mathematical model of a periodic vehicle routing problem (PVRP) in a competitive situation for obtaining more sales. In such a situation, the reaching time to customers affects the sale amount; therefore, distributors intend to service customers earlier than other rivals for obtaining the maximum sale. Moreover, a partial driver's benefit is related to the amount of their sale; thus, the balance of goods based on the vehicles capacity is important. Due to its complexity, it is so difficult to optimally solve this problem in a reasonable computational time. Hence, two algorithms are proposed based on multi-objective particle swarm optimization (MOPSO) and NSGAII algorithm. A comparison of our results with three performance metrics confirms that the proposed MOPSO is an efficient algorithm for solving the competitive PVRP with a reasonable computational time.
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