A new bi-objective periodic vehicle routing problem with maximization market share in an uncertain competitive environment.

This paper presents a new variant of periodic vehicle routing problem in which the reaching time to the customers affects market share. Thus, there is a competition between distributors to achieve more market share by reaching the customers earlier than others; moreover, travel time between each two pairs of customers is uncertain. This situation is called an uncertain competitive environment. For the given problem, a new bi-objective mathematical model including minimization of total traveled time and maximization of the market share is presented. In order to solve this model, a multi-objective particle swarm (MOPSO) and local MOPSO algorithms are applied; and to evaluate the algorithm performance, some samples are generated; and the results of algorithms are compared based on some comparison metrics. The results demonstrate that the proposed LMOPSO algorithm leads to a better performance compared to the MOPSO in most comparison metrics. [ABSTRACT FROM AUTHOR]