In this paper, a bi-level decision making model is proposed for a vehicle routing problem with multiple decision-makers (VRPMD) in a fuzzy random environment. In our model, the objective of the leader is to minimize total costs by deciding the customer sets, while the follower is trying to minimize routing costs by choosing routes for each vehicle. Demand for each item has considerable uncertainty, so customer demand is considered a fuzzy random factor in this paper. After setting up the bi-level programming model for VRPMD, a bi-level global-local-neighbor particle swarm optimization with fuzzy random simulation (bglnPSO-frs) is developed to solve the bi-level fuzzy random model. Finally, the proposed model and method are applied to construction material transportation in the Yalong River Hydropower Base in China to illustrate its effectiveness.

Keywords: Vehicle routing optimization, Multiple decision-makers, Construction material transportation, Fuzzy random variable, Particle swarm optimization

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