A Vehicle Routing Problem Considering a Balance of Goods Based on the Vehicle's Capacity by Improved Particle Swarm Optimization

This paper presents a new method for solution of a vehicle routing problem, which considers a balance of goods based on the vehicles’ capacity. A considerable part of the drivers’ benefits is related to their quantity of sales; therefore, the balance of goods based on vehicles’ capacities is important to obtain drivers’ satisfaction. This is one of the objectives of this paper, alongside minimizing the travel costs. Due to the complexity of solving such a difficult problem with exact methods in large-scale applications, a meta-heuristic method based on improved particle swarm optimization (IPSO) has been proposed. In addition, to show the efficiency of the proposed IPSO, a number of test problems in both small and large scales have been considered and solved. Then, the results obtained by calculation have been evaluated with the results obtained by the Lingo software. Furthermore, to run the proposed IPSO, a real case study in a dairy company located in Qazvin with 152 customers has been studied, and finally, the obtained results have been reported and discussed.