A bi-objective vehicle routing problem with time windows and multiple demands

Abstract

In the real world, the demands for some specific goods may increase in some special occasions. At such conditions, in-time delivery of the desired goods and minimization of the traveling costs will be found crucial importance for the customers and the suppliers, respectively. In this paper, a new mathematical model consisting of two objectives: minimizing traveling costs and maximizing customers’ demand satisfaction was proposed through a multi-objective optimization approach. The nonlinear equations were converted to linear equations and the proposed model was then solved using CPLEX solver by GAMS23.6.3 software. Two approaches were proposed to solve the problem based on the NSGA-II algorithm with different modifications in the mutation operator. A two-row structure was also employed for the chromosomes. This research contributes to vehicle routing literature considering time windows, multiple demands, and two conflict objectives and proposes two metaheuristic algorithms. The algorithm results were also compared with two criteria: covered non-dominated solutions and spread solutions. The results show that the improvements were made with the variation in the mutation operator in both criteria. In summary, the developed vehicle routing mathematical model works effectively for some real-world logistic problems with occasional goods, and the customer satisfaction in due time is incorporated in the mathematical model.

Keywords

• Vehicle routing
• Bi-objective problem
• Time-windows
• Multi-demands
• NSGA-II
• Pareto solutions