A Bi-Objective Vehicle-Routing Problem with Soft Time Windows and Multiple Depots to Minimize the Total Energy Consumption and Customer Dissatisfaction

Abstract

In recent years, the impact of the energy crisis and environment pollution on quality of life has forced industry to actively participate in the development of a sustainable society. Simultaneously, customer satisfaction improvement has always been a goal of businesses. It is recognized that efficient technologies and advanced methods can help transportation companies find a better balance between progress in energy saving and customer satisfaction. This paper investigates a bi-objective vehicle-routing problem with soft time windows and multiple depots, which aims to simultaneously minimize total energy consumption and customer dissatisfaction. To address the problem, we first develop mixed-integer programming. Then, an augmented ϵ -constraint method is adopted to obtain the optimal Pareto front for small problems. It is very time consuming for the augmented ϵ -constraint method to precisely solve even medium-sized problems. For medium- and large-sized problems, two Non-dominated Sorting Genetic Algorithm-II (NSGA-II)-based heuristics with different rules for generating initial solutions and offspring are designed. The performance of the proposed methods is evaluated by 100 randomly generated instances. Computational results show that the second NSGA-II-based heuristic is highly effective in finding approximate non-dominated solutions for small-size and medium-size instances, and the first one is performs better for the large-size instances.