A green vehicle routing problem with customer satisfaction criteria


1 Faculty of Industrial Engineering, Alborz Campus, University of Tehran, Tehran, Iran

2 Department of Economics and Social Sciences, Shahid Chamran University of Ahvaz, Ahvaz, Iran

3 Operations and Production Management Department, Faculty of Management, University of Tehran, Tehran, Iran

4 UNIDEMI, Department of Mechanical and Industrial Engineering, Faculty of Science and Technology, Universidade Nova de Lisboa, Lisbon, Portugal

5 Faculty of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran


This paper develops an MILP model, named Satisfactory-Green Vehicle Routing Problem. It consists of routing a heterogeneous fleet of vehicles in order to serve a set of customers within predefined time windows. In this model in addition to the traditional objective of the VRP, both the pollution and customers’ satisfaction have been taken into account. Meanwhile, the introduced model prepares an effective dashboard for decision-makers that determines appropriate routes, the best mixed fleet, speed and idle time of vehicles. Additionally, some new factors evaluate the greening of each decision based on three criteria. This model applies piecewise linear functions (PLFs) to linearize a nonlinear fuzzy interval for incorporating customers’ satisfaction into other linear objectives. We have presented a mixed integer linear programming formulation for the S-GVRP. This model enriches managerial insights by providing trade-offs between customers’ satisfaction, total costs and emission levels. Finally, we have provided a numerical study for showing the applicability of the model.