Bi-Objective green vehicle routing problem minimizing carbon emissions and maximizing service level

In this study, a bi-objective Green Vehicle Routing Problem is presented as an extension of the well-known Vehicle Routing Problem. Green Vehicle Routing Problem aims to improve routing decisions of companies using Alternative Fuel Vehicles to reduce carbon emissions. The presented problem herein has two objectives that are the minimization of total carbon emissions and the maximization of service level. While total carbon emission is assumed to be proportional to total distance, cargo delivery time window violations of customers are considered as an indicator of service level. The problem was modeled as Mixed-Integer Linear Programming and epsilon-constraint method, which is a multi-objective optimization method, is developed to solve it. To effectively solve large problem instances, a clustering-based heuristic method is proposed. The heuristic method achieved a good performance by finding near Pareto-optimal solutions that are found by the MILP model. Our proposed mathematical model and heuristic method are tested on seven realistically designed hypothetical case studies. According to the results, the minimization of carbon emission and maximization of service level are two conflicting objectives. As the service level increases, the number of vehicles and carbon emissions also increase. As carbon emission increases and time windows violation decreases, more vehicles and alternative fuel stations are used.