Hossein Jandaghi - Department of Industrial Engineering, Babol Noshirvani University of Technology, Babol, Iran.
Ali Divsalar - Department of Industrial Engineering, Babol Noshirvani University of Technology, Babol, Iran.
Mohammad Mahdi Paydar - Department of Industrial Engineering, Babol Noshirvani University of Technology, Babol, Iran.

In this research, a new bi-objective routing problem is developed in which a conventional vehicle routing problem with time windows (VRPTW) along with its environmental impacts and heterogeneous vehicles is considered. In this problem, minimization of fuel consumption (liter) as well as reduction of the length of the routes (meter) are themain objectives of this study. Therefore, a mathematical bi-objective model is solved to create Pareto s solutions. The objectives of the proposed mathematical model are to minimize the sum of distance costs as well as fuel consumption and Co2 emission. Then, the proposed Mixed-Integer Linear Program (MILP) is solved using the ε-constraintapproach. Furthermore, numerical tests are performed to quantify the benefits of using a comprehensive goal function with two different objectives. Managerial insights and sensitivity analysis are also performed to show how different parameters of the problem affect the computational speed and the solutions’ quality.

Vehicle routing problem;Time windows; Fuel consumption; Co2 emission; ε- constraint; Environmental impacts.