Vehicle routing problem with simultaneous pickups and deliveries and time windows considering fuel consumption and carbon emissions

Taking the cost of fuel consumption and carbon dioxide emissions into account, this paper studies the vehicle routing problem with simultaneous pickups and deliveries and time windows (VRP-SPDTW). Firstly, the mathematical model is proposed to describe the problem VRP-SPDTW. The model takes minimizing the total cost as its objective function and decides how many vehicles are employed to service the clients, which clients each vehicle services and in what order each vehicle services its clients. In the objective function the total cost is composed of fuel consumption and carbon dioxide emissions, the startup cost of vehicles, depreciation charge of vehicles and personnel cost. Then an improved genetic algorithm, which adopts effective encoding and a specific crossover operator, is designed to solve the problem. The simulation experiment results show that the algorithm can get a global satisfactory solution, and the loading rate of each vehicle is very high. Hence the mathematical model and the algorithm proposed in this paper can provide a good idea to solve the similar combinational optimization problems.