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In this paper the time-dependent sustainable vehicle routing problem is introduced as one of the less studied areas of VRP. Different challenges in city logistics including traffic congestion, path flexibility, and heterogeneous vehicles are also considered. The purpose of the problem is designing the service routes and determining optimal departure time from depot in a way that on the one hand, the amount of fuel consumed is minimized, and on the other hand, the workload of different drivers is balanced for more job satisfaction. Fuel consumption is a function of travelled distance, speed, load, and vehicle characteristics. The problem is formulated as a bi-objective MILP model and solved using augmented epsilon constraint method. To solve large-sized instances, two meta-heuristic algorithms based on genetic and fireworks algorithms are developed. In order to increase the efficiency of these algorithms, a clustering based heuristic method is proposed to generate good initial solutions. Numerical tests represent a better performance of the fireworks algorithm. Results show that striking workload balance among drivers has negligible effects on increment of fuel consumption. Also, optimization of departure time and stopping at the depot during rush hours has a considerable impact on the total fuel consumed.
Mirzabaghi et al. (Sun,) studied this question.