Vehicle routing problem (VRP) is about finding optimal routes for a fixed fleet of vehicles in order that they can meet the demands for a set of given customers by traveling through those paths. This problem and its numerous expansions are one of the most important and most applicable transportation and logistics problems. In this study, the green vehicle routing and scheduling problem with heterogeneous fleet including reverse logistics in the form of collecting returned goods along with weighted earliness and tardiness costs is studied to establish a trade-off between operational and environmental costs and to minimize both simultaneously. In this regard, a mixed integer non-linear programming (MINLP) model is proposed. Since the problem is categorized as NP-hard, two meta-heuristics, a simulated annealing (SA) and a genetic algorithm (GA) are suggested in order to find near-optimal solutions for large instances in a reasonable computational time. The performances of the proposed algorithms are evaluated in comparison with the mathematical model for small-sized problems and with each other for problems of all size using a set of defined test problems. Analysis of the results considering two criteria: solutions quality and computational times, indicates the satisfactory performance of the presented algorithms in a proper computational time. Meanwhile, a statistical hypothesis testing (T-test) is conducted. It can generally be observed that SA achieves relatively better results in terms of solution quality, while GA spends less computational time for all-sized test problems. Eventually, sensitivity analysis is conducted to investigate the effect of collecting returned goods on the cost of total CO${}_2$ emissions, variable costs of the fleet and the objective function value.

车辆路线问题（VRP）是为固定车队找到最佳路线，以使其能够通过这些路线行驶来满足一组给定客户的需求。这个问题及其众多扩展是最重要，最适用的运输和物流问题之一。在这项研究中，研究了具有异类车队的绿色车辆的路线和调度问题，其中包括以回收退货的方式进行逆向物流以及加权的提前期和延误成本，以建立运营成本与环境成本之间的权衡并同时最小化两者。在这方面，提出了混合整数非线性规划（MINLP）模型。由于该问题被归类为NP-hard，因此有两种元启发式算法，为了在合理的计算时间内为大型实例找到接近最优的解决方案，建议使用模拟退火（SA）和遗传算法（GA）。使用一组定义的测试问题，将所提出算法的性能与数学模型进行比较，以评估小问题，并评估所有大小的问题。考虑两个标准的结果分析：解决方案质量和计算时间，表明在适当的计算时间内所提出算法的令人满意的性能。同时，进行了统计假设检验（T检验）。通常可以观察到，SA在解决方案质量方面取得了相对较好的结果，而GA在所有规模的测试问题上花费的计算时间更少。最终，${}_2$ 排放，车队的可变成本和目标函数值。