The vehicle routing problem is a traditional combinatorial problem with practical relevance for a wide range of industries. In the literature, several specificities have been tackled by dedicated methods in order to better reflect real-world situations. Following this trend, this article addresses the fleet size and mix vehicle routing problem with time windows in which companies hire a third-party logistics company. The shipping charges considered in this work are calculated using step cost functions, in which values are determined according to the type of vehicle and the total distance traveled, with fixed values for predefined distance ranges. A mixed integer linear programming model is introduced and two sequential insertion heuristics are proposed. The introduced methods are examined through a computational comparative analysis in small-sized instances with known optimal solution, 168 benchmark instances from the literature, and 3 instances based on a real-world problem from the civil construction industry. The numerical experiments show that the proposed methods are efficient and show good performance in different scenarios.

车辆路径问题是传统的组合问题，具有广泛的行业实用性。在文献中，已经通过专用方法解决了一些特殊性，以便更好地反映现实情况。顺应这一趋势，本文讨论了带有时间窗的车队规模和混合车辆路线选择问题，在这些时间窗中公司雇用了第三方物流公司。这项工作中考虑的运输费用是使用分步成本函数计算的，其中根据车辆类型和总行驶距离确定值，并为预定义的距离范围确定固定值。介绍了一种混合整数线性规划模型，并提出了两种顺序插入启发式算法。在具有已知最佳解决方案的小型实例，文献中的168个基准实例以及基于民用建筑行业的实际问题的3个实例中，通过计算比较分析对引入的方法进行了检查。数值实验表明，所提出的方法是有效的，并且在不同情况下都具有良好的性能。