In this paper, the authors introduced a real world new problem, the multi-trip vehicle routing problem with time windows and the possible use of a less-than-truckload carrier to satisfy customer demands. The purpose of this paper is to develop a heuristic algorithm to route the private trucks with time windows and to make a selection between truckload and less-than-truckload carriers by minimizing a total cost function.,Both mathematical model and heuristic algorithm are developed for routing the private trucks with time windows and for selecting of less-than-truckload carriers by minimizing the total cost function.,In all, 40 test problems were examined with the heuristics. Computational results show that the algorithm obtains the optimal or near-optimal solutions efficiently in terms of time and accuracy.,The research described in this paper differs from the previous one on fleet planning or vehicle routing, in that it modifies the Clarke and Wright method by shifting the performance measure from a distance to cost and also incorporates the fixed cost of different types of trucks into the model. In addition, the authors simultaneously consider the multiple trip vehicle routing problems with time windows and the selection of less-than-truckload carriers that is an integrated scenario of real-world application. To the best of the authors’ knowledge, this scenario has not been considered in the literature.

中文翻译：

---

具有时间窗约束和外部承运人选择的多程车辆路径问题的启发式算法

在本文中，作者介绍了一个现实世界中的新问题，即带有时间窗的多程车辆路径问题，以及可能会使用低于卡车的载具来满足客户需求。本文的目的是开发一种启发式算法，通过最小化总成本函数，在带时间窗的路线上引导私家卡车，并在卡车载货量和非卡车载货量之间做出选择。开发了数学模型和启发式算法通过时间窗给私人卡车安排路线，并通过使总成本函数最小化来选择小于卡车的运输工具。使用启发式方法总共检查了40个测试问题。计算结果表明，该算法在时间和精度上均能有效地获得最优解或接近最优解。本文所描述的研究与先前的有关车队规划或车辆路线选择的研究的不同之处在于，它通过将绩效指标从远距离转变为成本来修改了Clarke和Wright方法，并且将不同类型卡车的固定成本纳入了研究范围。模型。此外，作者同时考虑了带有时间窗的多程车辆路径问题以及选择小于卡车的载具，这是实际应用中的一个集成方案。就作者所知，文献中尚未考虑这种情况。它通过将绩效指标从远距离转变为成本来修改Clarke和Wright方法，并且还将不同类型卡车的固定成本纳入模型中。此外，作者同时考虑了带有时间窗的多程车辆路径问题以及选择小于卡车的载具，这是实际应用中的一个集成方案。就作者所知，文献中尚未考虑这种情况。它通过将绩效指标从远距离转变为成本来修改Clarke和Wright方法，并且还将不同类型卡车的固定成本纳入模型中。此外，作者同时考虑了带有时间窗的多程车辆路径问题以及选择小于卡车的载具，这是实际应用中的一个集成方案。就作者所知，文献中尚未考虑这种情况。