Abstract We study two integer programming (IP) models for the multi-trip vehicle routing problem with time windows, service-dependent loading times, and limited trip duration (MTVRPTW-SDLT). Our first two-index formulation model represents vehicle returns to the depot in a graph with multiple copies of the depot node. The second two-index formulation model has just one depot node per vehicle, but includes a parallel arc for each pair of customer nodes representing an intermediate vehicle return to the depot. We compare these formulations against three-index formulations available in the literature over a set of benchmark instances. Results show that our models outperform existing formulations. We also adapt the proposed formulations for a relaxation of the MTVRPTW-SDLT without trip duration limit (LT). Our computational results also suggest that our models also improve their performance on MTVRPTW-SD instances.

中文翻译：

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具有时间窗的多行程车辆路径问题的新紧凑整数规划公式

摘要 我们研究了两个整数规划 (IP) 模型，用于具有时间窗、服务相关加载时间和有限行程持续时间 (MTVRPTW-SDLT) 的多行程车辆路由问题。我们的第一个双指数公式模型在具有多个站点节点副本的图中表示车辆返回站点。第二个双指标公式模型每辆车只有一个站点节点，但包括每对客户节点的平行弧线，代表中间车辆返回站点。我们在一组基准实例中将这些公式与文献中可用的三指数公式进行比较。结果表明，我们的模型优于现有的公式。我们还调整了建议的公式，以在没有行程持续时间限制 (LT) 的情况下放宽 MTVRPTW-SDLT。