论文标题

随机需求和部分重新优化的车辆路线

Vehicle Routing with Stochastic Demands and Partial Reoptimization

论文作者

Florio, Alexandre M., Feillet, Dominique, Poggi, Marcus, Vidal, Thibaut

论文摘要

我们考虑使用随机需求的车辆路由问题(VRPSD),其中在路线计划阶段知道客户需求在分配阶段已知,并在到达每个客户时在路线执行期间揭示。关于VRPSD的一个长期的公开问题涉及允许在路线执行期间部分重新排序计划的客户访问的好处。鉴于该问题的实际重要性以及在最佳补货中对VRPSD的兴趣日益增长的兴趣,我们在称为“开关政策”的追索权中研究VRPSD。交换策略是一种规范的重新优化策略,仅允许对连续的客户重新排序。我们将这项政策共同考虑使用最佳的预防性补货,并引入分支机构和价格算法来计算最佳先验路由计划。该算法具有定价例程,其中价值功能代表所有可能状态和重新排序决策的计划途径的预期成本。为了确保定价障碍性,我们采用了一种将基本定价与各种复杂性的完成范围相结合的策略,并在不依赖优势规则的情况下解决定价问题。我们的数值实验证明了该算法在求解最多50个客户的实例中的有效性。值得注意的是,它们还为我们提供了重新优化价值的新见解。当计划的路线来自基于数据的确定性近似构建的算法时,开关策略可以节省大量成本,以节省最佳的补货。在比较最佳的先验VRPSD解决方案时,这些效率是较小的。看来,在上下文允许的情况下,进一步节省的成本可能需要重新排序并重新分配车辆之间的客户访问。

We consider the vehicle routing problem with stochastic demands (VRPSD), a problem in which customer demands are known in distribution at the route planning stage and revealed during route execution upon arrival at each customer. A long-standing open question on the VRPSD concerns the benefits of allowing, during route execution, partial reordering of the planned customer visits. Given the practical importance of this question and the growing interest on the VRPSD under optimal restocking, we study the VRPSD under a recourse policy known as the switch policy. The switch policy is a canonical reoptimization policy that permits only pairs of successive customers to be reordered. We consider this policy jointly with optimal preventive restocking and introduce a branch-cut-and-price algorithm to compute optimal a priori routing plans. This algorithm features pricing routines where value functions represent the expected cost-to-go along planned routes for all possible states and reordering decisions. To ensure pricing tractability, we adopt a strategy that combines elementary pricing with completion bounds of varying complexity, and solve the pricing problem without relying on dominance rules. Our numerical experiments demonstrate the effectiveness of the algorithm for solving instances with up to 50 customers. Notably, they also give us new insights into the value of reoptimization. The switch policy enables significant cost savings over optimal restocking when the planned routes come from an algorithm built on a deterministic approximation of the data, an important scenario given the difficulty of finding optimal VRPSD solutions. The benefits are smaller when comparing optimal a priori VRPSD solutions obtained for both recourse policies. As it appears, further cost savings may require joint reordering and reassignment of customer visits among vehicles when the context permits.

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