This paper proposes a new integer L-shaped method for solving two-stage stochastic integer programs whose first-stage solutions can decompose into disjoint components, each one having a monotonic recourse function. In a minimization problem, the monotonicity property stipulates that the recourse cost of a component must always be higher or equal to that of any of its subcomponents. The method exploits new types of optimality cuts and lower bounding functionals that are valid under this property. The stochastic vehicle routing problem is particularly well suited to be solved by this approach, as its solutions can be decomposed into a set of routes. We consider the variant with stochastic demands in which the recourse policy consists of performing a return trip to the depot whenever a vehicle does not have sufficient capacity to accommodate a newly realized customer demand. This work shows that this policy can lead to a non-monotonic recourse function, but that the monotonicity holds when the customer demands are modeled by several commonly used families of probability distributions. We also present new problem-specific lower bounds on the recourse that strengthen the lower bounding functionals and significantly speed up the solving process. Computational experiments on instances from the literature show that the new approach achieves state-of-the-art results.

中文翻译：

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单调资源随机车辆路径问题的分解整数L形方法


本文提出了一种新的整数L形方法来求解两阶段随机整数规划，其第一阶段解可以分解为不相交的分量，每个分量都具有单调的追索函数。在最小化问题中，单调性属性规定组件的资源成本必须始终高于或等于其任何子组件的资源成本。该方法利用了在此属性下有效的新型最优割和下界函数。随机车辆路径问题特别适合用这种方法来解决，因为它的解决方案可以分解为一组路线。我们考虑具有随机需求的变体，其中追索政策包括每当车辆没有足够的容量来满足新实现的客户需求时执行返回车库的行程。这项工作表明，该策略可以导致非单调追索函数，但当客户需求由几个常用的概率分布族建模时，单调性仍然成立。我们还提出了新的针对特定问题的资源下界，以加强下界函数并显着加快解决过程。对文献中实例的计算实验表明，新方法取得了最先进的结果。