ABSTRACT

A common approach to model stochastic programming problems is based on scenarios. An option to manage the difficulty of these problems corresponds to reduce the original set of scenarios. In this paper we study a new fast scenario reduction method based on Conditional Scenarios (CS). We analyse the degree of similarity between the original large set of scenarios and the small set of conditional scenarios in terms of the first two moments. In our numerical experiment, based on the stochastic capacitated facility location problem, we compare two fast scenario reduction methods: the CS method and the Monte Carlo (MC) method. The empirical conclusion is twofold: On the one hand, the achieved expected costs obtained by the two approaches are similar, although the MC method obtains a better approximation to the original set of of scenarios in terms of the moment matching criterion. On the other hand, the CS approach outperforms the MC approach with the same number of scenarios in terms of solution time.

摘要

对随机规划问题建模的常用方法是基于场景。管理这些问题的难度的选项对应于减少原始场景集。在本文中，我们研究了一种基于条件场景（CS）的新的快速场景缩减方法。我们根据前两个矩来分析原始大场景集和小条件场景集之间的相似程度。在我们的数值实验中，基于随机容量设施选址问题，我们比较了两种快速场景缩减方法：CS 方法和 Monte Carlo (MC) 方法。实证结论是双重的：一方面，两种方法获得的预期成本相似，尽管 MC 方法在矩匹配标准方面获得了对原始场景集的更好近似。另一方面，在求解时间方面，CS 方法在相同数量的场景下优于 MC 方法。