增强随机规划解的可解释性：一种多参数方法
Enhancing Interpretability of Stochastic Programming Solutions: A Multiparametric Approach
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中文总结 AI 辅助
该研究在Benders分解框架内采用多参数编程，提出一种确定性方法，将随机规划的不确定性空间划分为临界区域，通过分析聚类场景，为供应链规划的随机解提供透明解释。
中文摘要 AI 辅助
随机规划（SP）是处理不确定性下决策的强大框架，但其在工业中的实际应用常因难以理解驱动最优解的因果关系而受阻。在两阶段SP中，战略层面的第一阶段决策与运营层面的第二阶段 recourse（补偿）决策耦合；当考虑的场景数量庞大时，理解不确定性实现与最优补偿策略之间的直接联系在计算和认知层面都极具挑战性。常见的提升可解释性的方法包括训练分类树或场景缩减，即用代表性子集替代庞大的场景集，这类方法通常基于不确定性实现或最优补偿决策的事后聚类（如k-means）。这些方法虽有用，但仅能提供解空间的统计近似，可能无法揭示驱动最优第一阶段决策的补偿问题的潜在结构特性。本研究在Benders分解框架内引入一种新颖的确定性可解释性方法，采用多参数编程（mp）；我们将补偿子问题重新表述为多参数线性规划，生成临界区域（CRs，即不确定性空间的多面体划分）的显式映射，这使我们能以分析方式而非统计方式对场景进行聚类。我们在需求不确定下的供应链规划中验证该方法，结果显示100个随机场景恰好映射为6个临界区域聚类，该映射使我们能将最优产能规划决策解释为特定运营模式间的精确权衡，为随机解提供完全透明的解释。
英文摘要
Stochastic programming (SP) is a powerful framework for decision-making under uncertainty, but its practical adoption in industry is often hindered by the difficulty in understanding the causal relationships that drive optimal solutions. In the two-stage SP, strategic first-stage decisions are coupled with operational second-stage recourse decisions. When the number of scenarios under consideration is large, understanding the direct link between the uncertainty realization and optimal recourse strategy becomes computationally and cognitively demanding. Common approaches to improve interpretability include trained classification trees or scenario reduction, replacing the large scenario set with a representative subset. This is often achieved through post-hoc clustering (e.g., k-means) based on uncertainty realizations or optimal recourse decisions. While useful, these methods only provide a statistical approximation of the solution space and may fail to reveal the underlying structural properties of the recourse problem that drive optimal first-stage decisions. This work introduces a novel, deterministic approach to explainability using multiparametric programming (mp) within a Benders decomposition framework. We reformulate the recourse subproblem as a multiparametric linear program, generating an explicit map of Critical Regions (CRs), which are polyhedral partitions of the uncertainty space. This allows us to cluster scenarios analytically rather than statistically. We demonstrate this methodology on a supply chain planning under demand uncertainty. Our results show that 100 stochastic scenarios map to exactly six critical region clusters. This mapping allows us to explain optimal capacity planning decisions as a precise trade-off between specific operational modes, providing a fully transparent interpretation of the stochastic solution.
发表机构
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison（威斯康星大学麦迪逊分校化学与生物工程系）
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