This paper studies two-stage disruption exposure minimization problems, motivated by the supply disruption issues in the energy and water supply systems. In particular, we address the ambiguity in both the probability distribution and risk preference of decision-makers towards disruption exposures. First, we propose a two-stage distributionally robust model with adjustable uncertainty sets, which solves a supply system solution with the least possible disruption exposures. We show that this two-stage robust disruption exposure model can be reduced to a computationally attractive single-stage mixed-integer linear program. We then propose an extended almost-robust disruption guarantee model to account for the ambiguity in the risk preference of decision-makers. We demonstrate that this almost-robust guarantee model can reveal clear preferences of most decision-makers under limited distribution information, which however does not resort to any particular disutility function specification and can be solved efficiently using a binary search algorithm. A decision support framework is also developed to guide users on how to apply the proposed disruption exposure models. Finally, we apply the proposed models to a distributed energy supply system design problem. Numerical results show that our models significantly outperform a risk-neutral model in hedging against a broad set of supply distributions. Moreover, the almost-robust guarantee model exhibits its advantages in hedging against high disruption levels, and performs the best under the vast majority of distributions regarding all tested statistical criteria.

本文研究了两阶段中断暴露最小化问题，其动机是能源和供水系统中的供应中断问题。特别是，我们解决了决策者对中断风险的概率分布和风险偏好的模糊性。首先，我们提出了一个具有可调不确定性集的两阶段分布鲁棒模型，该模型解决了具有最小可能中断风险的供应系统解决方案。我们表明，这种两阶段稳健的中断暴露模型可以简化为计算上有吸引力的单阶段混合整数线性程序。然后我们提出了一个扩展的几乎稳健的中断保证模型解释决策者风险偏好的模糊性。我们证明，这种几乎稳健的保证模型可以在有限的分布信息下揭示大多数决策者的明确偏好，然而，这并不求助于任何特定的无效函数规范，并且可以使用二分搜索算法有效地解决。还开发了一个决策支持框架来指导用户如何应用建议的中断暴露模型。最后，我们将所提出的模型应用于分布式能源供应系统设计问题。数值结果表明，我们的模型在对冲广泛的供应分布时明显优于风险中性模型。此外，几乎稳健的担保模型在对冲高中断级别方面表现出优势，