An almost robust model for minimizing disruption exposures in supply systems

This paper studies two-stage disruption exposure minimization problems, motivated by the supply dis-ruption 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 ambi-guity 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 how-ever 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. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

The paper introduces two-stage disruption exposure minimization problems and an extended almost-robust disruption guarantee model to address the ambiguity in decision-makers' risk preferences. These models demonstrate strong performance and efficiency in solving supply system design problems.