Distributionally robust optimization under a decision-dependent ambiguity set with applications to machine scheduling and humanitarian logistics

Noyan, Nilay and Rudolf, Gábor and Lejeune, Miguel (2022) Distributionally robust optimization under a decision-dependent ambiguity set with applications to machine scheduling and humanitarian logistics. INFORMS Journal on Computing, 34 (2). pp. 729-751. ISSN 1091-9856 (Print) 1526-5528 (Online)

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Abstract

We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets, we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover's distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main computational challenges in solving the problems of interest and provide an overview of various settings leading to tractable formulations. Some of the arising side results, such as the mathematical programming expressions for robustified risk measures in a discrete space, are also of independent interest. Finally, we rely on state-of-the-art modeling techniques from machine scheduling and humanitarian logistics to arrive at potentially practical applications, and present a numerical study for a novel risk-averse scheduling problem with controllable processing times. Summary of Contribution: In this study, we introduce a new class of optimization problems that simultaneously address distributional and decision-dependent uncertainty. We present a unified modeling framework along with a discussion on possible ways to specify the key model components, and discuss the main computational challenges in solving the complex problems of interest. Special care has been devoted to identifying the settings and problem classes where these challenges can be mitigated. In particular, we provide model reformulation results, including mathematical programming expressions for robustified risk measures, and describe how these results can be utilized to obtain tractable formulations for specific applied problems from the fields of humanitarian logistics and machine scheduling. Toward demonstrating the value of the modeling approach and investigating the performance of the proposed mixed-integer linear programming formulations, we conduct a computational study on a novel risk-averse machine scheduling problem with controllable processing times.We derive insights regarding the decision-making impact of our modeling approach and key parameter choices.
Item Type: Article
Uncontrolled Keywords: controllable processing times; decision-dependent ambiguity; decision-dependent probabilities; Distributionally robust optimization; earth mover's distances; endogenous uncertainty; network interdiction; random link failures; robust scheduling robust pre-disaster; robustified risk; stochastic scheduling; Wasserstein metric
Divisions: Faculty of Engineering and Natural Sciences > Academic programs > Industrial Engineering
Faculty of Engineering and Natural Sciences
Depositing User: Nilay Noyan
Date Deposited: 20 Aug 2022 14:26
Last Modified: 20 Aug 2022 14:26
URI: https://research.sabanciuniv.edu/id/eprint/44276

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