Robust Stochastic Facility Location: Sensitivity Analysis and Exact Solution

Tianqi Liu (), Francisco Saldanha-da-Gama (), Shuming Wang () and Yuchen Mao ()
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Tianqi Liu: School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China
Francisco Saldanha-da-Gama: Department of Statistics and Operations Research, University of Lisboa, 1649-004 Lisboa, Portugal
Shuming Wang: School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China; Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing 100049, China
Yuchen Mao: School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China

INFORMS Journal on Computing, 2022, vol. 34, issue 5, 2776-2803

Abstract: This work focuses on a broad class of facility location problems in the context of adaptive robust stochastic optimization under the state-dependent demand uncertainty. The demand is assumed to be significantly affected by related state information , such as the seasonal or socio-economic information. In particular, a state-wise ambiguity set is adopted for modeling the distributional uncertainty associated with the demand in different states. The conditional distributional characteristics in each state are described by a support, as well as by mean and dispersion measures, which are assumed to be conic representable. A robust sensitivity analysis is performed, in which, on the one hand, we analyze the impact of the change in ambiguity-set parameters (e.g., state probabilities, mean value abounds, and dispersion bounds in different states) onto the optimal worst-case expected total cost using the ambiguity dual variables. On the other hand, we analyze the impact of the change in location design onto the worst-case expected second-stage cost and show that the sensitivity bounds are fully described as the worst-case expected shadow-capacity cost. As for the solution approach, we propose a nested Benders decomposition algorithm for solving the model exactly, which leverages the subgradients of the worst-case expected second-stage cost at the location decisions formed insightfully by the associated worst-case distributions. The nested Benders decomposition approach ensures a finite-step convergence, which can also be regarded as an extension of the classic L -shaped algorithm for two-stage stochastic programming to our state-wise, robust stochastic facility location problem with conic representable ambiguity. Finally, the results of a series of numerical experiments are presented that justify the value of the state-wise distributional information incorporated in our robust stochastic facility location model, the robustness of the model, and the performance of the exact solution approach.

Keywords: stochastic facility location; robust optimization; state-wise distributional uncertainty; Benders decomposition (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:34:y:2022:i:5:p:2776-2803

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