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Robust Stochastic Facility Location: Sensitivity Analysis and Exact Solution.
- Source :
-
INFORMS Journal on Computing . Sep/Oct2022, Vol. 34 Issue 5, p2776-2803. 28p. - Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10919856
- Volume :
- 34
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- INFORMS Journal on Computing
- Publication Type :
- Academic Journal
- Accession number :
- 159864767
- Full Text :
- https://doi.org/10.1287/ijoc.2022.1206