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【明理讲堂2021年第77期】12-31中国科学院大学王曙明副教授:Robust Stochastic Facility Location: Sensitivity Analysis and Exact Solution





中国科学院大学经济与管理学院副教授,主要从事鲁棒优化、随机规划研究及其在物流与供应链管理、健康医疗管理等领域的应用。担任Journal of Systems Science and Complexity (JSSC) 期刊编委以及Computers and Operations Research 特刊Managing Guest Editor。研究成果分别发表于Production and Operations Management, INFORMS Journal on Computing, Transportation Science, IISE Transactions, Naval Research Logistics, IEEE Trans. Cybernetic, EJOR等权威杂志上。


In this work, we investigate a broad class of facility location problems in the context of adaptive robust stochastic optimization. A state-wise ambiguity set is employed to model the distributional uncertainty associated with the demand in different states, where the conditional distributional characteristics in each state are described by support, mean as well as dispersion measures, which are 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 which 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.