This paper studies a variant of the two-stage last mile relief network problem by introducing a centrality metric objective including the distance centrality metric, the demand centrality value-at-risk and the residua...
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This paper studies a variant of the two-stage last mile relief network problem by introducing a centrality metric objective including the distance centrality metric, the demand centrality value-at-risk and the residual supplies centrality metric. Under the scenario-based design, the demand in each scenario is described as a random fuzzy variable whose probability distribution is ambiguous. In order to characterize its ambiguousness, this paper designs a Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm based on sample data to construct a data-driven ambiguity set containing the support and mean, which not only realizes the visualization of the ambiguous probability distribution, but also provides a finite set of scenarios for the uncertain demand. Given the constructed data-driven ambiguity set, this paper proposes a data-driven adaptive distributionally robust equilibrium programming (DDADREP) method for the last mile relief network problem (LMRNP). In view of its computational difficulty, the safe approximation, duality technique and credibility measure theory are used to approximate it as a mixed integer second order cone programming with significant computational advantages. Finally, the proposed model is validated with two real-world cases, and its effectiveness as well as advantages is demonstrated by comparison with the classical robust optimization and the nominal equilibrium optimization, respectively.& COPY;2023 Elsevier Inc. All rights reserved.
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