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Robust weighted vertex $$p$$-center model considering uncertain data: an application to emergency management. (English) Zbl 1317.90166
Summary: This paper presents a generalized weighted vertex $$p$$-center (WVPC) model that represents uncertain nodal weights and edge lengths using prescribed intervals or ranges. The objective of the robust WVPC (RWVPC) model is to locate $$p$$ facilities on a given set of candidate sites so as to minimize worst-case deviation in maximum weighted distance from the optimal solution. The RWVPC model is well-suited for locating urgent relief distribution centers (URDCs) in an emergency logistics system responding to quick-onset natural disasters in which precise estimates of relief demands from affected areas and travel times between URDCs and affected areas are not available. To reduce the computational complexity of solving the model, this work proposes a theorem that facilitates identification of the worst-case scenario for a given set of facility locations. Since the problem is $$NP$$-hard, a heuristic framework is developed to efficiently obtain robust solutions. Then, a specific implementation of the framework, based on simulated annealing, is developed to conduct numerical experiments. Experimental results show that the proposed heuristic is effective and efficient in obtaining robust solutions. We also examine the impact of the degree of data uncertainty on the selected performance measures and the tradeoff between solution quality and robustness. Additionally, this work applies the proposed RWVPC model to a real-world instance based on a massive earthquake that hit central Taiwan on September 21, 1999.

##### MSC:
 90B80 Discrete location and assignment