This paper presents an integer program formulation of a reliable location-routing problem wherebuilt facilities are subject to the risk of probabilistic disruptions. The objective is to determinefacility locations, outbound delivery routing, and backup plans under disruptions, so as to minimizethe total cost including the facility set-up cost, the expected routing cost, and the customer penalty(if no delivery is possible). A variety of solution approaches (i.e., Lagrangian relaxation withembedded column generation, ring sweep heuristics, and local search) are proposed to solve theproblem. We also present an alternative continuum approximation model for large-scale instancesof this problem. This model not only provides analytical formulas to predict the optimal systemcost but also can be used to generate high quality feasible solutions. A series of numerical casestudies are conducted to test the performance of the proposed models and solution algorithms.Managerial insights are also drawn on how various system parameters impact the optimal solution.
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