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Medal, Hugh R.; Pohl, Edward A.; Rossetti, Manuel D.
European journal of operational research, 08/2014, Volume: 237, Issue: 1Journal Article
•We present a new model for integrating facility location and hardening decisions.•We convert a natural three-level formulation to a single-level formulation.•We present algorithms for the single- and bi-objective versions of the problem.•We report the runtime of the single- and bi-objective algorithms.•Risk was sizably improved without a comparable degradation to normal performance. Two methods of reducing the risk of disruptions to distribution systems are (1) strategically locating facilities to mitigate against disruptions and (2) hardening facilities. These two activities have been treated separately in most of the academic literature. This article integrates facility location and facility hardening decisions by studying the minimax facility location and hardening problem (MFLHP), which seeks to minimize the maximum distance from a demand point to its closest located facility after facility disruptions. The formulation assumes that the decision maker is risk averse and thus interested in mitigating against the facility disruption scenario with the largest consequence, an objective that is appropriate for modeling facility interdiction. By taking advantage of the MFLHP’s structure, a natural three-stage formulation is reformulated as a single-stage mixed-integer program (MIP). Rather than solving the MIP directly, the MFLHP can be decomposed into sub-problems and solved using a binary search algorithm. This binary search algorithm is the basis for a multi-objective algorithm, which computes the Pareto-efficient set for the pre- and post-disruption maximum distance. The multi-objective algorithm is illustrated in a numerical example, and experimental results are presented that analyze the tradeoff between objectives.
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