Hedging against disruptions with ripple effects in location analysis

• Published in: Omega (Oxford) Vol. 40; no. 1; pp. 21 - 30
• Main Authors: Liberatore, Federico, Scaparra, Maria P., Daskin, Mark S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 2012; Elsevier; Pergamon Press Inc
• Series: Omega
• Subjects: Applied sciences; Computing; Earthquakes; Exact sciences and technology; Ganzzahlige Optimierung; Hedging; Humanitäre Hilfe; Integer programming; Katastrophe; Lieferkette; Location; Location analysis; Location Integer programming Optimization Computing; Mathematical programming; Operational research and scientific management; Operational research. Management science; Operations Research; Optimization; Optimization algorithms; Reliability theory. Replacement problems; Studies; Integer programming; Computing; Optimization; Location; Filtering; Warranty; Disease; Expert system; Interconnected power system; Mixed integer programming; Disaster; System reliability; Modeling; Exact solution; Weather; Flood; Earthquakes; Fires; Capacity constraint; Pruning(tree); Search tree; Localization; Hurricane
• ISSN: 0305-0483; 1873-5274
• DOI: 10.1016/j.omega.2011.03.003

Supply systems are subject to disruptions whose impact may not remain confined, but might actually propagate across the network. We consider the problem of optimally protecting a capacitated median system with a limited amount of protective resources subject to disruptions. Specifically, the type of disruption studied is characterized by correlation effects between the facilities, and may result in partial or complete disruption of the facilities involved. The model optimizes protection plans in the face of large area disruptions; i.e., disruptions that affect regions rather than single elements of the system. Examples may be earthquakes, storms, floods, fires, hurricanes, droughts, the spread of diseases, the spread of chemical agents, and cascading failures. The model is also a general framework for the family of fortification problems in the context of location analysis, as it includes uncapacitated facilities and single-target disruptions as special cases. We provide a tri-level formulation of the problem, and we propose an exact solution algorithm which makes use of a tree-search procedure to identify which facilities to protect. The procedure is enhanced by a dual-based pruning rule. The underlying disruption problem is reformulated as a single-level mixed-integer program. The algorithm has been tested on a dataset based on the 2009 L’Aquila earthquake. We verify empirically the efficiency of the pruning rule, and we provide an evaluation of the importance of considering propagation effects in the disruptions.