Analysis offacilityprotectionstrategiesagainstanuncertainnumberof attacks:ThestochasticR-interdictionmedianproblemwithfortification

We presenttheStochasticR-InterdictionMedianProblemwithFortification(S-RIMF).Thismodel optimallyallocatesdefensiveresourcesamongfacilitiestominimizetheworst-caseimpactofan intentionaldisruption.Sincetheextentofterroristattacksandmaliciousactionsisuncertain,the problemdealswitharandomnumberofpossiblelosses.Amax-coveringtypeformulationforthe S-RIMFisdeveloped.Sincetheproblemsizegrowsveryrapidlywiththeprobleminputs,wepropose pre-processingtechniquesbasedonthecomputationofvalidlowerandupperboundstoexpeditethe solution ofinstancesofrealisticsize.Wealsopresentheuristicapproachesbasedonheuristic concentration-typerules.Theheuristicsareabletofindanoptimalsolutionforalmostalltheproblem instancesconsidered.Extensivecomputationaltestingshowsthatboththeoptimalalgorithmandthe heuristicsareverysuccessfulatsolvingtheproblem.Finally,adiscussionoftheimportanceof recognizingthestochasticnatureofthenumberofpossibleattacksisprovided.