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1、Computers&OperationsResearch35(2008)1905–1923www.elsevier.com/locate/corAbilevelmixed-integerprogramforcriticalinfrastructureprotectionplanningMariaP.Scaparraa,∗,RichardL.ChurchbaKentBusinessSchool,UniversityofKent,Canterbury,Kent,UKbDepartmentofGeography,UniversityofCaliforni
2、a,SantaBarbara,CA,USAAvailableonline25October2006AbstractVulnerabilitytosuddenservicedisruptionsduetodeliberatesabotageandterroristattacksisoneofthemajorthreatsoftoday.Inthispaper,wepresentabilevelformulationofther-interdictionmedianproblemwithfortification(RIMF).RIMFidentifiest
3、hemostcost-effectivewayofallocatingprotectiveresourcesamongthefacilitiesofanexistingbutvulnerablesystemsothattheimpactofthemostdisruptiveattacktorunprotectedfacilitiesisminimized.Themodelisbasedupontheclassicalp-medianlocationmodelandassumesthattheefficiencyofthesystemismeasure
4、dintermsofaccessibilityorserviceprovisioncosts.Inthebilevelformulation,thetoplevelprobleminvolvesthedecisionsaboutwhichfacilitiestofortifyinordertominimizetheworst-caseefficiencyreductionduetothelossofunprotectedfacilities.Worst-casescenariolossesaremodeledinthelower-levelinter
5、dictionproblem.Wesolvethebilevelproblemthroughanimplicitenumeration(IE)algorithm,whichreliesontheefficientsolutionofthelower-levelinterdictionproblem.Extensivecomputationalresultsarereported,includingcomparisonswithearlierresultsobtainedbyasingle-levelapproachtotheproblem.2006
6、ElsevierLtd.Allrightsreserved.Keywords:Bilevelprogramming;Protectionmodels;Medianlocationproblems1.IntroductionAcrucialissueintoday’sdistribution,supplyandemergencyresponsesystemsistoguaranteecontinuityandeffi-ciencyinserviceprovisioninthefaceofnaturalandman-madethreats.Iflimit
7、edprotectiveresourcesareavailabletoincreasesystemrobustnessandresiliency,akeyquestionistoidentifywhichfacilitiestoprotectorfortifyinor-dertopreservethefunctionalityofthesystemasmuchaspossibleincaseofsabotageorexternaldisruptions.Thispaperpresentsanewformulationandanewsolutiona
8、pproachforsolvingther-interdictionmedianproblemwithfortificati
