PowerPoint Presentation

Reliable Infrastructure Location Design under Interdependent DisruptionsXiaopeng Li, Ph.D.Department of Civil and Environmental Engineering,Mississippi State University

Joint work with Yanfeng Ouyang, University of Illinois at Urbana-ChampaignFan Peng, CSX Transportation

The 20th International Symposium on Transportation and Traffic TheoryNoordwijk, Netherlands, July 17, 2013

1OutlineBackgroundInfrastructure network designFacility disruptionsMathematical Model Formulation challengesModeling approachNumerical ExamplesSolution qualityCase studies

#2Facilities are to be built to serve spatially distributed customers Trade-off one-time facility investment day-to-day transportation costsOptimal locations of facilities?

Logistics Infrastructure Network3Transp.costFacility costCustomer Facility

#3Infrastructure Facility DisruptionsFacilities may be disrupted due toNatural disastersPower outagesStrikesAdverse impactsExcessive operational costReduced service quality Deteriorate customer satisfactionEffects on facility planning Suboptimal system designErroneous budget estimation

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Impacts of Facility DisruptionsExcessive operations cost (including travel & penalty)Visit the closest functioning facility within a reachable distanceIf all facilities within the penalty distance fail, the customer will receive a penalty costReliable design?

Reachable DistanceOperations CostFacility cost#5Literature ReviewTraditional modelsDeterministic models (Daskin, 1995; Drezner, 1995)Demand uncertainty (Daskin, 1982, 1983; Ball and Lin, 1993; Revelle and Hogan, 1989; Batta et al., 1989) Continuum approximation (Newell 1973; Daganzo and Newell, 1986; Langevin et al.,1996; Ouyang and Daganzo, 2006)Reliable modelsI.i.d. failures (Snyder and Daskin, 2005; Chen et al., 2011; An et al.,2012) Site-dependent (yet independent) failures (Cui et al., 2010;)Special correlated failures (Li and Ouyang 2010, Liberatore et al. 2012) Most reliable location studies assume disruptions are independent6#6Disruption Correlation 7

Northeast Blackout (2003)Shared disaster hazardsHurricane Sandy (2012)

Shared supply resourcesPower PlantFactories

Many systems exhibit positively correlated disruptions #7Prominent Example: Fukushima Nuclear Leak

(Sources: ibtimes.com; www.pmf.kg.ac.rs/radijacionafizika)

Earthquake Power supply failure Reactors meltdown

Power supply for cooling systems Reactors#88correlated disruption scenariosnormal scenarioOperationscostResearch QuestionsHow to model interdependent disruptions in a simple way?

How to design reliable facility network under correlated disruptions?minimize system cost in the normal scenariohedge against high costs across all interdependent disruption scenariosInitial investmentOperationscost#9OutlineBackgroundInfrastructure network designFacility disruptionsMathematical Model Formulation challengesModeling approachNumerical ExamplesSolution qualityCase studies

#10A facility is either disrupted or functioningDisruption probability = long-term fraction of time when the facility is in the disrupted stateFacility state combination specifies a scenario

Facility 3Facility 2Facility 1timeNormal scenarioDisrupted stateFunctioning stateNormal scenarioNormal scenarioScenario 1Scenario 2Scenario 3Probabilistic Facility Disruptions#Modeling ChallengesDeterministic facility location problem is NP-hardEven for given location design, # of failure scenarios increases exponential with # of facilitiesDifficult to consolidate scenarios under correlationScenario 1Scenario 2Scenario N+1Scenario 2NFunctioningDisrupted#12Correlation Representation: Supporting StructureEach supporting station is disrupted independently with an identical probability (i.i.d. disruptions)A service facility is operational if and only if at least one of its supporting stations is functioningSupporting Stations:Service Facilities:#13Supporting Structure PropertiesProposition: Site-dependent facility disruptions(Cui et al., 2010) can be represented by a properly constructed supporting structureIdea: # of stations connected to a facility determines disruption probability#14Supporting Structure PropertiesProposition: General positively-correlated facility disruptions can be represented by a properly constructed supporting structure.Structure construction formula:

ABC

#A more important property we have proven is that any positive correlations among facilities can be equivalently converted to this structure. We proposed rigorous formulas for this equivalent conversion, which we are not going to detail here. But the basic idea is that an arbitrary probability of disruptions of certain facilities conditioning on functioning states of some other facilities can be configured by properly setting station sharing. For example, here any probability value of disruptions of both BC conditioning on As functioning can be configured by setting a proper number of stations that support facilities B and C, and a proper number of stations connected to A only. 15System Performance - Expected Costi: demand li; penalty pitransp. cost dijk:cons. cost ckj:cons. cost fjConstruction costExpected operations cost#16Expected System Cost Evaluation

Consolidated cost formula

Scenario consolidation principlesSeparate each individual customerRank infrastructure units according to a customers visiting sequence

#17Reliable Facility Location Model

subject toExpected system costAssignment feasibilityFacility existenceStation existenceIntegralityCompact Linear Integer Program#18OutlineBackgroundInfrastructure network designFacility disruptionsMathematical Model Formulation challengesModeling approachNumerical ExamplesSolution qualityCase studies

#19Hypothetical ExampleSupporting stations are givenIdentical network setting except for # of shared stations Identical facility disruption probabilities Case 1: Correlated disruptions Neighboring facilities share stations

Case 2: Independent disruptions (not sharing stations)Each facility is supported by an isolated station#20

Comparison ResultCase 1: Correlated disruptionsCase 2: Independent disruptions#21Case StudyCandidate stations: 65 nuclear power plantsCandidate facilities and customers: 48 state capital cities & D.C.

Data sources: US major city demographic data from Daskin, 1995 eGRID http://www.epa.gov/cleanenergy/energy-resources/egrid/index.html#22Optimal Deployment

Supporting station: Service facility:#23SummarySupporting station structureSite-dependent disruptionsPositively correlated disruptionsScenario consolidationExponential scenarios polynomial measureInteger programming design modelSolved efficiently with state-of-the-art solversFuture researchMore general correlation patterns (negative correlations)Application to real-world case studiesAlgorithm improvement

#24AcknowledgmentU.S. National Science Foundation CMMI #1234936CMMI #1234085 EFRI-RESIN #0835982CMMI #0748067

#Xiaopeng Lixli@cee.msstate.eduThank You!26