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Reliable Infrastructure Location Design under Interdependent Disruptions Xiaopeng Li, Ph.D. Department of Civil and Environmental Engineering, Mississippi State University Joint work with Yanfeng Ouyang, University of Illinois at Urbana-Champaign Fan Peng, CSX Transportation The 20th International Symposium on Transportation and Traffic Theory Noordwijk, Netherlands, July 17, 2013

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2 Outline Background Infrastructure network design Facility disruptions Mathematical Model Formulation challenges Modeling approach Numerical Examples Solution quality Case studies

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3 Facilities are to be built to serve spatially distributed customers Trade-off one-time facility investment day-to-day transportation costs Optimal locations of facilities? Logistics Infrastructure Network 3 Transp. cost Facility cost Customer Facility …

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4 Infrastructure Facility Disruptions Facilities may be disrupted due to Natural disasters Power outages Strikes… Adverse impacts Excessive operational cost Reduced service quality Deteriorate customer satisfaction… Effects on facility planning Suboptimal system design Erroneous budget estimation 4

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5 Impacts of Facility Disruptions Excessive operations cost (including travel & penalty) Visit the closest functioning facility within a reachable distance If all facilities within the penalty distance fail, the customer will receive a penalty cost Reliable design? Reachable Distance Operations Cost Facility cost

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6 Literature Review Traditional models Deterministic 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 models I.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 independent 6

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7 Disruption Correlation 7 Northeast Blackout (2003) Shared disaster hazards Hurricane Sandy (2012) Shared supply resources Power Plant Factories Many systems exhibit positively correlated disruptions

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8 Prominent Example: Fukushima Nuclear Leak (Sources: ibtimes.com; Earthquake → Power supply failure → Reactors meltdown Power supply for cooling systems Reactors

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9 correlated disruption scenarios normal scenario Operations cost Research Questions How to model interdependent disruptions in a simple way? How to design reliable facility network under correlated disruptions? minimize system cost in the normal scenario hedge against high costs across all interdependent disruption scenarios Initial investment Operations cost

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10 Outline Background Infrastructure network design Facility disruptions Mathematical Model Formulation challenges Modeling approach Numerical Examples Solution quality Case studies

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11 A facility is either disrupted or functioning Disruption probability = long-term fraction of time when the facility is in the disrupted state Facility state combination specifies a scenario Facility 3 Facility 2 Facility 1 time Normal scenario Disrupted state Functioning state Normal scenario Scenario 1 Scenario 2 Scenario 3 Probabilistic Facility Disruptions

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12 Modeling Challenges Deterministic facility location problem is NP-hard Even for given location design, # of failure scenarios increases exponential with # of facilities Difficult to consolidate scenarios under correlation Scenario 1 … Scenario 2 … … … Scenario N+1 … … Scenario 2 N FunctioningDisrupted

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13 Correlation Representation: Supporting Structure Each 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 functioning … … Supporting Stations: Service Facilities:

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14 Supporting Structure Properties Proposition: Site-dependent facility disruptions(Cui et al., 2010) can be represented by a properly constructed supporting structure Idea: # of stations connected to a facility determines disruption probability … …

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15 Supporting Structure Properties Proposition: General positively-correlated facility disruptions can be represented by a properly constructed supporting structure. Structure construction formula: A BC

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16 System Performance - Expected Cost i: demand – i ; penalty i transp. cost d ij k:cons. cost c k j: cons. cost f j Construction cost Expected operations cost

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17 Expected System Cost Evaluation Consolidated cost formula Scenario consolidation principles Separate each individual customer Rank infrastructure units according to a customer’s visiting sequence

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18 Reliable Facility Location Model subject to Expected system cost Assignment feasibilityFacility existence Station existence Integrality Compact Linear Integer Program

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19 Outline Background Infrastructure network design Facility disruptions Mathematical Model Formulation challenges Modeling approach Numerical Examples Solution quality Case studies

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20 Hypothetical Example Supporting stations are given Identical 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 … …

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21 Comparison Result Case 1: Correlated disruptions Case 2: Independent disruptions

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22 Case Study Candidate stations: 65 nuclear power plants Candidate facilities and customers: 48 state capital cities & D.C. Data sources: US major city demographic data from Daskin, 1995 eGRID

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23 Optimal Deployment Supporting station: Service facility:

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24 Summary Supporting station structure Site-dependent disruptions Positively correlated disruptions Scenario consolidation Exponential scenarios → polynomial measure Integer programming design model Solved efficiently with state-of-the-art solvers Future research More general correlation patterns (negative correlations) Application to real-world case studies Algorithm improvement

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25 Acknowledgment U.S. National Science Foundation CMMI # CMMI # EFRI-RESIN # CMMI #

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Xiaopeng Li Thank You!

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