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
Slide 2
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; www.pmf.kg.ac.rs/radijacionafizika) 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 customers 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
http://www.epa.gov/cleanenergy/energy-resources/egrid/index.htmlhttp://www.epa.gov/cleanenergy/energy-resources/egrid/index.html
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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
#1234936 CMMI #1234085 EFRI-RESIN #0835982 CMMI #0748067