Reliable Infrastructure Location Design under Interdependen - PowerPoint Presentation

Slide1

Reliable Infrastructure Location Design under Interdependent Disruptions

Xiaopeng Li, Ph.D.Department of Civil and Environmental Engineering,Mississippi State UniversityJoint work with Yanfeng Ouyang, University of Illinois at Urbana-ChampaignFan Peng, CSX TransportationThe 20th International Symposium on Transportation and Traffic TheoryNoordwijk, Netherlands, July 17, 2013Slide2

Outline

BackgroundInfrastructure network designFacility disruptionsMathematical Model Formulation challengesModeling approachNumerical ExamplesSolution quality

Case studiesSlide3

Facilities 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 Network

3

Transp.

cost

Facility

cost

Customer

Facility

…Slide4

Infrastructure Facility Disruptions

Facilities may be disrupted due toNatural disastersPower outagesStrikes…Adverse impactsExcessive operational costReduced service quality Deteriorate customer satisfaction…Effects on facility planning Suboptimal system designErroneous budget estimation4Slide5

Impacts of Facility Disruptions

Excessive 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 Distance

Operations

Cost

Facility costSlide6

Literature Review

Traditional 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 independent

6Slide7

Disruption Correlation

7Northeast Blackout (2003)Shared disaster hazardsHurricane Sandy (2012)

Shared supply

resources

Power Plant

Factories

Many

systems exhibit positively correlated disruptions Slide8

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

ReactorsSlide9

correlated

disruption scenariosnormal scenarioOperationscost

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

costSlide10

Outline

BackgroundInfrastructure network designFacility disruptionsMathematical Model Formulation challengesModeling approachNumerical ExamplesSolution quality

Case studiesSlide11

A facility is either disrupted or functioning

Disruption probability = long-term fraction of time when the facility is in the disrupted stateFacility state combination specifies a scenario

Facility 3

Facility 2

Facility 1

time

Normal scenario

Disrupted

state

Functioning

state

Normal scenario

Normal scenario

Scenario

1

Scenario

2

Scenario

3

Probabilistic Facility DisruptionsSlide12

Modeling Challenges

Deterministic facility location problem is NP-hardEven for given location design, # of failure scenarios increases exponential with # of facilitiesDifficult to consolidate scenarios under correlationScenario 1

…

Scenario 2

…

…

…

Scenario

N

+1

…

…

Scenario 2

N

Functioning

DisruptedSlide13

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:Slide14

Supporting Structure Properties

Proposition: 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

…

…Slide15

Supporting Structure Properties

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

A

B

CSlide16

System Performance - Expected Cost

Supporting stations K: (i.i.d. failure probability p)Service facilities J:Customers I:All scenarios S = {s}; each scenario s occurs at probability PsIn s, i is assigned to js ; js J (functioning facility), or js = 0, d

i0 := p

i

(penalty

)

Expected total system cost:

i

: demand –

l

i

; penalty

p

i

transp. cost

d

ij

k:

cons. cost

c

kj:

cons. cost fj

Construction cost

Expected operations costSlide17

Expected System Cost Evaluation

Consolidated cost formulaScenario consolidation principles

Separate each individual customer

Rank infrastructure units according to a customer’s visiting sequenceSlide18

Reliable Facility Location Model

subject to

Expected system cost

Assignment feasibility

Facility existence

Station existence

Integrality

Compact Linear Integer ProgramSlide19

Outline

BackgroundInfrastructure network designFacility disruptionsMathematical Model Formulation challengesModeling approachNumerical ExamplesSolution quality

Case studiesSlide20

Hypothetical Example

Supporting stations are givenIdentical network setting except for # of shared stations Identical facility disruption probabilities Case 1: Correlated disruptions Neighboring facilities share stationsCase 2: Independent disruptions (not sharing stations)Each facility is supported by an isolated station

…

…Slide21

Comparison Result

Case 1: Correlated disruptionsCase 2: Independent disruptionsSlide22

Case Study

Candidate 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.htmlSlide23

Optimal Deployment

Supporting station: Service facility:Slide24

Summary

Supporting 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 improvementSlide25

Acknowledgment

U.S. National Science Foundation CMMI #1234936CMMI #1234085 EFRI-RESIN #0835982CMMI #0748067Slide26

Xiaopeng Li

xli@cee.msstate.eduThank You!