Reliable Infrastructure Location Design under Interdependent Disruptions

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

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

Transp. cost Facility cost Logistics Infrastructure Network • 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? Customer Facility … 3

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

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? Facility cost Operations Cost Reachable Distance

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

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

Prominent Example: Fukushima Nuclear Leak • Earthquake • → Power supply failure • → Reactors meltdown Power supply for cooling systems Reactors (Sources: ibtimes.com; www.pmf.kg.ac.rs/radijacionafizika)

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 normal scenario correlated disruption scenarios Operations cost Initial investment Operations cost

Probabilistic Facility Disruptions • 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 1 Facility 2 Facility 3 Scenario 3 Scenario 1 Normal scenario Normal scenario Normal scenario Scenario 2 time Functioning state Disrupted state

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 2N Disrupted Functioning

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:

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 … …

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

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 Ps • In s, i is assignedto js;js J (functioning facility), orjs= 0, di0 := pi (penalty) • Expected total system cost: k: cons. cost ck transp. cost dij j: cons. cost fj i: demand – li; penalty pi Expected operations cost Construction cost

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

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

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 … …

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

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 eGRIDhttp://www.epa.gov/cleanenergy/energy-resources/egrid/index.html

Optimal Deployment Supporting station: Service facility:

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

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

Thank You! Xiaopeng Li xli@cee.msstate.edu

Reliable Infrastructure Location Design under Interdependent Disruptions