Intermodal Hazmat Transportation Problem with Timedependent Travel Risk

1
Inter-modal Hazmat Transportation Problem with
Time-dependent Travel Risk

• Vaggelis Floros, University of Thessaly, Greece
• Thanasis Ziliaskopoulos, Northwestern University
• Elaine Chang, University of South Florida
• January 25, 2006

2
Introduction

• The problem of computing minimum cost routes is
  considered in a transportation network with
  transshipment stations and a variety of
  alternative modes
• Risk is incorporated into the cost function
  without affecting the quality and speed of the
  computation
• The parameters of the transportation network are
  time-dependent, resulting in more realistic
  network representation
• Possible transfer delays, risks and costs between
  transport modes are easily accounted for

3
Background

• List, Mirchandani, Turnquist and Zografos (1991)
• Sivakumar, Batta and Karwap (1995)
• McCord and Leu (1995)
• Brainard, Lovett and Parfitt (1996)
• Frank, Thill and Batta (2000)
• Zografos and Androutspoulos (2004)
• Huang and Fery (2005 TRB CD-ROM)

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Problem Formulation

• A hazmat shipment is to be carried along an
  optimal path between origin and destination by
  combining the available modes, while accounting
  for travel times, costs and risks

arc travel cost
arc travel time
arc risk
transfer cost
transfer time
transfer risk
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Solution Algorithm

• Label-correcting approach
• Time-varying
• Maintain both cost and time labels, accounting
  for risk
• Account for transfer costs, time and risk

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Solution Algorithm

• Step 1 Initialize labels ?ijm(t), ? ijm(t) ?,
  ?iDm(t), ? iDm(t) 0
• Insert the destination node D into the Scan
  Eligible (SE) list.
• Step 2 While SE list not empty, delete the first
  node k from the list
• For every link-mode hjk m2?? -1(k)
• For every link-mode hij m1?? -1(j)
• For all time intervals t?T
• If ? ijm(t) gt ? ijkm1m2(t)?jkm2(t?ij
  km1m2(t))
• ?jkm2(t?ijkm1m2(t
  ) ?jkm2(t?ijkm1m2(t)))
• Then update ? ijm(t) , ? ijm(t) and
  insert node j into the SE list.
• Step 3 Terminate.

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CheckCost / Risk Label
some route to D
??jkm2
k
D
j
??ijm1
?
i
?ijm1(t)gt ? ijkm1m2(t)
?jkm2(t?ijkm1m2(t)) ?jkm2(t?ijkm1m2(t)
?jkm2(t?ijkm1m2(t)))
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UpdateCost / Risk Label
some route to D
??jkm2, ?jkm2
k
D
j
? ijm1, ?ijm1
?ijm1(t) ? ijkm1m2(t)
?jkm2(t?ijkm1m2(t)) ?jkm2(t?ijkm1m2(t)
?jkm2(t?ijkm1m2(t)))
i
?ijm1(t) ?ijkm1m2(t) ?jkm2(t?ijkm1m2(t
)) ?jkm2(t?ijkm1m2(t)
?jkm2(t?ijkm1m2(t)))
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UpdateSuccessor Label
some route to D
k
D
j
successorijm1(t) k, m2
successor to j on least cost path from j to D,
when arriving at j at time t from i and m1
i
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TDIMCP Convergence

• Algorithm terminates in a finite number of
  iterations - O( T2X2NH )
• At termination every cost label ?ijm(t) is either
• An infinite number no path exists, or
• A finite number cost of least-cost path

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Computational Complexity

• Linear with N, as expected

12
Computational Complexity

• Almost linear with T (ltT2)

13
Test Network
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Test Network
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Scenario 0 Base
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Scenario 1 Link Closure
X
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Scenario 2 Reduced Rail 3-4
X
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Scenario 3 High Risk Facility
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Scenario 4 Time-Varying Risk
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Summary

• An algorithm for computing intermodal routes is
  for hazmat shipments was presented, accounting
  for transfer delays, risks and costs between
  transport modes were considered
• Risk was incorporated into the cost function
  without affecting the quality and speed of the
  computation
• The parameters of the transportation network are
  time-dependent, resulting in more realistic
  network representation
• Computational tests show reasonable computation
  time and scenario results
• Future research Hazmat scenarios may be tested
  in a dynamic traffic assignment environment to
  capture realistic traffic congestion

21
Acknowledgements

• This work was partially funded by the European
  Unions INTERREG IIIc Project RESCUE A
  Catastrophe Response and Recovery Logistics and
  Transport Decision Support System

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Questions?

• Elaine Chang
• Phone [phone]
• Email echang_at_eng.usf.edu