Empty Railcar and Locomotive Distribution at NS

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Empty Railcar and Locomotive Distribution at NS
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Agenda

• Car distribution model (CDM)
• Locomotive routing model (LRM)
• Network planning and disruption management using
  OR models

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Car Distribution Model (CDM)

• CDM is a decision support system for car
  distributors and management.
• Recommend optimal empty car distribution plan to
  assist car distributors.
• Provide decision support reports using historical
  data.
• Goal of efficient car distribution is to reduce
  empty transit time for a given load and increase
  the number of orders furnished using existing car
  fleet.
• Provide what-if scenarios capability to test
  impacts of business rule and supply/demand
  changes

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Car Cycle in CDM
Minimize time
Unload car
Move empty car
Move loaded car
Move empty car
Load car
M
T
W
Th
F
Sa
Su
M
T
W
Th
F
Sa
Su
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Modeling the Business

• Model uses a planning period of 3 weeks.
• Car demand is a combination of orders placed and
  forecasted.
• Car supply is projected from car movement events,
  and next earliest empty available times are
  computed from OPD (plan) and DTSR (train
  arrival).
• Other car distribution business rules are
  modeled.
• Unit train moves
• Different car preferences with priorities
• Customer priorities
• Destination of orders
• Cars going offline

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Optimization frameworks

• Using standard network transformation

Each link captures the marginal reward of an
additional car.
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A car distribution problem

• Using value function approximations, we may
  reposition cars before orders become known

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Multistage problems
t
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Multistage problems
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Multistage problems
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CDM Computational Approach

• Formulates a decision flow problem in a
  time-space network.
• In this network, arcs are decisions and nodes are
  resources.
• Solves this using optimizing-simulator technology
  to maximize car utilization.
• Invokes solution methods from dynamic programming
  with learning.

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Mathematical Formulation

• The full simulation problem is very large. So the
  problem is decomposed into manageable Network
  LP sub-problems over several time periods.
• Minimize sub-problem objective function
• Decision flow costs penalty costs - decision
  benefits.

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Multiple Decisions on Resources
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CDM Outputs

• Car Movements (hold, reposition, loaded,
  empty-to-load, load-to-empty).
• Order Decisions (hold, loaded move,
  empty-to-load, load-to-empty, dropped).
• VFAs that portray the values of various moves at
  the end of optimization.
• Many other stats and details
• Mileage
• Transit time
• Cycle time
• Order furnishing rate

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Current Status

• The car distribution model for open coil cars
  rolled out in January 2005. The improvement in
  car utilization has been significant.

• There was a reduction in empty transit time of
  open coils cars in spite of an overall reduction
  in network velocity during the corresponding
  period.

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Open Coil Statistics
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Next Steps

• Continue Implementation of CDM for the following
  car types
• Covered coil cars in November 2005
• Gondola cars in March 2006 .
• Proposal for extending CDM for boxcars has
  received full support from NS management and
  capital fund has been allocated for boxcar in
  2006.
• Enhance the model to be flexible and scalable so
  that it can be applied to boxcars.

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Locomotive Routing Model (LRM)

• A real-time system that
• Assigns locomotives to trains over a planning
  horizon given a train schedule.
• Uses complex business rules developed in
  co-ordination with the cage.
• Uses the locomotive operating plan as input.
• Produces a realistic flow of trains and
  locomotives for the given time horizon.
• Uses optimization model to recommend locomotive
  repositioning and light engine moves to balance
  the surplus and deficit of locomotives.
• Uses an optimization engine to improve locomotive
  utilization and reduce train delay.
• Developed jointly by Norfolk Southern and Castle
  Lab of Princeton University.

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Inputs

• Train schedules
• TSR/DTSR
• Train tonnages and historical performance
• Locomotives available for future assignment
• Existing NS fleet
• Locomotive Operating Plan
• Inbound/outbound connection
• Business Rules and Constraints
• Power termination locations by train symbol
• Special equipment (LSL,CAB,TOILET) requirements
  by train symbol
• Special locomotive consist configuration (number
  of leaders, back-to-back) requirements by train
  symbol
• Foreign Cycles and Coupled Trains
• Locomotive tonnage ratings
• Locomotive characteristics
• Consist busting
• FRA mandated maintenance

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Outputs

• Locomotive assignment recommendations
• Locomotive surplus/deficit by terminal, division
  and region
• Consist on each train.
• Train Delays due to locomotive unavailability.
• Locomotive terminal dwells.
• Locomotive operating plan compliance.
• Locomotive Utilization.

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Status and Next Steps

• LRM started in 1996, but was put on hold in 2002
  due to
• Lack of user support
• Variations in train departures and arrivals
• Poor visibility of on-demand (or unscheduled)
  trains
• Currently, there are interests at NS to use LRM
  for strategic planning
• Impact of train performance on locomotive
  utilization and requirements
• Locomotive fleet sizing