Optimizing Railroads Train Schedules: Case Studies from the Field

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Optimizing Railroads Train Schedules Case
Studies from the Field
Arvind Kumar Ravindra K. Ahuja
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Collaborators

• Development Partnership with BNSF
• Architects Designers
• Pooja Dewan, BNSF Railway
• Krishna C. Jha, Innovative Scheduling
• Arvind Kumar, Innovative Scheduling
• Ravindra K. Ahuja, Innovative Scheduling

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Motivation

• Train schedules significantly impact railroad
  costs
• Car hire costs
• Crew costs
• Locomotive costs
• Railroads are looking for ways to cut costs and
  improve productivity.
• Train plans are currently generated manually and
  leave significant room for improvement.
  Optimization-based train schedule can save costs
  dramatically.
• This presentation describes some case studies on
  railroads data using our Innovative Train
  Scheduling Optimizer (ITSO).

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Overview of the Presentation

• Innovative Train Scheduling Optimizer An
  Overview
• Case Studies Optimizing Train Schedules
• Innovative Train Scheduling Decision Support
  System

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Train Schedule Optimizer Overview
Train Scheduling Optimizer
Blocks
Trains
Optimizes Objectives
Block-to-Train Assignments
Shipments
Trip Plan
Shipment-BlockAssignments
Balanced CrewAssignment
Crew
Honors Constraints
Balanced Locomotive Assignment
Locomotive
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Decision Variables

• Decision
• Train origins, destinations, and routes
• Train days of operation and train times
• Train block-to-train assignment by day of the
  week
• Trip plans for all cars
• Locomotive assignment
• Crew assignment

• Constraints
• Yard capacity constraints
• Line capacity constraints
• Train capacity constraints
• Business rules

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Constraints

• Yard Constraints
• Number of trains originating at any node in each
  given time window is limited.
• Number of trains terminating at any node in each
  given time window is limited.
• Number of trains passing through each node in
  each given time window is limited.
• Number of car handlings and block swaps at each
  yard in each given time window is limited.
• Track Constraints
• Speed of a train on a track depends upon the type
  of train.
• Number of trains passing through any corridor in
  any given time window is limited.
• Satisfy headway constraints.

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Constraints (contd.)

• Train Capacity Constraints
• The number of cars on any train is limited
• The length of any train is limited
• The weight-carrying capacity of any train is
  limited
• No more than specified number of blocks per train
  
• Number of stops of a train is limited
• Locomotive Constraints
• Honor locomotive minimum connection times between
  trains
• Provide number of locomotive based on train
  tonnages
• Crew Constraints
• Honor crew minimum connection times between
  trains
• Honor crew union rules related to work and rest

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Objective Function Terms
Car days
Car miles
Block swaps
Train miles
Loco cost
Train starts
Crew cost
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Contribution Integration of Railroad Resources
Railcar
ITSO
Constrained by Operating Rules
Constrained by Network Capacity
Locomotive
Crew

• We consider these three resources by maintaining
  three time-space networks.

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Railcar Flow Network
Ground Nodes
Train 1
Train 1
car
car
car
car
Train 2
car
car
Time
car
car
car
Train 2
car
car
car
car
Train 3
car
Train 5

• We construct the weekly time-space train network
  and flow railcars through this network.

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Locomotive Flow Network
Train 1
Train 4
Train 2
Train 5
Train 3
Train 6

• We construct the weekly space-time train network
  and locomotives cycle through this network.

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Crew Flow Network
Home Terminal

• We construct the weekly space-time crew network
  and crews cycle through this network.
• We create a separate network for each crew
  district.

Away Terminal
Time
Train Arcs
Deadhead Arcs
Rest Arcs
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Our Contribution

• Problem size (per week)
• Number of railcars 100,000 200,000
• Number of locomotives 2,000 4,000
• Number of crew districts 300 400
• Number of crews 4,000 6,000
• We have developed a computer program to solve
  this problem within 2 hours on a standard
  workstation.
• Uses a variety of operations research techniques
• Construction heuristics
• Network flows Linear programming
• Neighborhood search
• Very large-scale neighborhood (VLSN) search

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A Two-Stage Decomposition Process
Train Route Optimization

• Train schedule without time
• Train routes
• Block-train assignment
• Locomotive assignment
• Crew assignment

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Three Time-Space Networks
Railcar Network
Crew Network
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Clean-Slate Train Scheduling

• Determines a zero-base optimized train plan.
• Can also be used for various types of what-if
  analysis or for special studies.

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Incremental Train Scheduling
Network, Block and Shipment Inputs
Current Train Schedule

• The user can specify the extent of changes in the
  current train schedule.
• It can be used periodically to improve the
  current train schedule.

Scope of change in train plan
Optimizer
Revised Train Schedule, Block-Train Assign.,
Trip Plans
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Overview of the Presentation

• Train Scheduling Optimizer An Overview
• Case Studies Optimizing Train Schedules
• Innovative Train Scheduling Decision Support
  System

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Case Study Overview

• We are conducting studies for two Class I
  railroads to improve their current train
  schedules and estimate the cost savings of our
  train plans. We do not wish to disclose the
  identity of these railroads.
• These results are still being evaluated by our
  railroad partners, thus the results may change.
• However, we believe that these savings estimates
  are realizable.

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Case Study 1 Incremental Optimization

• Objective
• Reduce the number of crew starts by at least 100
  per week.
• Constraints
• Do not add any new train.
• Do not change train frequencies or train timings.
  
• Degrees of Freedom
• May eliminate some trains completely.
• Optimally re-assign the blocks riding on deleted
  trains to other trains.

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Case Study 1 Results

• Conclusions
• Trains starts reduced by 4.8 resulting in 2.2
  decrease in crew starts.
• A reduction in over 100 crew starts was achieved
  even with the tight constraints imposed.

• These results have been evaluated by our railroad
  partner and they find the incremental train
  schedule implementable.

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Case Study 2 Incremental Optimization

• Objective
• Reduce the number of crew starts by at least 200
  per week.
• Constraints
• Do not change train timings.
• Degrees of Freedom
• May eliminate some trains completely.
• Model may add some trains (less than we delete)
• Change frequencies of few trains.
• Optimally re-assign the blocks riding on deleted
  trains to other trains.

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Case Study 2 Results

• Conclusions
• Trains starts reduced by 7.31 resulting in 4.52
  decrease in crew starts.
• A reduction in over 200 crew starts was achieved.

• These results are being evaluated by our railroad
  partner.

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Case Study 3 Clean-Slate Optimization

• Objective
• Determine a zero-base or clean-slate train
  schedule and obtain the maximum possible cost
  savings in car-hire, crew and locomotive costs.
  
• Constraints
• Use network capacities as used in the railroads
  current plan
• Degrees of Freedom
• May delete or/and some trains.
• May change train frequencies.
• May change train timings.
• May change block-train assignments.

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Case Study 3 Results
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Summary

• Determining a railroads train schedule is a very
  complex optimization problem.
• Optimization-based methods promise significant
  improvements over a railroads manually generated
  train schedule.
• The savings obtained by the train scheduling
  optimizer are very impressive. Though these
  savings estimate are yet to be fully verified by
  our railroad partners, we believe that these are
  quite realistic and attainable.

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Overview of the Presentation

• Train Scheduling Optimizer An Overview
• Case Studies Optimizing Train Schedules
• Innovative Train Scheduling Decision Support
  System

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ITSO A Web-Based Decision Support System

• We have built a web-based decision support system
  for train scheduling that can be used for
  clean-slate and incremental train scheduling.
• Features of this system
• Ability to create and manage multiple scenario.
• Each scenario can store multiple train schedules.
• Ability to analyze any solution in any scenario
  and drill-down to the desired level of details.
• Ability to compare two solutions in the same
  scenario in great detail.
• Ability to calibrate constraints and costs to
  perform extensive what-if analysis.
• Ability to enable users to manually modify the
  model generated solutions.

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Next Steps

• Our train scheduling software is available for
  consulting activities.
• We will be happy to work with you to reduce your
  train operating costs and create significant
  value for you.

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• www.InnovativeScheduling.com