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A mathematical modeling approach to improving locomotive utilization at a freight railroad. Kuo and Nicholls. Introduction. Rail has lost business to other modes in the past but is recapturing lost business Fuel efficiency advantage Computerized scheduling and routing

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a mathematical modeling approach to improving locomotive utilization at a freight railroad

A mathematical modeling approach to improving locomotive utilization at a freight railroad

Kuo and Nicholls

introduction
Introduction
  • Rail has lost business to other modes in the past but is recapturing lost business
    • Fuel efficiency advantage
    • Computerized scheduling and routing
    • Upgrading of equipment, terminals, etc.
    • Improved railcar identification system
    • M&A for scale economies
  • This paper discusses one approach which Conrail has taken to improve efficiency
slide3

Background

  • Conrail (at the time of study)
    • 11,700-mile rail network
    • Over 2,000 engines
  • Challenges
    • Efficiently position train crews and engines
    • 12-hour on-duty constraint
    • Return home or lodging after 12 hours
    • Geographic imbalances of locomotive availability due to variable traffic pattern
    • “Light” engine moves are necessary
    • Minimize light engine moves
slide4

Purpose

  • Develop a math model to minimize cost of light engine moves
  • Cost savings can be large because
    • Engines value $1.1 billion
    • Current operation is based on expert judgment
  • Difference from previous studies
    • Schedule assumed to repeat on a 7-dat cycle (not 24 hours)
    • Cost of light engine moves emphasized (not treated as sub-problem)
slide5

Model

  • Minimize the cost of light engine move
  • Fixed cost = labor cost, taxi cost, lodging cost, over-mileage cost
  • Variable cost = fuel cost
  • Decision variables
    • Distribution of engines among yards at the start of each week
    • Necessary light engine moves between yards
  • Constraints
    • Engine (horsepower) requirements
    • No more than 15 light engine moves per day
    • Other “common sense” conditions
slide6

Illustrative Application

  • Data
    • Three-yard data (from Conrail)
    • Assumed closed system
    • 16 available engines (minimum needed)
    • 105 decision variables, 106 constraints
  • Results
    • Minimized cost = $4,920.22
    • Current method = $6,233.97
    • Saving of $1,313.75 (about 21%)
    • In reality, cost savings can be larger (more opportunities for savings)
slide7

Sensitivity Analysis

  • Increased the available engines from 16 to 17
  • Investigate if increasing the fleet size is better (trade off between fleet size and light move)
  • Minimized cost = $3,823.26 (saving of $1,096.96)
  • Equivalent to $57,000 per year
  • Worth increasing the fleet size?
    • Acquisition cost of an engine = $1.5 million
    • Can be used for 30 years
    • In reality the savings can be larger
slide8

Conclusion and limitation

  • Cost saving potential
  • Can learn from airline industry
  • But be aware of limitations
    • Engines are often exchanged among carriers
    • Crews do not always stay at hotels (go home, “held-away-from-home” cost
    • Train schedules change constantly over time
    • Only the scheduled trains are considered
    • One type of engine is assumed
    • Maintenance downtime is ignored
slide9

Discussion questions

  • What are implications of this study to railroads?
  • Are railroads doing better job than airlines or motor carriers (in efficiency)?
  • Is the proposed model usable in the field?
  • What are pros and cons of railroads (as opposed to other mdoes)?
  • What are the future of railroads? What should they do to increase the share of business?