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

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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


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

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


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

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)


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

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


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

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)


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

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


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

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


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

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?


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