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

1. A mathematical modeling approach to improving locomotive utilization at a freight railroad Kuo and Nicholls

2. 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

3. 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

4. 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)

5. 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

6. 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)

7. 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

8. 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

9. 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?