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 Fuel efficiency advantage Computerized scheduling and routing Computerized scheduling and routing Upgrading of equipment, terminals, etc. Upgrading of equipment, terminals, etc. Improved railcar identification system Improved railcar identification system M&A for scale economies 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 11,700-mile rail network Over 2,000 engines Over 2,000 engines  Challenges Efficiently position train crews and engines Efficiently position train crews and engines 12-hour on-duty constraint 12-hour on-duty constraint Return home or lodging after 12 hours Return home or lodging after 12 hours Geographic imbalances of locomotive availability due to variable traffic pattern Geographic imbalances of locomotive availability due to variable traffic pattern “Light” engine moves are necessary “Light” engine moves are necessary Minimize light engine moves 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 Engines value $1.1 billion Current operation is based on expert judgment Current operation is based on expert judgment  Difference from previous studies Schedule assumed to repeat on a 7-dat cycle (not 24 hours) Schedule assumed to repeat on a 7-dat cycle (not 24 hours) Cost of light engine moves emphasized (not treated as sub-problem) 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 Distribution of engines among yards at the start of each week Necessary light engine moves between yards Necessary light engine moves between yards  Constraints Engine (horsepower) requirements Engine (horsepower) requirements No more than 15 light engine moves per day No more than 15 light engine moves per day Other “common sense” conditions Other “common sense” conditions

6. Illustrative Application  Data Three-yard data (from Conrail) Three-yard data (from Conrail) Assumed closed system Assumed closed system 16 available engines (minimum needed) 16 available engines (minimum needed) 105 decision variables, 106 constraints 105 decision variables, 106 constraints  Results Minimized cost = $4,920.22 Minimized cost = $4,920.22 Current method = $6,233.97 Current method = $6,233.97 Saving of $1,313.75 (about 21%) Saving of $1,313.75 (about 21%) In reality, cost savings can be larger (more opportunities for savings) 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 Acquisition cost of an engine = $1.5 million Can be used for 30 years Can be used for 30 years In reality the savings can be larger 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 Engines are often exchanged among carriers Crews do not always stay at hotels (go home, “held-away-from-home” cost Crews do not always stay at hotels (go home, “held-away-from-home” cost Train schedules change constantly over time Train schedules change constantly over time Only the scheduled trains are considered Only the scheduled trains are considered One type of engine is assumed One type of engine is assumed Maintenance downtime is ignored 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?