Strategic, Tactical and Real-time Planning of Locomotives at Norfolk Southern Using Approximate Dynamic Programming

Locomotive planning has been a popular application of classical optimization models for decades, but with very few success stories. There are a host of complex rules governing how locomotives should be used. In addition, it is necessary to simultaneously manage locomotive inventories by balancing the need for holding power against the need for power at other yards. At the same time, we have to plan the need to return foreign power, and move power to maintenance facilities for scheduled FRA appointments. An additional complication arises as a result of the high level of uncertainty in transit times and delays due to yard processing, and as a result we may have to plan additional inventories in order to move outbound trains on time despite inbound delays. We describe a novel modeling and algorithmic strategy known as approximate dynamic programming, which can also be described as a form of “optimizing simulator” which uses feedback learning to plan locomotive movements in a way that closely mimics how humans plan real-world operations. This strategy can be used for strategic and tactical planning, and can also be adapted to real-time operations. We describe the strategy, and summarize experiences at Norfolk Southern with a strategic planning system. INTRODUCTION Locomotive planning is one of the most complex operational problems in freight transportation. Planners have to take into consideration a host of operational characteristics that describe a locomotive to best utilize the fleet to meet the service requirements of the trains. Locomotive fleets can represent billions of dollars in investments, and as a result railroads have every incentive to manage this investment as efficiently as possible. The complexity of the problem has put it well past the capabilities of even today’s advanced optimization solvers. Completely overlooked in these models are the important sources of uncertainty such as transit time delays, the dynamics of scheduling commodities such as coal and grain, and the ever present problem of equipment failures and maintenance. Railroads face three classes of planning problems when managing railroads:  Strategic planning – The major question here is fleet size and mix, but other questions can include understanding the impact of improvements in transit time reliability, the effect of changes in train plans and changes in interchange policies with other railroads.  Tactical planning and operational forecasting – Here the horizon is 1-7 days, and the question is whether there will be significant shortages of power that might require additional repositioning, short-term modifications in leasing decisions and perhaps the decision to retain locomotives that belong to other railroads (known as “foreign power”) and incur additional per diem charges.  Real-time planning – The decision here is the assignment of specific locomotives to specific trains that are departing over the immediate horizon (typically the next 12 hours).