Locomotive planning at norfolk southern: An optimizing simulator using approximate dynamic programming

Warren Buckler Powell, Belgacem Bouzaiene-Ayari, Coleman Lawrence, Clark Cheng, Sourav Das, Ricardo Fiorillo

Research output: Contribution to journalReview articlepeer-review

17 Scopus citations


For decades, locomotive planning has been approached using the classical tools of mathematical programming; the result has been very large-scale integer programming models that are beyond the capabilities of modern solvers but still require a host of simplifying assumptions that limit their use for analyzing important planning problems. The primary interest of Norfolk Southern was in developing a model that could assist it with fleet sizing. However, the cumulative effect of the simplifications required to produce a practical integer programming formulation resulted in models that underestimated the required fleet. We use the modeling and algorithmic framework of approximate dynamic programming, which uses an intuitive balance of simulation and optimization with feedback learning, to produce a highly detailed model that calibrates accurately against historical metrics. The result was a model that can be used to plan fleet size and mix, be sensitive to a wide range of operating parameters, and adapt to many scenarios.

Original languageEnglish (US)
Pages (from-to)567-578
Number of pages12
Issue number6
StatePublished - Nov 1 2014

All Science Journal Classification (ASJC) codes

  • Strategy and Management
  • Management Science and Operations Research
  • Management of Technology and Innovation


  • Approximate dynamic programming
  • Locomotives
  • Programming: dynamic
  • Transportation: rail


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