Optimal Dynamics is drawing on over 30 years of research by CASTLE Laboratory into developing strategic, operational, and real-time models for a variety of problems in transportation, logistics, and energy.  Rather than building a series of specialized models, we work with a fundamental model for resource allocation problems that can be adapted to a wide range of settings.  Some examples of major projects include:

Transportation and logistics

  • Real-time driver assignment for truckload trucking
  • Strategic and operational planning of locomotives
  • Strategic and operational planning of linehaul operations for less-than-truckload trucking
  • Management of high-value spare parts
  • Simultaneous scheduling of pilots, aircraft and customers, or the scheduling of drivers, tractors, tanker trailers, product and customer tanks.


  • Detailed simulation of energy markets and the power grid for a major independent system operator
  • Simulation of the distribution grid of a major utility to plan response strategies from storms
  • Replacement policies for high-voltage transformers

Our models are able to capture a very high level of detail: resources with over a dozen attributes (drivers, pilots, aircraft, energy generators), timing of activities down to the minute, simultaneous planning of multiple resource layers (locomotives/trains, pilots/aircraft/customers, driver/tractor/trailer/product).  Where appropriate, we also model uncertainty, allowing us to capture the cost of uncertainty in our strategic planning models, or to produce robust policies for operational planning.

We can adapt the same core model to handle both strategic and real-time/operational planning:

  • Strategic planning - Our attention to modeling detail allows us to accurately capture productivity of people and equipment, producing realistic estimates of fleet sizes and inventories for different scenarios.  We can test operating policies and work rules, taking advantage of our powerful optimization algorithms to determine how a system might respond to new situations.
  • Real-time/operational planning - Our models are detailed enough to make assignments of people and equipment to handle specific tasks, while handling a variety of operational goals and constraints.

You may not have a problem as complex as optimizing 2000 locomotives for a major railroad...  but don't you like the idea of using a technology that can?