Transportation Resource Management

Abstract In this article, we describe a variety of modeling and solution approaches for transportation resource management problems. The solution approaches that we propose either build on deterministic linear programming formulations, or formulate the problem as a dynamic program and use tractable approximations to the value functions. We describe two classes of methods to construct approximations to the value functions. The first class of methods relax certain constraints in the dynamic programming formulation of the problem by associating Lagrange multipliers with them, in which case, we can solve the relaxed dynamic program by concentrating on one location at a time. The second class of methods use a stochastic approximation idea along with sampled trajectories of the system to iteratively update and improve the value function approximations. After describing several solution approaches, we provide a flexible paradigm that is useful for modeling and communicating complex resource management problems. Our numerical experiments demonstrate the benefits from using models that explicitly address the randomness in resource management problems.