Abstract: Discrete dynamic programming, widely used in addressing optimization over time, suffers from the so-called curse of dimensionality, the exponential increase in problem size as the number of system variables increases. One method to reduce the computational resources required to find solutions is to avoid the use of state transition probability matrices, which grow in the square of the size of the state space. This can be done through the use of expected value (EV) functions, which compute the expectation of functions of the future state variables conditioned on current variables. Two ways that this leads to potential gains arise when the state transition can be broken into separate phases and when the transitions for different state variables are conditionally independent. Both of these situations arise in models that are used in natural resource management and are illustrated with several examples including the dynamic reserves site selection problem, managing invasive species on a spatial network and managing wildlife harvests with multiple population stage classes. Efficiency gains include far lower memory requirements and orders of magnitude reductions in computing time.
Paul L. Fackler is a professor of agricultural and resource economics and associate professor of applied ecology at North Carolina State University and an internationally recognized teacher and scholar in the areas of decision analysis and computational methods. He co-authored a widely used textbook on the use of computational methods (Applied Computational Economics and Finance) along with the CompEcon Toolbox, a package of computer programs used in both teaching and research. The main focus of his research currently is the application of dynamic optimization tools to problems involving the management of natural resources. He is also the developer of the MDPSolve package for solving dynamic optimization problems.