Approximate Dynamic Programming for High-Dimensional Resource Allocation Problems

Abstract

The allocation of human and physical resources over time is a fundamental problem that is central to management science. In this paper we review a mathematical model of dynamic resource allocation that is motivated by problems in transportation and logistics. In principle, problems of this type can be solved via dynamic programming. However, three "curses of dimensionality" give rise to intractable computational requirements. We present computationally efficient approximate dynamic programming algorithms developed by the first author and collaborators for application to problems in freight transportation. We discuss how these algorithms address the three curses of dimensionality and how they relate to other independent threads of research on mathematical programming and approximate dynamic programming.