Stochastic optimal control for a general class of dynamic resource allocation problems

Abstract

We consider a general class of dynamic resource allocation problems within a stochastic optimal control framework. This class of problems arises in a wide variety of applications, each of which intrinsically involves resources of different types and demand with uncertainty and/or variability. The goal is to dynamically allocate capacity for every resource type in order to serve the uncertain/ variable demand and maximize the expected net-benefit over a time horizon of interest based on the rewards and costs associated with the different resources. We derive the optimal control policy within a singular control setting, which includes easily implementable algorithms for governing the dynamic adjustments to resource allocation capacities over time. Numerical experiments investigate various issues of both theoretical and practical interest, quantifying the significant benefits of our approach over alternative optimization approaches.