Survey of Dynamic Resource Constrained Reward Collection Problems: Unified Model and Analysis

Abstract

Dynamic resource allocation problems arise under a variety of settings and have been studied across disciplines such as Operations Research and Computer Science. The present paper introduces a unifying model for a very large class of dynamic optimization problems, that we call dynamic resource constrained reward collection (DRC2). We show that this class encompasses a variety of disparate and classical dynamic optimization problems such as dynamic pricing with capacity constraints, dynamic bidding with budgets, network revenue management, on- line matching, or order fulfillment, to name a few. Furthermore, we establish that the class of DRC2 problems, while highly general, is amenable to analysis. In particular, we characterize the performance of the fluid certainty equivalent control heuristic for this class. Notably, this very general result recovers as corollaries some existing specialized results, generalizes other existing results by weakening the assumptions required, but also yields new results in specialized settings for which no such characterization was available. As such, the DRC2 class isolates some common features of a broad class of problems, and offers a new object of analysis.

Keywords: dynamic optimization, resource allocation, certainty equivalent, model predictive control, online matching, dynamic pricing, dynamic bidding, network revenue management