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

Santiago R. Balseiro (), Omar Besbes () and Dana Pizarro ()
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Santiago R. Balseiro: Graduate School of Business, Columbia University, New York, New York 10027
Omar Besbes: Graduate School of Business, Columbia University, New York, New York 10027
Dana Pizarro: Institute of Engineering Sciences, O’Higgins University, 611 Rancagua, Chile

Operations Research, 2024, vol. 72, issue 5, 2168-2189

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 ( DRC 2 ) problems. 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, online matching, and order fulfillment, to name a few. Furthermore, we establish that the class of DRC 2 problems, although 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, and also yields new results in specialized settings for which no such characterization was available. As such, the DRC 2 class isolates some common features of a broad class of problems and offers a new object of analysis. Funding: The work of D. Pizarro was supported by the Artificial and Natural Intelligence Toulouse Institute, which is funded by the French “Investing for the Future—PIA3” program [Grant ANR-19-P3IA-0004]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2441 .

Keywords: Stochastic Models; dynamic optimization; resource allocation; certainty equivalent; model predictive control; online matching; dynamic pricing; dynamic bidding; network revenue management; multi-secretary (search for similar items in EconPapers)
Date: 2024
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