Stochastic Assignment with Expiration

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dc.contributor.advisorPerez-Salazar, Sebastianen_US
dc.creatorShapoval, Boris Alexandrovichen_US
dc.date.accessioned2025-05-30T21:06:09Zen_US
dc.date.available2025-05-30T21:06:09Zen_US
dc.date.created2025-05en_US
dc.date.issued2025-04-25en_US
dc.date.submittedMay 2025en_US
dc.date.updated2025-05-30T21:06:09Zen_US
dc.description.abstractThis thesis introduces a capacitated online stochastic bipartite matching problem, where offline nodes may be matched multiple times and expire at unknown stochastic times. This problem is PSPACE hard; thus we first focus on the subproblem where each offline node can be matched at most once and aim to develop algorithms that achieve large expected overall values from the matchings. A decision maker (DM) must balance obtaining a matching reward now and keeping enough possibilities for the future with possible expirations. Since this problem is intractable, we first provide a compact linear program (LP) formulation that upper bounds the expected value of an optimal algorithm. Based on this LP, we design a polynomial-time algorithm that guarantees an expected value of at least a $1 - 1/e$ fraction of the optimal expected value. We demonstrate the tightness of our LP-based analysis by providing tight integrality gaps as well as worst-case instances. Returning to the capacitated problem, we provide another LP relaxation. We generalize our previous algorithms to evaluate their numerical performance on the harder, capacitated problem. We observe that some natural ideas do not generalize, while others seem to remain competitive.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.urihttps://hdl.handle.net/1911/118526en_US
dc.language.isoenen_US
dc.subjectonline stochastic matchingen_US
dc.subjectlinear programmingen_US
dc.titleStochastic Assignment with Expirationen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineComputational & Applied Math, Operations Researchen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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