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We consider the problem of online allocation (matching and assortments) ofreusable resources where customers arrive sequentially in an adversarialfashion and allocated resources are used or rented for a stochastic durationthat is drawn independently from known distributions. Focusing on the case oflarge inventory, we give an algorithm that is $(1-1/e)$ competitive for generalusage distributions. At the heart of our result is the notion of a relaxedonline algorithm that is only subjected to fluid approximations of thestochastic elements in the problem. The output of this algorithm serves as aguide for the final algorithm. This leads to a principled approach forseamlessly addressing stochastic elements (such as reusability, customerchoice, and combinations thereof) in online resource allocation problems, thatmay be useful more broadly.

Online Allocation of Reusable Resources via Algorithms Guided by Fluid Approximations