The Online Reservation Problem

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Problem definition: Many sharing economy platforms operate as follows. Owners list availability of resources (such as apartments, cars, or tutoring services), prices, and contract-length limits. Customers propose contract start times and lengths. Owners decide immediately (or within a short time window) whether to accept or decline each proposal, even if the contract is for a future date. Accepted proposals generate a revenue for the owner. Declined proposals are lost. At any decision epoch, the owner has no information about future proposals. The owner seeks easy-to-implement algorithms that have the best the worst-case relative performance (also called competitive ratio, CR). Academic/Practical Relevance: On the academic side, we propose algorithms with provable CRs for the owner's problem described above. On the practical side, we model trade-offs faced by owners on popular sharing economy platforms and present easy-to-implement algorithms for their use. Methodology: We first derive a lower bound on the CR of any algorithm. We then analyze CRs of all intuitive algorithms that are fair in the sense that no proposal is declined whenever a resource is available. We propose two new algorithms and analyze their CRs. Results: We prove that the CRs of algorithms proposed by us are significantly better than that of any fair algorithm for certain parameter-value ranges. Managerial Implications: Owners may have the intuition that reserving capacity for higher value jobs that arrive later helps improve the CR and that this may be operationalized using thresholds. Our algorithms prove that this intuition is indeed correct. Moreover, we show that if non-optimal thresholds are chosen, then they may hurt the CR. By analyzing the CRs of fair algorithms and those proposed by us, we provide a rigorous method by which an owner can choose an appropriate algorithm to use.