Constant-Factor Algorithms for Revenue Management with Consecutive Stays
Ming Hu, Tongwen Wu
TL;DR
This work studies network revenue management with requests that require a consecutive interval of slots on one of $M$ resources, motivated by railway and hotel applications. It develops polynomial-time policies with constant-factor guarantees against the online optimum for two scenarios: accept-or-reject and BAM-based assortment decisions; Bernoulli arrivals yield a $1 - \frac{1}{e}$-approximation for accept-or-reject and $0.25$ for BAM, with general arrivals reducing guarantees by a factor $1 - \frac{1}{e}$. The algorithmic framework combines a decomposable structural property via maximal free-slot sequences, the proposal-discarding approach, and coupling techniques; for BAM, a sales-based fluid relaxation (SBLP) guides assortments and a randomized coupling preserves independence across resources. Extending to general arrivals, the results become $(1 - \frac{1}{e})^2$ for accept-or-reject and $\tfrac{1}{4}(1 - \frac{1}{e})$ for BAM, with corresponding integrality-gap analyses and NP-hardness results illustrating the limits of approximation. Overall, the paper delivers the first constant-factor guarantees for online algorithms in revenue management with consecutive stays, bridging online matching techniques and assortment optimization, and providing a foundation for practical policies in railway and hotel contexts.
Abstract
We study network revenue management problems motivated by applications such as railway ticket sales and hotel room bookings. Requests, each requiring a resource for a consecutive stay, arrive sequentially with known arrival probabilities. We investigate two scenarios: the accept-or-reject scenario, where a request can be fulfilled by assigning any available resource; and the BAM-based scenario, which generalizes the former by incorporating customer preferences through the basic attraction model (BAM), allowing the platform to offer an assortment of available resources from which the customer may choose. We develop polynomial-time policies and evaluate their performance using approximation ratios, defined as the ratio between the expected revenue of our policy and that of the optimal online algorithm. When each arrival has a fixed request type (e.g., the interval of the stay is fixed), we establish constant-factor guarantees: a ratio of 1 - 1/e for the accept-or-reject scenario and 0.25 for the BAM-based scenario. We further extend these results to the case where the request type is random (e.g., the interval of the stay is random). In this setting, the approximation ratios incur an additional multiplicative factor of 1 - 1/e, resulting in guarantees of at least 0.399 for the accept-or-reject scenario and 0.156 for the BAM-based scenario. These constant-factor guarantees stand in sharp contrast to the prior nonconstant competitive ratios that are benchmarked against the offline optimum.