Constant-Factor Algorithms for Revenue Management with Consecutive Stays

TL;DR

This paper develops polynomial-time algorithms with constant-factor approximation guarantees for revenue management problems involving requests for consecutive stays, applicable to railway and hotel booking scenarios, improving upon prior nonconstant ratios.

Contribution

The paper introduces new policies with proven constant-factor approximation ratios for revenue management with consecutive stays, including scenarios with fixed and random request types, and customer preferences.

Findings

Achieves a 1 - 1/e approximation ratio for accept-or-reject scenario with fixed request types.

Provides a 0.25 approximation ratio for BAM-based scenario with fixed request types.

Extends results to random request types, with ratios at least 0.399 and 0.156 respectively.

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.