Single-Leg Revenue Management with Advice

Abstract

Single-leg revenue management is a foundational problem of revenue management that has been particularly impactful in the airline and hotel industry: Given n units of a resource, e.g. flight seats, and a stream of sequentially-arriving customers segmented by fares, what is the optimal online policy for allocating the resource. Previous work focused on designing algorithms when forecasts are available, which are not robust to inaccuracies in the forecast, or online algorithms with worst-case performance guarantees, which can be too conservative in practice. In this work, we look at the single-leg revenue management problem through the lens of the algorithms-withadvice framework, which attempts to optimally incorporate advice/predictions about the future into online algorithms. In particular, we characterize the Pareto frontier that captures the tradeoff between consistency (performance when advice is accurate) and competitiveness (performance when advice is inaccurate) for every advice. Moreover, we provide an online algorithm that always achieves performance on this Pareto frontier. We also study the class of protection level policies, which is the most widely-deployed technique for single-leg revenue management: we provide an algorithm to incorporate advice into protection levels that optimally trades off consistency and competitiveness. Moreover, we empirically evaluate the performance of these algorithms on synthetic data. We find that our algorithm for protection level policies performs remarkably well on most instances, even if it is not guaranteed to be on the Pareto frontier in theory.

Online Bipartite Matching with Advice: Tight Robustness-Consistency Tradeoffs for the Two-Stage Model

“…Optimality results in prediction-augmented online algorithms. Tight robustnessconsistency tradeoffs have become recently understood in prediction-augmented ski rental (Purohit et al 2018, Bamas et al 2020, Wei and Zhang 2020 and single-commodity accept/reject problems (Sun et al 2021, Balseiro et al 2022. Our online matching problem contrasts these by having a multi-dimensional state space, for which to our knowledge tightness results are rare.…”

Bicriteria Multidimensional Mechanism Design with Side Information

“…This is an extremely active area of research (Mitzenmacher and Vassilvitskii [36] provide a survey of work in this area). There have been recent explicit connections of the algorithms-with-predictions paradigm to mechanism design in specific settings such as strategic scheduling, facility location, online Nash social welfare maximization, and single-leg revenue management [3,[13][14][15]24]. Most related to our work, Xu and Lu [49] study the design of high-revenue auctions to sell a (single copy of a) single item to multiple bidders when the mechanism designer has access to point predictions on the bidders' values for the items.…”

Online Resource Allocation with Samples

“…Improving the worst-case guarantee of online algorithms with the help of extra information has been the topic of recent literature on algorithm design with machinelearned advice. See, for example, Antoniadis et al (2020) for using advice on the maximum value of secretaries in the online secretary problems, Lattanzi et al (2020) for using advice on the weights of jobs in online scheduling problems, Lykouris and Vassilvtiskii (2018) for using the advice in the online caching problem, Balseiro et al (2022) for using advice in single leg revenue management problems, 7 and Jin and Ma (2022) for using advice in online bipartite matching problems. Our work contributes to this line of work by presenting the first algorithm that optimally exploits rather unstructured advice obtained through the sample information in an online resource allocation problem.…”

“…To account for this challenge, we go beyond having a point estimate for the demand vector (i.e., the number of customers of different types) as done in Balseiro et al (2022). (For a detailed comparison between our work and Balseiro et al (2022), refer to Sections 1.2 and 7.) Instead, we adopt the approach of utilizing an uncertainty set for the demand vector.…”

“…See alsoHwang et al (2021),Esfandiari et al (2015) for works that consider a hybrid arrival model with both adversarial and stochastic components. For such models, the stochastic component can reduce the uncertainty in the demand process.7 InBalseiro et al (2022), the advice is a predicted demand vector.…”