This paper discusses the revenue management (RM) problem to maximize revenue by pricing items or services. One challenge in this problem is that the demand distribution is unknown and varies over time in real applications such as airline and retail industries. In particular, the time-varying demand has not been well studied under scenarios of unknown demand due to the difficulty of jointly managing the remaining inventory and estimating the demand. To tackle this challenge, we first introduce an episodic generalization of the RM problem motivated by typical application scenarios. We then propose a computationally efficient algorithm based on posterior sampling, which effectively optimizes prices by solving linear programming. We derive a Bayesian regret upper bound of this algorithm for general models where demand parameters can be correlated between time periods, while also deriving a regret lower bound for generic algorithms. Our empirical study shows that the proposed algorithm performs better than other benchmark algorithms and comparably to the optimal policy in hindsight. We also propose a heuristic modification of the proposed algorithm, which further efficiently learns the pricing policy in the experiments.

翻译：本文探讨了通过定价商品或服务以最大化收益的收益管理问题。该问题的一个挑战在于，现实应用如航空和零售行业中，需求分布未知且随时间变化。特别地，在需求未知情境下，由于需同时管理剩余库存与估计需求，时变需求尚未得到充分研究。为解决这一挑战，我们首先基于典型应用场景引入收益管理问题的周期性泛化模型。随后提出一种基于后验采样的高效算法，通过求解线性规划有效优化定价。我们推导了该算法在需求参数可跨时段关联的通用模型下的贝叶斯遗憾上界，同时给出了通用算法的遗憾下界。实证研究表明，所提算法优于其他基准算法，且与事后最优策略性能相当。我们还提出了算法的启发式改进，该改进在实验中能进一步高效学习定价策略。