In addition to maximizing the total revenue, decision-makers in lots of industries would like to guarantee balanced consumption across different resources. For instance, in the retailing industry, ensuring a balanced consumption of resources from different suppliers enhances fairness and helps main a good channel relationship; in the cloud computing industry, resource-consumption balance helps increase customer satisfaction and reduce operational costs. Motivated by these practical needs, this paper studies the price-based network revenue management (NRM) problem with both demand learning and fair resource-consumption balancing. We introduce the regularized revenue, i.e., the total revenue with a balancing regularization, as our objective to incorporate fair resource-consumption balancing into the revenue maximization goal. We propose a primal-dual-type online policy with the Upper-Confidence-Bound (UCB) demand learning method to maximize the regularized revenue. We adopt several innovative techniques to make our algorithm a unified and computationally efficient framework for the continuous price set and a wide class of balancing regularizers. Our algorithm achieves a worst-case regret of $\widetilde O(N^{5/2}\sqrt{T})$, where $N$ denotes the number of products and $T$ denotes the number of time periods. Numerical experiments in a few NRM examples demonstrate the effectiveness of our algorithm in simultaneously achieving revenue maximization and fair resource-consumption balancing

翻译：除最大化总收益外，众多行业中的决策者还需保证不同资源间的消耗平衡。例如，零售业中确保来自不同供应商的资源消耗平衡能增强公平性并维护良好的渠道关系；云计算行业中资源消耗平衡有助于提升客户满意度并降低运营成本。受这些实际需求驱动，本文研究了同时考虑需求学习与资源消耗公平平衡的基于价格的网络收益管理（NRM）问题。我们引入正则化收益（即带有平衡正则化的总收益）作为目标函数，将资源消耗公平平衡纳入收益最大化目标。我们提出一种基于上置信界（UCB）需求学习方法的原-对偶型在线策略以最大化正则化收益。我们采用多项创新技术，使算法成为针对连续价格集和广泛平衡正则化器的统一且计算高效的框架。该算法实现了最坏情况下的遗憾界$\widetilde O(N^{5/2}\sqrt{T})$，其中$N$表示产品数量，$T$表示时段数量。在若干NRM示例上的数值实验证明了该算法在同时实现收益最大化与资源消耗公平平衡方面的有效性。