We study dynamic joint assortment and pricing where a seller updates decisions at regular accounting/operating intervals to maximize the cumulative per-period revenue over a horizon $T$. In many settings, assortment and prices affect not only what an arriving customer buys but also how many customers arrive within the period, whereas classical multinomial logit (MNL) models assume arrivals as fixed, potentially leading to suboptimal decisions. We propose a Poisson-MNL model that couples a contextual MNL choice model with a Poisson arrival model whose rate depends on the offered assortment and prices. Building on this model, we develop an efficient algorithm PMNL based on the idea of upper confidence bound (UCB). We establish its (near) optimality by proving a non-asymptotic regret bound of order $\sqrt{T\log{T}}$ and a matching lower bound (up to $\log T$). Simulation studies underscore the importance of accounting for the dependency of arrival rates on assortment and pricing: PMNL effectively learns customer choice and arrival models and provides joint assortment-pricing decisions that outperform others that assume fixed arrival rates.

翻译：我们研究动态联合品类与定价问题，其中卖方在固定的会计/运营周期内更新决策，以最大化在时间范围 $T$ 内的累积单周期收入。在许多场景中，品类和价格不仅影响到达顾客的购买选择，还会影响该周期内到达的顾客数量，而经典的多项逻辑特（MNL）模型假设到达顾客数是固定的，这可能导致次优决策。我们提出一个泊松-MNL 模型，该模型将上下文相关的 MNL 选择模型与一个到达率依赖于所提供品类和价格的泊松到达模型相结合。基于此模型，我们利用上置信界（UCB）的思想开发了一种高效算法 PMNL。我们通过证明其具有 $\sqrt{T\log{T}}$ 阶的非渐近遗憾界以及一个匹配的（至多相差 $\log T$）下界，确立了其（近乎）最优性。仿真研究强调了考虑到达率对品类和定价依赖性的重要性：PMNL 能有效学习顾客选择和到达模型，并提供优于那些假设固定到达率方法的联合品类-定价决策。