Motivated by real-world applications such as rental and cloud computing services, we investigate pricing for reusable resources. We consider a system where a single resource with a fixed number of identical copies serves customers with heterogeneous willingness-to-pay (WTP), and the usage duration distribution is general. Optimal dynamic policies are computationally intractable when usage durations are not memoryless, so existing literature has focused on static pricing, whose steady-state reward rate converges to optimality at rate $\mathcal{O}(c^{-1/2})$ when supply and demand scale with $c$. We show, however, that this convergence rate is suboptimal, and propose a class of dynamic "stock-dependent" policies that 1) preserves computational tractability and 2) has a steady-state reward rate converging to optimality faster than $c^{-1/2}$. We characterize the tight convergence rate for stock-dependent policies and show that they can in fact be achieved by a simple two-price policy, that sets a higher price when the stock is below some threshold and a lower price otherwise. Finally, we demonstrate this "minimally dynamic" class of two-price policies to perform well numerically, even in non-asymptotic settings, suggesting that a little dynamicity can go a long way.

翻译：受租赁和云计算服务等实际应用的启发，我们研究了可重用资源的定价问题。我们考虑一个系统，其中单一资源拥有固定数量的相同副本，为具有异质支付意愿（WTP）的客户提供服务，且使用时长分布具有一般性。当使用时长非无记忆性时，最优动态策略在计算上难以处理，因此现有文献集中于静态定价——在供需按比例$c$缩放时，其稳态报酬率以$\mathcal{O}(c^{-1/2})$的速率收敛至最优性。然而，我们证明这一收敛速率是次优的，并提出一类动态"库存依赖"策略，该策略：1）保持计算易处理性，2）稳态报酬率以快于$c^{-1/2}$的速率收敛至最优性。我们刻画了库存依赖策略的紧致收敛速率，并证明这些速率实际上可通过一种简单的两价格策略实现——当库存低于某个阈值时设定较高价格，反之设定较低价格。最后，我们通过数值实验表明，即使在非渐近设定下，这类"最小动态"的两价格策略也表现良好，这表明微小的动态性可产生显著效果。