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, which incurs a steady-state performance loss of ${O}(\sqrt{c})$ compared to optimality when supply and demand scale with $c$. We propose a class of dynamic "stock-dependent" policies that 1) are computationally tractable and 2) can attain a steady-state performance loss of $o(\sqrt{c})$. We give parametric bounds based on the local shape of the reward function at the optimal fluid admission probability and show that the performance loss of stock-dependent policies can be as low as ${O}((\log{c})^2)$. We characterize the tight performance loss 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. We extend our results to settings with multiple resources and multiple customer classes. Finally, we demonstrate this "minimally dynamic" class of two-price policies performs 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，我们研究了可复用资源的定价问题。我们考虑一个系统，其中包含固定数量相同副本的单一资源为具有异质支付意愿的客户提供服务，且使用时长分布是任意的。当使用时长的分布不具备无记忆性时，最优动态策略在计算上是难以处理的，因此现有文献主要关注静态定价。当供应和需求随参数 $c$ 成比例增长时，静态定价与最优策略相比，其稳态性能损失为 ${O}(\sqrt{c})$。我们提出了一类动态的"库存依赖"策略，该策略 1) 在计算上是易于处理的，并且 2) 能够实现 $o(\sqrt{c})$ 的稳态性能损失。我们基于最优流体接纳概率处奖励函数的局部形状给出了参数化界限，并表明库存依赖策略的性能损失可低至 ${O}((\log{c})^2)$。我们刻画了库存依赖策略的紧性能损失，并证明实际上可以通过一个简单的双价格策略来实现，该策略在库存低于某个阈值时设定较高价格，否则设定较低价格。我们将结果扩展到具有多种资源和多类客户的场景。最后，我们通过数值实验证明，即使在非渐近场景下，这种"最小动态"的双价格策略类也表现良好，这表明微小的动态性可以产生显著的效果。