Dynamic Pricing for Reusable Resources: The Power of Two Prices

Abstract: 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.