The Power of Static Pricing for Reusable Resources

Abstract

We consider the problem of pricing a reusable resource service system. Potential customers arrive according to a Poisson process and purchase the service if their valuation exceeds the current price. If no units are available, customers immediately leave without service. Serving a customer corresponds to using one unit of the reusable resource, where the service time has a general distribution. The objective is to maximize the steady-state revenue rate. This system is equivalent to the classical Erlang loss model with price-sensitive customers, which has applications in vehicle sharing, cloud computing, and spare parts management. With general service times, the optimal pricing policy depends not only on the number of customers currently in the system but also on how long each unavailable unit has been in use. We prove several results that show a simple static policy is universally near-optimal for any service time distribution, arrival rate, and number of units in the system. When there are multiple classes of customers with regular valuation distributions, we prove that static pricing guarantees 78.9% of the revenue of the optimal dynamic policy, achieving the same guarantee known for a single class of customers with exponential service times. When there is one class of customers who have a monotone hazard rate valuation distribution, we prove that a static pricing policy guarantees 97.5% of the revenue from the optimal inventory-based policy. In addition, we prove that the optimal static policy can be easily computed, resulting in the first polynomial-time approximation algorithm for the multi-class problem. Finally, we consider the extensions to irregular valuation distributions and general multi-resource networks.