Static Pricing: Universal Guarantees for Reusable Resources
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We consider a fundamental pricing model in which a fixed number of units of a reusable resource are used to serve customers. Customers arrive to the system according to a stochastic process and upon arrival decide to purchase or not the service depending on their willingness to pay and the current price. The service time during which the resource is used by the customer is stochastic and the firm may incur a service cost. This model represents various markets for reusable resources such as cloud computing, shared vehicles, rotable parts, and hotel rooms. In the present paper, we analyze this pricing problem when the firm attempts to maximize a weighted combination of three central metrics: profit, market share, and service level. Under Poisson arrivals, exponential service times, and standard assumptions on the willingness to pay distribution, we establish series of results that characterize the performance of static pricing in such environments. In particular, while an optimal policy is fully dynamic in such a context, we prove that a static pricing policy simultaneously guarantees 78.9 optimal policy. Notably this result holds for any service rate and number of units the firm operates. In the special case where there are two units and the induced demand demand is linear, we also prove that the static policy guarantees 95.5 on a large testbed of instances suggest that the latter result is quite indicative of the profit obtained by the static pricing policy across all parameters.
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