Jiaqi Shi

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 price. If no units are available, customers immediately leave. Serving a customer corresponds to using one unit for an exponential service time. The objective is to maximize the steady-state revenue rate. Although an optimal policy is fully dynamic, we provide two main results that show a simple static policy is universally near-optimal for any service rate, arrival rate, and number of units in the system. When there is one class of customers who have a monotone hazard rate (MHR) valuation distribution, we prove that a static pricing policy guarantees 90.2% of the optimal policy. When there are multiple classes of customers, we prove that static pricing guarantees 78.9% of the optimal policy.

Considering the real-world situations where past purchases could influence future prices, this research examines the multi-product price optimization problem under a multi-stage choice model. Particularly, the seller commits to a multi-stage pricing policy and determines product prices based on the customer’s purchase history, and the customer makes purchase decisions such that the expected utility is maximized. We show that the pricing problem has a unique optimal solution under some mild conditions and the optimal solution satisfies a modified equal adjusted markup property. Moreover, the optimal pricing policy has an important property, namely, the product with a higher adjusted markup in earlier stages should always lead to lower prices in subsequent stages. We also show that compared to customers that are myopic, the seller should offer higher first-stage prices and lower second-stage prices to forward-looking customers, which will lead to a higher profit.