Optimal pricing problem for a pay-per-use system based on the Internet of Things with intertemporal demand

In recent years, pay-per-use (PPU) services have been introduced that involve metered billing based on data collected from sensor devices. Although such a PPU service provides benefits to customers who are not planning to use the product frequently, the company is exposed to uncertainty regarding the amount of revenue that will be generated. This study examines the conditions under which a PPU service will be effective at increasing a firm's profit in the presence of uncertainty regarding customers' expected and actual usage frequencies. We consider two pricing problems. First, we formulate a single-period model for when the selling price of the product is given and derive an optimal PPU fee to maximize the expected profit. Then, we analytically show that the PPU service has higher profits than the case without the service when the actual usage is higher than the expected usage. Second, we formulate a joint pricing model in which the firm determines jointly the PPU fee and the selling price to maximize the expected profit. Then, we numerically show that the firm benefits from the PPU service when both the customers' valuation and the actual usage are high.