Continuous-time Dynamic Pricing for Stabilizing Stochastic Demand

In this paper, we consider the pricing decision of a retailer who experiences peak demand for a product during a given time interval and wishes to stabilize the demand by adjusting the sales price. The stabilization of demand brings about desirable outcomes such as a reduction in the need for capacity investment and improves the production efficiency in the supply chain. We establish a continuous-time model to analyze the effect of dynamic pricing on peak demand. We find that a closed-form optimal pricing policy minimizes the difference between the actual demand and target level. It is shown that the dynamic pricing not only reduces peak demand but also mitigates fluctuations in the peak demand. Using electricity consumption data as a case study, we show that the proposed pricing policy is effective for reducing the mean peak demand compared to a constant pricing policy.