Optimality of (s,S)-policies in a dynamic pricing model with replenishment opportunities: A sample path approach

This paper studies discrete-time inventory replenishment decisions in a continuous-time dynamic-pricing setting where customer arrivals follow a non-homogeneous Poisson process. Each replenishment order incurs a linear variable cost and a fixed cost. Using a novel sample-path approach, we prove that the optimal inventory policy in the presence of dynamic pricing is of (s,S)-type.