A technical note on the dynamic nonstationary inventory-pricing control model with lost sale

This paper studies a non-stationary, periodic review and finite horizon dynamic inventory-pricing problem with lost sale. The existing research on this problem suffers from a lack of concavity. Thus, strong conditions have to be assumed to obtain the optimal policy, i.e. stationary system and additive demand. This paper uses multiplicative demand model, which significantly outperforms the additive demand models from statistical prediction accuracy prospect. We establish the concavity which results in the optimality of Base Stock List Price (BSLP) policy. The conditions for the concavity can be satisfied by many commonly used convex demand and distributions in the literature. Our results complement the existing research for the non-stationary lost sale models in this area.