Dynamic Nonlinear Pricing of Inventories over Finite Sales Horizons

We consider a finite-horizon, finite-capacity dynamic pricing model where consumers may purchase multiple units of the same product. We present three models that differ in their complexity and revenue potential. The dynamic nonlinear pricing (DNP) model allows the seller to dynamically selecting a price for each bundle size. The dynamic linear pricing model restricts the seller to dynamically select a unit price for all bundle sizes. There can be a significant revenue gap between the two models, but the additional revenues require a nonlinear policy that may be more challenging to implement. This motivates the study of dynamic block pricing as an intermediate pricing model where prices are linear within each block. A heuristic for this last model provides almost as much revenue as DNP while avoiding its complexity.