Profit Optimization with a Power-Law Adjustable Coefficient for Zero Ending Inventories Dynamic Pricing Model, Stochastic Demand, and Fixed Lifetime Product

Abstract

We consider a single product with a fixed lifetime and price sensitive intensity of a Poisson customers flow. A model with a power adjustable coefficient of a dynamic retail price control through the intensity of the demand is considered providing almost surely zero ending inventories at the end of the product's lifetime. To obtain probabilistic characteristics of the selling process and the expected profit, the diffusion approximation of the stock level process is used. The task of the expected profit maximization with respect to the adjustable coefficient for a linear approximation of the intensity-of-price dependence is solved.