Distribution of Selling Duration for Zero Ending Inventory Dynamic Pricing Model with Exponentially Distributed Purchases

Abstract

Abstract We consider a perishable product with a fixed shelf life under fixed-order quantity policy. The demand is a compound Poisson process with a price sensitive intensity and an exponential batch size’s distribution. A model of retail price control is considered allowing us to sell a lot without leftovers almost surely during the product’s lifetime. The Laplace transforms of the conditional probability density function of the time to the end of the session and the conditional mean of this time are obtained. The simulation results of the session duration are also presented and compared with previously obtained approximate ones.