A full information pricing problem for the sale of several identical commodities

Abstract

k commodities of the same kind are for sale in a finite time interval I, and potential customers arrive according to a Poisson process. It is assumed that no customer may buy more than one unit. The seller has to fix, for each t ∈I, a price for which he is willing to sell a commodity at time t. This decision is based on the knowledge of the probabilities that a customer appearing at time t will accept a price of at most x monetary units (for all t ∈I and x > 0). There is no possibility of recall of previous customers. We characterize an optimal price function and the maximal expected gain. Further the relation to the persistency problem of Elfving (1967) is exhibited. © 1990 Physica-Verlag.