Revenue management with learning of a market factor

Description/Abstract

We study the selling of a fixed quantity of a perishable product where conditional on a random variable V, customer arrivals obey a Poisson process whose rate is a known multiple of V. Price is either bid by customers or set by the seller. In each case, we approximate the seller’s optimal policy via a discrete-time, finite-horizon dynamic program that incorporates learning of V via a sufficient statistic, cumulative arrivals or sales. When customers bid a price, a minimal acceptable price exists and decreases in quantity. We then assume the seller sets a price and a customer purchases only if his reservation price, modeled by a general distribution, exceeds the price. For the sub-problem of pricing one unit that has a salvage value, there exists a unique optimum price that increases in the salvage value, provided the reservation price has increasing hazard. In selling k > 1 units, the price is that of the one-unit problem with salvage value being the value difference of k and k − 1 units, one step ahead. Thus, provided these differences decrease as k increases, price decreases. With gamma and right-truncated gamma priors, we find empirically that price decreases in time and in k, and it increases in the sufficient statistic and in the prior variance. Empirically, the right-truncated gamma with identical mean and variance to a gamma and minimum kurtosis yields higher prices below some mean demand, and lower ones above it.