Kellogg Operations Seminar Series
presents
Victor Araman
NYU
“Dynamic Pricing for Non-Perishable
Products with Demand Learning”
October 8, 2004
Room 561, 10am
We consider the long-term operations of a retailer selling non-perishable products. The
retailer continuously observes his inventory, learns about demand, and dynamically
chooses the price to maximize the total discounted revenues. When all units are sold, a
terminal value is incurred representing expected benefits from future businesses. We
assume that a Poisson process governs the demand with a price sensitive intensity.
We study first the full information case, where the retailer knows exactly how the
demand rate is affected by the price. Second, we move to the case where the demand
rate is parameterized by an unknown parameter to which the retailer has a prior. The
retailer then conducts a Bayes updating to learn on the demand. Finally, we consider a
“learning by selling” scheme, where the current demand rate is affected by the number
of units already sold.
In each of the three cases, we formulate the HJB equation and solve for the optimal
dynamic pricing strategy. We characterize the optimal value function and obtain
managerial insights on how to evaluate the profitability of such business. In particular,
we show that in the Bayes update case the value function is asymptotically linear in the
prior.