On the Performance of Certainty-equivalent Pricing

Abstract

Certainty equivalent (CE) policies, based on solutions to the deterministic relaxation of a stochastic optimization problem, are widely used in practice due to their fewer computational and informational requirements. In revenue management, the effectiveness of CE pricing policies has been theoretically studied when demands are independent across periods and prices can be changed continuously. This paper addresses an existing gap by analyzing how CE policies perform in a more general setting: when demand is affected by past sales and by remaining inventory and under a setting with periodic price reviews. We show that CE policies are asymptotically optimal: as the market size m grows, the percentage loss, as compared to the optimal policy, decreases at the rate of O(m^{-0.5}). Our numerical results are even more promising. Even with a relatively small market size and very few price changes, CE policies perform well and often result in revenues that are only few percentages lower than optimal. We also theoretically establish the benefit of a closed-loop CE policy over an open-loop policy. Lastly, we look at the joint optimization of pricing and initial inventory show that CE policies remain asymptotically optimal even if inventory is optimized.