Certainty-Equivalent Pricing with Dependent Demand and Limited Price-Changing Opportunities

When underlying demand follows a complex stochastic process, pricing problems are difficult to solve. In such cases, certainty equivalent (CE) policies, based on the solution to the deterministic relaxation of the stochastic pricing problem, can be used as practical alternatives. CE policies have lighter computational and informational requirements compared with solving the problem to optimality. Although the effectiveness of CE pricing policies has been theoretically studied when demands are independent, performance is not well known when demands are state-dependent and price-changing opportunities are limited. This paper analyzes the performance of CE policies in a pricing problem where future demand depends on sales and inventory, and the firm has limited opportunities to change prices. We show that CE policies are asymptotically optimal; as the problem scale (denoted by m) becomes large, the percentage revenue loss decreases at the rate of $\mathrm{\Theta }(1/\sqrt{m})$. We also extend the result to the joint pricing and (initial) inventory problem.