A Maximum Entropy Joint Demand Estimation and Capacity Control Policy

We propose a tractable, data-driven demand estimation procedure based on the use of maximum entropy (ME) distributions, and apply it to a stochastic capacity control problem motivated from airline revenue management. Specifically, we study the two fare class “Littlewood” problem in a setting where the firm has access to only potentially censored sales observations; this is also known as the repeated newsvendor problem. We propose a heuristic that iteratively fits an ME distribution to all observed sales data, and in each iteration selects a protection level based on the estimated distribution. When the underlying demand distribution is discrete, we show that the sequence of protection levels converges to the optimal one almost surely, and that the ME demand forecast converges to the true demand distribution for all values below the optimal protection level. That is, the proposed heuristic avoids the “spiral down” effect, making it attractive for problems of joint forecasting and revenue optimization problems in the presence of censored observations.