Maximum likelihood approach for demand unconstraining problem with censoring information incompleteness

The forecast of passenger demand in Revenue Management is usually based on historical booking data that reflects the number of sales rather than true demand which is constrained by booking limits. That is why the process of demand forecasting under such circumstances is called unconstraining. The goal of every unconstraining approach is to get empirical or theoretical estimation of true demand. The application of the maximum likelihood method to unconstraining problems in Revenue Management is advocated in the article based on the construction of the distribution function for the censored demand depending on availability of the censoring information. Numerical results are presented on comparative analysis of existing unconstraining methods and the method used in the article. It is demonstrated that maximum likelihood method proves to be more efficient in case of high percentage of censoring. Another important advantage of the method connected to the fact that it enables one to process the situation of censoring information incompleteness when some elements of the observed sample data are known to be censored or not and for the others this information is not available. Mathematical computer environment Wolfram Mathematica has been used for obtaining all the numerical results presented in the article.