Modelling Revenue Management Problem under Fare Class Interval Customer Choice

In order to explain customer choice conditioned on opened classes more realistically and efficiently, I assume a customer considers a discrete choice as a fare class interval and buys the lowest opened class with that interval. Unlike the traditional one-dimensioned, unstructured choice model, I model customer choice as a two-dimensioned fare class interval distribution. I take closed set as a more efficient research angle, and find out an additive principle to reduce computation. Then I turn the traditional maximized decision principle into minimized decision principle and get a new model for the maximized total revenue management problem. This model builds the foundation for more efficient explorations to revenue management problem.