Three-class static revenue management model with buy-up behavior

We study the optimal booking limits in a three-class static revenue management model with customers' buy-up behavior, where given fraction of customers rejected seat reservation requests each period try to book following periods at higher fares. However, it is difficult apply backward recursion dynamic programming approach this optimization problem, owing dependence demands for period. Specifically, factor $ \beta from third second and another \alpha first period, we derive set two simultaneous equations terms multiple definite integrals involving distribution functions original demand Numerical examples are provided illustrate on $. The maximized expected increases as and/or increase by reducing limits.