A computer based system for maximizing revenue by determining an optimal quantity of a product to be sold is disclosed. The system determines the optimal number of seats to be sold for a flight based upon the flight's capacity and forecasted costs associated with the flight. The forecasting is based upon probabilistic distribution models takes into account passenger itinerary data, passenger and market historical data, whether a passenger has flown on a previous leg of an itinerary, the ripple denied boarding effect of reaccommodating a denied passenger. The system evaluates the potential effect of double selling a unit of inventory (e.g., seats). Downstream inventory control, revenue management and reservations systems may use the optimization data to affect the operation of the airline.