A model of pricing perishable inventories using two restrictions, with an application to airline pricing

The existing literature in revenue management does not explicitly solve the ‘pricing problem’ per se in the sense that the fare structure is a solution from the model. In fact, fare prices must be pre–set and the demand forecasting each fare class, which is critical to revenue management models, is contingent on the fare price. It is also found that the persuasive feature of ‘fences’ or ‘restrictions’ used by airlines has not been properly addressed in the literature either. This paper studies the optimal pricing problem of perishable inventories using two restrictions. Linear programming techniques will be used to characterise the optimal pricing policies under three different scenarios: nested restrictions, mutually exclusive restrictions and the general case. For the first two scenarios, an optimal pricing policy exists, consisting of at most four price levels that sells restricted units at lower prices. For the general case, it is shown that an optimal pricing policy exists, consisting of at most five price levels. As an application, the airline pricing problem when a membership restriction and a product restriction are used together will be discussed. Applying the models developed in this paper can give airlines additional insights into how to pursue simple fare structures while, in the meantime, capitalising on additional revenue opportunities.