The two class model

Littlewood proposed the first static single resource quantity based RM model . It was a solution method for the seat inventory problem for a single leg flight with two fare classes. Those two fare classes have a fare of ₁ and ₂, whereby ₁ > ₂. The total capacity is and demand for class is indicated with _j. The demand is distributed via a distribution

Distribution (mathematics)

In mathematical analysis, distributions are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative...

 that is indicated with _j. The demand for class 2 comes before demand for class 1. The question now is how much demand for class 2 should be accepted so that the optimal mix of passengers is achieved and the highest revenue is obtained. Littlewood suggests closing down class 2 when the certain revenue from selling another low fare seat is exceeded by the expected revenue of selling the same seat at the higher fare . In formula form this means: accept demand for class 2 as long as:
_{2 11}

where
₂ is the value of the lower valued segment₁ is the value of the higher valued segment₁ is the demand for the higher valued segment and is the capacity left

This suggests that there is an optimal protection limit ₁^*. If the capacity left is less than this limit demand for class 2 is rejected. If a continuous distribution _j is used to model the demand, then ₁^* can be calculated using what is called Littlewood’s rule:
₁^*₁^-1₂₁

This gives the optimal protection limit, in terms of the division of the marginal revenue of both classes.

Alternatively bid prices can be calculated via
₁₁

Littlewood's model is limited to two classes. P. Belobaba developed a model based on this rule called Expected marginal seat revenue

Expected marginal seat revenue

EMSR stands for Expected Marginal Seat Revenue and is a very popular heuristic in Revenue Management. There are two versions: EMSRa and EMSRb, both of which were introduced by Belobaba. Both methods are for n-class, static, single-resource problems...

, abbreviated as EMSR, which is an -class model

See also

• Yield management
  Yield management
  Revenue management is the process of understanding, anticipating and influencing consumer behavior in order to maximize yield or profits from a fixed, perishable resource...
  
  
• Expected marginal seat revenue
  Expected marginal seat revenue
  EMSR stands for Expected Marginal Seat Revenue and is a very popular heuristic in Revenue Management. There are two versions: EMSRa and EMSRb, both of which were introduced by Belobaba. Both methods are for n-class, static, single-resource problems...