Littlewood's rule

The earliest Revenue Management model is known as Littlewood’s rule.

The two class model

Littlewood proposed the first static single resource quantity based RM model [1]. 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 R1 and R2, whereby R1 > R2. The total capacity is C and demand for class j is indicated with Dj. The demand is distributed via a distribution that is indicated with Fj( ). 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 [2]. In formula form this means: accept demand for class 2 as long as:

R2 \ge R1 * Prob( D1>x )

where

R2 is the value of the lower valued segment
R1 is the value of the higher valued segment
D1 is the demand for the higher valued segment and
x is the capacity left

This suggests that there is an optimal protection limit y1*. If the capacity left is less than this limit demand for class 2 is rejected. If a continuous distribution Fj(x) is used to model the demand, then y1* can be calculated using what is called Littlewood’s rule:

y1* = F1-1(1-R2/R1)

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

\pi(x) = R1 * Prob( D1>x )

Littlewood's model is limited to two classes. P. Belobaba developed a model based on this rule called Expected marginal seat revenue, abbreviated as EMSR, which is an n-class model [3]

References

  1. ^ Pak, K. and N. Piersma (2002). Airline Revenue Management: An overview of OR Techniques 1982-2001. Rotterdam, Erasmus university
  2. ^ Littlewood, K. (1972). "Forecasting and Control of Passenger Bookins." AGIFORS Symposium Proc. 12
  3. ^ Belobaba, P. P. (1987). Air Travel Demand and Airline Seat Inventory Management. Flight Transportation Laboratory. Cambridge, MIT. PhD

See also