Closely related to the newsboy problem (in a mathematical sense) is the airline overbooking problem. Given that a certain percentage of fliers with reservations will not show up for a flight, airlines that don't overbook will be sending most planes up with empty seats. Assuming the penalty cost for overbooking is not too high, an airline that hopes to maximize revenue should overbook its flights. The following model determines the optimal number of reservations to allow on a flight and assumes the number of no-shows on a flight has a binomial distribution.

MODEL:

!

This overbooking model determines the number of

reservations, M, to allow on a flight if the

no-show distribution is binomial;

 

! Some available data ;

  N = 16;   ! Total seats available;

  V = 225;  ! Revenue from a sold seat;

  P = 100;  ! Penalty for a turned down customer;

  Q = .04;  ! Probability a customer is a no-show;

 

! The probability to turn down customers is

 @PBN( Q, M, M - N), therefore the corresponding

 expected loss due to imperfect information is:

 ( V + P) * @PBN( Q, M, M - N), and we want the

 loss to equal the revenue V on the margin. So,

 the break-even equation is:;

 

  ( V + P) * @PBN( Q, M, M - N) = V;

 

! Note, you should round up if M is fractional;

 

END

Model: OBOOKO