MODEL:
! A strategy for airlines to minimize the loss from
noshows is to overbook flights. Too little
overbooking results in lost revenue. Too much
overbooking results in excessive penalties. This
model computes expected profits for various levels
of overbooking.;
SETS:
SEAT/1..16/; ! seats available ;
EXTRA/1..6/: EPROFIT; ! expected profits from
overbooking 16 seats;
ENDSETS
! Available data;
V = 225; ! Revenue from a sold seat;
P = 100; ! Penalty for a turned down customer;
Q = .04; ! Probability customer is a noshow;
! No. of seats available;
N = @SIZE( SEAT);
! Expected profit with no overbooking;
EPROFIT0 = V * @SUM( SEAT(I):
(1  @PBN(1 Q, N, I  1)));
! Expected profit if we overbook by 1 is:
EPROFIT0 + Prob(he shows) * ( V  (V + P) *
Prob(we have no room));
EPROFIT( 1) = EPROFIT0 +
( 1  Q) * ( V  ( V + P) * @PBN( Q, N, 0));
! In general;
@FOR( EXTRA( I) I #GT# 1:
EPROFIT( I) = EPROFIT( I  1) +
(1  Q) * ( V  ( V + P) *
@PBN( Q, N + I  1, I  1));
);
END
