Page 202 -

182 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

The optimal solution to the Leisure Air revenue management problem is shown in
Figure 4.11. The value of the optimal solution is E103,103. The optimal solution
shows that GAQ ¼ 33, GSQ ¼ 44, GVQ ¼ 22, GAY ¼ 16 and so on. Thus, to max-
imize revenue Leisure Air should allocate 33 Q class seats to Glasgow–Amsterdam,
44 Q class seats to Glasgow–Salzburg, 22 Q class seats to Glasgow–Geneva, 16 Y class
seats to Glasgow–Amsterdam and so on.
Over time, reservations will come into the system and the number of remaining seats
available for each ODIF will decrease. For example, the optimal solution allocated 44
Q class seats to Glasgow–Salzburg. Suppose that two weeks prior to the departure date,
Dual prices tell all 44 seats have been sold. Now, suppose that a new customer calls the Leisure Air
reservation agents the reservation office and requests a Q class seat for the flight. Should Leisure Air accept
additional revenue
associated with the new reservation even though it exceeds the original 44-seat allocation? The dual
overbooking each ODIF. price for the Glasgow–Salzburg Q class demand constraint will provide information
that will help a Leisure Air reservation agent make this decision.
Constraint 6, GSQ 44, restricts the number of Q class seats that can be
allocated to Glasgow–Salzburg to 44 seats. In Figure 4.11 we see that the dual price
for constraint 6 is E85. The dual price tells us that if one more Q class seat was
available from Glasgow–Salzburg, revenue would improve by E85. This increase in
revenue is referred to as the bid price for this origin-destination-itinerary fare. In
general, the bid price for an ODIF tells a Leisure Air reservation agent the value of
one additional reservation once a particular ODIF has been sold out.
By looking at the dual prices for the demand constraints in Figure 4.11, we see
that the highest dual price (bid price) is E376 for constraint 8, GAY 16. This
constraint corresponds to the Glasgow–Amsterdam Y class itinerary. Thus, if all 16
seats allocated to this itinerary have been sold, accepting another reservation will
provide additional revenue of E376. Given this revenue contribution, a reservation
agent would most likely accept the additional reservation even if it resulted in an
overbooking of the flight. Other dual prices for the demand constraints show a bid
price of E358 for constraint 20 (AVY) and a bid price of E332 for constraint 10
(GVY). Thus, accepting additional reservations for the Amsterdam–Geneva Y class
and the Glasgow–Geneva Y class itineraries is a good choice for increasing revenue.
A revenue management system like the one at Leisure Air must be flexible and adjust
to the ever-changing reservation status. Conceptually, each time a reservation is
accepted for an origin-destination-itinerary fare that is at its capacity, the linear pro-
gramming model should be updated and re-solved to obtain new seat allocations along
with the revised bid price information. In practice, updating the allocations on a real-
time basis is not practical because of the large number of itineraries involved. However,
the bid prices from a current solution and some simple decision rules enable reservation
agents to make decisions that improve the revenue for the firm. Then, on a periodic basis
such as once a day or once a week, the entire linear programming model can be updated
and resolved to generate new seat allocations and revised bid price information.

4.6 Data Envelopment Analysis

Data envelopment analysis (DEA) is a specialist application of LP that analyzes the
relative performance of a group of similar organizations. For example, we may have
a company that operates with different business units across the world. We may want
to compare the performance of the business unit in Asia with those in other parts of
the world. We may have a large retail company that has stores located in different
parts of the country. Again, we want to compare the performance of stores in
relation to each other. We may have different university business schools running

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has
deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.