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178 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

NOTES AND COMMENTS

1 The optimal solution for the Hewlitt Corporation solution. If an optimal integer solution were
problem shows fractional numbers of required, the methods of integer linear
government bonds at 144.988, 187.856 and programming covered in Chapter 15 would have
228.188 units, respectively. However, fractional to be used.
bond units usually are not available. If we were 2 We implicitly assumed that interest from the
conservative and rounded up to 145, 188 and government bonds is paid annually. Investments
229 units, respectively, the total funds required for such as treasury notes actually provide interest
the eight-year retirement programme obligation payments every six months. In such cases, the
would be approximately E1254 more than the model can be reformulated with six-month
total funds indicated by the objective function. periods, with interest and/or cash payments
Because of the magnitude of the funds involved, occurring every six months.
rounding up probably would provide a workable

Revenue Management
Revenue management involves managing the short-term demand for a fixed perish-
able inventory in order to maximize the revenue potential for an organization. The
methodology, originally developed for American Airlines, was first used to deter-
mine how many airline flight seats to sell at an early reservation discount fare and
how many airline flight seats to sell at a full fare. By making the optimal decision for
the number of discount-fare seats and the number of full-fare seats on each flight,
the airline is able to increase its average number of passengers per flight and
maximize the total revenue generated by the combined sale of discount-fare and
full-fare seats. Today, all major airlines use some form of revenue management.
Given the success of revenue management in the airline industry, it was not long
before other industries began using revenue management. Models have been
expanded to include pricing strategies, overbooking policies, short-term supply
decisions and the management of nonperishable assets. Application areas now
include hotels, apartment rentals, car rentals, cruise lines and golf courses. The
Management Science in Action, Revenue Management at National Car Rental,
discusses how National Car Rental implemented revenue management.
The development of a revenue management system can be expensive and time-
consuming, but the potential payoffs can be substantial. For instance, the revenue
management system used at American Airlines generates nearly $1 billion in annual
incremental revenue. To illustrate the fundamentals of revenue management, we
will use a linear programming model to develop a revenue management plan for
Leisure Air. The company is based in Scotland and, in the winter months, offers a
service aimed at holidaymakers going on a skiing/snowboarding holiday in Switzer-
land and Austria. The company offers a daily flight from Glasgow to Salzburg and
from Edinburgh to Geneva using two Boeing 737-400 aeroplanes each with a 132
seat capacity. Both flights stopover briefly in Amsterdam. The return flights are
available later the same day.
Figure 4.10 illustrates the logistics of the Leisure Air problem situation. To keep
the size of the problem manageable and understandable we shall look only at the
outbound leg of the flights.
Leisure Air uses two fare classes: a discount-fare Q class and a full-fare Y class.
Reservations using the discount-fare Q class must be made at least 14 days in

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