Goal Programming at Antique Airlines

Antique Airlines has a fleet of 100 Jetliners and 150 Commuter aircraft.  Due to new, stricter safety requirements, no planes can be flown next month unless they are inspected this month.  Antique management has two conflicting goals: one is Short Term Net Revenue, the other is the Prestige necessary to remain profitable int he long run.  set a preliminary goal of achieving 80% of normal levels of revenue and 80% of normal prestige next month.

40 of the Jetliners and 75 of the Commuter planes MUST be inspected this month if the airline is to avoid bankruptcy or worse.

A Jetliner has three engines, a Commuter plane has two engines, and there are only enough engine work crews to inspect 455 engines in the next month.

A Jetliner has five computers, a Commuter plane has two computers, and there are only enough computer work crews to inspect 594 computers.

A Jetliner has seven exits, a Commuter plane has two exits, and there are only enough exit work crews to inspect 751 exits.

All other resources are in ample supply.

Because of lower operating costs and less competition on commuter routes, flying a Commuter plane gives the company twice as much short term net revenue as flying a Jetliner. Thus, the total net revenue is (J+2C) times the revenue of a single Jetliner.  The ultimate revenue goal is to return all 250 planes to service, yielding a total net revenue of  100+2*150 = 400 times the revenue of a single Jetliner.

However, this revenue can only be maintained in the long run if the airline retains its prestige; flying a Commuter plane contributes only one tenth as much prestige as flying a Jetliner. Thus, the total prestige is (10J+c) times the prestige of a single Commuter plane. (J+0.1C) times the prestige of a single JetlinerThe ultimate prestige goal is to return all 250 planes to service, yielding a total net revenue of  10*100+150 = 1150 times the prestige of a single Commuter plane. Jetliner.

Antique management has set a preliminary goal of achieving 80% of normal levels of revenue and 80% of normal prestige next month.

How many of each kind of aircraft should Antique Airlines inspect this month?

ANSWER: It depends on how they want to trade off the conflicting goals of revenue and prestige.

First Viewpoint:

Loss of prestige and loss of revenue in a given month both decrease the value of the company. Let's try to figure out the total harm to the company as a linear function of lost revenue and lost prestige, and minimize this function to maximize the health of Antique Airlines.

Second Viewpoint:

Let's decide which is more important, revenue or prestige, then minimize the loss to that component. If more than one solution optimizes the most important criterion, then use the other criterion to break the tie.

Third Viewpoint

In order to avoid taking too big a "hit" on either criterion, let's concentrate on improving whichever criterion is weakest.