Freedom Express

Freedom Express (FreeEx), affectionately known as the Filibuster Fly, is a small commuter airline based in Washington, D.C., that serves the U.S. East coast. It runs nonstop flights between several cities and Reagan National Airport (DCA). DCA frequently is congested, and at such times, planes are required to fly in a "stack" over the field. In other words, planes in the process of landing and those waiting for permission to land are deployed above the field. FreeEx management is interested in determining how long its planes will have to wait so that an adequate amount of fuel can be loaded before departure from the outlying city to cover both the intercity flying time and the time in the stack. Excess fuel represents an unnecessary cost, however, because it reduces the payload capacity. Equally important is the present cost of aviation fuel, $2.80 per gallon, and an average consumption rate of 20 gallons per minute.

The rate of arrival for all planes at DCA varies by the hour. The arrival rate and time in the stack are greatest each weekday between 4 and 5 PM. and so FreeEx selected this time period for an initial study. The study indicated that the mean arrival rate is 20 planes per hour, or one every 3 minutes. The variance about this mean, resulting from flight cancellations as well as charter and private flights, is characterized by a Poisson distribution. During clear weather, the DCA control tower can land 1 plane per minute, or 60 planes per hour. Landings cannot exceed this rate in the interest of air safety.

When the weather is bad, the landing rate is 30 per hour. Both good-and bad-weather landing rates are mean rates with a Poisson distribution. FreeEx's flights are short enough that management usually can tell before takeoff in an outlying city whether or not the rate of landings in DCA will be reduced because of weather considerationsWhen a plane runs short of fuel while in the stack, it is given priority to land out of order. DCA rules, however, make clear that the airport will not tolerate abuse of this consideration. Therefore, FreeEx ensures that its planes carry enough fuel so that it will take advantage of the policy no more than 1 time in 20.

Questions

1. During periods of bad weather, as compared with periods of clear weather, how many additional gallons of fuel on average should FreeEx expect its planes to consume because of airport congestion?

2. Given FreeEx's policy of ensuring that its planes do not run out of fuel more than 1 in 20 times while waiting to land, how many reserve gallons (i.e., gallons over and above expected usage) should be provided for clear-weather flights? For bad-weather flights?

3. During bad weather, FreeEx has the option of instructing the Washington air controller to place its planes in a holding pattern from which planes are directed to land either at Reagan National or at Dulles International, whichever becomes available first.

Assume that the Dulles landing rate in bad weather also is 30 per hour, Poisson distributed, and that the combined arrival rate for both airports is 40 per hour. If FreeEx must pay $200 per flight to charter a bus to transport its passengers from Dulles to Reagan National, should it exercise the option of permitting its aircraft to land at Dulles during bad weather?

Assume that if the option is used, FreeEx's aircraft will be diverted to Dulles about one half the time.