USAir South Airlines operates a hub at the Pittsburgh International Airport. During the summer,

the airline schedu les 7 flights daily from Pittsburgh to Orlando and 10 fli ghts daily from Orl ando

to Pittsburgh, according to the foll owing schedul e:

Flight Pittsburgh Orlando Fl ight Orlando Pittsburgh

2 8 A.M. 11 A.M. B 7 A.M. 10 A.M.

3 9 A.M. Noon c 8 A.M. 11 A. M.

4 3 P.M. 6 P.M. D l0A.M. l P.M.

5 5 P.M . 8 P.M. E Noon 3 P.M.

6 7 P.M. JO P.M. F 2 P.M . 5 P.M.

7 8 P.M. 11 P.M. G 3 P.M . 6 P.M.

Leave Arrive Leave Arrive

6 A.M. 9 A.M. A 6 A.M . 9 A.M.

The fli ght crews live in Pittsburgh or Orlando, and each day a new crew must fl y one fli ght from

Pittsburgh to Orlando and one fli ght from Orlando to Pittsburgh. A crew must return to its home

city at the end of each day. For example, if a crew originates in Orlando and fl ies a fli ght to

Pittsburgh, it must then be schedul ed for a return fli ght from Pittsburgh back to Orlando. A crew

must have at least l hour between flights at the city where it arrives. Some scheduling combina-
tions are not possible; for example, a crew on fli ght 1 from Pittsburgh cannot return on fli ghts

A, B, or C from Orlando. It is also possible for a fli ght to ferry one additi onal crew to a city in

order to fl y a return flight, if there are not enough crews in that city.

The airline wants to schedule its crews in order to minimize the total amount of crew ground

time (i.e., the time the crew is on the ground between flights). Excessive ground time for a crew

lengthens its workday, is bad for crew morale, and is expensive for the airline. Formulate a linear

programming model to determine a flight schedule for the airline and solve by using the com-
puter. How many crews need to be based in each city? How much ground time will each crew

experience?

pur-new-sol

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