USAir South Airlines operates a hub at the Pittsburgh International Airport. During the summer, the airline schedules 7 flights daily from Pittsburgh to Orlando and 10 flights daily from Orlando to Pittsburgh, according to the following schedule:

Flight Leave Pittsburgh Arrive Orlando Flight Leave Orlando Arrive Pittsburgh 1 6 a.m. 9 a.m. A 6 a.m. 9 a.m.

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 10 a.m. 1 p.m.

5 5 p.m. 8 p.m. E Noon 3 p.m.

6 7 p.m. 10 p.m. F 2 p.m. 5 p.m.

7 8 p.m. 11 p.m. G 3 p.m. 6 p.m.

H 6 p.m. 9 p.m.

I 7 p.m. 10 p.m.

J 9 p.m. Midnight The flight crews live in Pittsburgh or Orlando, and each day a new crew must fly one flight from Pittsburgh to Orlando and one flight 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 flies a flight to Pittsburgh, it must then be scheduled for a return flight from Pittsburgh back to Orlando. A crew must have at least 1 hour between flights at the city where it arrives. Some scheduling combinations are not possible; for example, a crew on flight 1 from Pittsburgh cannot return on flights A, B, or C from Orlando. It is also possible for a flight to ferry one additional crew to a city in order to fly 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 computer.

How many crews need to be based in each city? How much ground time will each crew experience? LO.1