A small airline company maintains 2 daily flights between Salt Lake City, Chicago and Dallas. How should the company schedule the crews to minimize cost? Flight Schedule From To Departure Arrival Departure Arrival Salt Lake City Dallas 9:00 AM 12:00 PM 2:00 PM 5:00 PM Salt Lake City Chicago 10:00 AM 2:00 PM 3:00 PM 7:00 PM Dallas Salt Lake City 8:00 AM 11:00 AM 2:00 PM 5:00 PM Dallas Chicago 9:00 AM 11:00 AM 3:00 PM 5:00 PM Chicago Salt Lake City 8:00 AM 12:00 PM 2:00 PM 6:00 PM Chicago Dallas 10:00 AM 12:00 PM 4:00 PM 6:00 PM A crew must leave and arrive in the same city. It is possible to fly the crew back aboard another airline. This would always be on a 8:00 PM flight. There are 6 airplanes in use. When a crew is actually flying a plane, the entire crew is paid \$200 per hour. The other time spent (waiting between flights or flying aboard another airplane) costs the company \$75 per hour. Possible Crew Rotations (S=Salt Lake City, D=Dallas, C=Chicago, ( )=Back with other company) Flying Hours Other Hours Cost Decision SD+DS 6 2 \$1,350 0 SD+(DS) 3 11 \$1,425 0 SD+DC+(CS) 5 10 \$1,750 0 SC+(CS) 4 10 \$1,550 0 SC+CD+(DS) 6 5 \$1,575 0 DS+SD 6 3 \$1,425 0 DS+(SD) 3 12 \$1,500 0 DS+SC+(CD) 7 7 \$1,925 0 DC+CS+(SD) 6 5 \$1,575 0 DC+CD 4 5 \$1,175 0 CS+SD+(DC) 7 7 \$1,925 0 CS+SC 8 3 \$1,825 0 CD+DC 4 3 \$1,025 0 CD+DS+(SC) 7 9 \$2,075 0 Total Cost \$0 Twelve Flight Constraints Flight Number of crews SD 1 0 SD 2 0 SC 1 0 SC 2 0 DS 1 0 DS 2 0 DC 1 0 DC 2 0 CS 1 0 CS 2 0 CD 1 0 CD 2 0 Problem An airline company maintains a schedule of two daily flights between Salt Lake City, Dallas and Chicago. A crew that leaves a city in the morning has to return there at night. The crew can be brought back on another airline. There are 6 airplanes in use. When a crew is flying, the cost is \$200 per hour. When a crew is waiting or being flown back, the cost is \$75. How should the company schedule its crews to minimize cost? Solution 1) The airline has already determined what all the possible crew rotations can be. The variables are the binary integer decisions to accept rotations. In worksheet Crew these are defined as Rotation_decisions. 2) The constraints are simple. We want only one crew per flight. This gives Crews_on_flight = 1 and the logical constraint gives Rotation_decisions = binary 3) The objective is to minimize total cost. On worksheet Crew this cell is given the name Total_cost. Remarks Please confirm for yourself that the crew rotations chosen meet the required schedule. More sophisticated versions of this model are widely used in the airline industry, but the same approach can be used in scheduling truck drivers, boat crews, etc.