| 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. | ||||||
