Definitions(again p passengers that are denied booking due to capacity restrictions Recapture passengers that are recaptured back to the airline after being spilled from another flight les For each fleet- flight combination Cost= Operating cost Spill cost 2/212021 Barnhart 1.206J/16.77J/ESD. 15J
2/21/2021 Barnhart 1.206J/16.77J/ESD.215J 6 Definitions (again) • Spill – passengers that are denied booking due to capacity restrictions • Recapture – passengers that are recaptured back to the airline after being spilled from another flight leg • For each fleet - flight combination: Cost Operating cost + Spill cost
Fleet Assignment References Abara( 1989), Daskin and Panayotopoulos 1989),Hane, Barnhart, Johnson, Marsten, Neumhauser, and Sigismondi(1995) Hane, et al. The Fleet Assignment Problem Solving a large integer program Mathematical programming, Vol. 70, 2, PP 211 232.1995 2/212021 Barnhart 1.206J/16.77J/ESD. 15J
2/21/2021 Barnhart 1.206J/16.77J/ESD.215J 7 Fleet Assignment References • Abara (1989), Daskin and Panayotopoulos (1989), Hane, Barnhart, Johnson, Marsten, Neumhauser, and Sigismondi (1995) • Hane, et al. “The Fleet Assignment Problem, Solving a Large Integer Program,” Mathematical Programming, Vol. 70, 2, pp. 211- 232, 1995
Network representation Topologically sorted time-line network Nodes Flght arrivals/ departures(time and space) Arcs Flight arcs: one arc for each scheduled flight Ground arcs: allow aircraft to sit on the ground between flights 2/212021 Barnhart 1.206J/16.77J/ESD. 15J
2/21/2021 Barnhart 1.206J/16.77J/ESD.215J 8 Network Representation • Topologically sorted time-line network – Nodes: • Flight arrivals/ departures (time and space) – Arcs: • Flight arcs: one arc for each scheduled flight • Ground arcs: allow aircraft to sit on the ground between flights
Time-Line Network Ground arcs City a City B City c City d 8:0012:0016:0020:00 8:0012:0016:002000 2/212021 Barnhart 1.206J/16.77J/ESD. 15J
2/21/2021 Barnhart 1.206J/16.77J/ESD.215J 9 Time-Line Network 8:00 12:00 16:00 20:00 8:00 12:00 16:00 20:00 City A City B City C City D • Ground arcs
Time-Line Network Daily"p1 roblem Wrap-around (or overnight) arcs Washington, D.C. Baltimore Boston 2/212021 Barnhart 1.206J/16.77J/ESD. 15J
2/21/2021 Barnhart 1.206J/16.77J/ESD.215J 10 Time-Line Network • “Daily” problem – Wrap-around (or overnight) arcs Washington, D.C. Baltimore New York Boston Time