《航线进度计划》（英文版） lec6 fleet assignment

Spill calculation: Results For a 3 fleet. 226 flights problem The best representative fare solution results in a gap with the optimal solution of $2, 600/day U Sing a shared fare scheme and integration approach, we found a solution with an $8/day gap By simply modifying the basic spill model, Significant gains can be achieved 2/212021 Barnhart 1.206J/16.77J/ESD. 15J

2/21/2021 Barnhart 1.206J/16.77J/ESD.215J 16 Spill Calculation: Results • For a 3 fleet, 226 flights problem: – The best representative fare solution results in a gap with the optimal solution of $2,600/day – Using a shared fare scheme and integration approach, we found a solution with an $8/day gap. • By simply modifying the basic spill model, significant gains can be achieved

FAM-PMIX: Measures the spill Approximation Error FAM PMX Fleeting decision Net Operating costs revenues Fleeting contributions 2/212021 Barnhart 1.206J/16.77J/ESD. 15J

2/21/2021 Barnhart 1.206J/16.77J/ESD.215J 17 FAM-PMIX: Measures the Spill Approximation Error Fleeting decision FAM PMIX Net revenues Operating costs Fleeting contributions

Passenger mix Passenger Mix Model (pmix Kniker(1998) Given a fixed. fleeted schedule. unconstrained passenger demands by itinerary (requests), and recapture rates find maximum revenue for passengers on each flight leg Network effects and Recapture 2/212021 Barnhart 1.206J/16.77J/ESD. 15J

2/21/2021 Barnhart 1.206J/16.77J/ESD.215J 18 Passenger Mix • Passenger Mix Model (PMIX) – Kniker (1998) – Given a fixed, fleeted schedule, unconstrained passenger demands by itinerary (requests), and recapture rates find maximum revenue for passengers on each flight leg PMIX Network Effects and Recapture

FAM NOtations Decision variables fe equals 1 if fleet type k is assigned to flight leg i, and o otherwise Jk.a, is the number of aircraft of fleet type k, on the ground at station o. and time t Parameters , i 1s the cost of assigning fleet k to flight leg Ne is the number of available aircraft of fleet type k t is the‘ count time -Lis the set of all flight legs i K is the set of all fleet types k O is the set of all stations o CLk)is the set of all flight arcs for fleet type k crossing the count time 2/21/2021 Barnhart 1.206J/16.77J/ESD. 15J

2/21/2021 Barnhart 1.206J/16.77J/ESD.215J 19 FAM Notations • Decision Variables – fk,i equals 1 if fleet type k is assigned to flight leg i, and 0 otherwise – yk,o,t is the number of aircraft of fleet type k, on the ground at station o, and time t • Parameters – Ck,i is the cost of assigning fleet k to flight leg i – Nk is the number of available aircraft of fleet type k – t n is the “count time” • Sets – L is the set of all flight legs i – K is the set of all fleet types k – O is the set of all stations o – CL(k) is the set of all flight arcs for fleet type k crossing the count time

Fleet Assignment Model (FAm Min∑xcMk k∈Ki∈L Subject to kefk;=1Vi∈L ∑ Yk r.o.t ∑fk;=0Wk,o i∈I(k,o,) iEO(, o, t) ∑Mon+∑f;≤NkVk∈K i∈CI(k) f∈lka20 Hane et al. (1995), Abara(1989), and Jacobs, Smith and Johnson(2000) 2/212021 Barnhart 1.206J/16.77J/ES D 2 15J

2/21/2021 Barnhart 1.206J/16.77J/ESD.215J 20 Fleet Assignment Model (FAM) kK   kKiL k i k i Min c f , , 1  , = kK k i f 0 ( , , ) , , , ( , , ) , , , +  − −  =   − + i O k o t k i k o t i I k o t k i k o t y f y f k i CL k k i o O yk o t f N n  +     ( ) , , , f k,i 0,1 0 yk,o,t  iL k,o,t Subject to: kK   kKiL k i k i Min c f , , 1  , = kK k i f 0 ( , , ) , , , ( , , ) , , , +  − −  =   − + i O k o t k i k o t i I k o t k i k o t y f y f k i CL k k i o O yk o t f N n  +     ( ) , , , f k,i 0,1 0 yk,o,t  iL k,o,t Subject to: kK   kKiL k i k i Min c f , , 1  , = kK k i f 0 ( , , ) , , , ( , , ) , , , +  − −  =   − + i O k o t k i k o t i I k o t k i k o t y f y f k i CL k k i o O yk o t f N n  +     ( ) , , , f k,i 0,1 0 yk,o,t  iL k,o,t Subject to: Hane et al. (1995), Abara (1989), and Jacobs, Smith and Johnson (2000)