Minimizing sum of Disrupted Passengers Objective: Minimize sum of Mimc∑nxp disrupted passengers pe P Flight coverage constraints ∑x+Zf tETf Aircraft balance for each sub ∑x+y=∑x+ fleet type (f,t血n(j (f, tEOut(j Xf+yf=res(a, ft, . Initial and end of the day aircraft resource constraints Passenger cancellation constraints +∑x2 Missed connected passengers gEC(u)d(gka(f) constraints p∈0l:xra∈0y20 Only flight copy variables, x, have to be binary
p p p P t f f t Tf tt tt ff ff (f ,t) In(j) (f,t) Out(j) f f p f t u f gp g C(u) d(g) a(f ) t t p f,a f Minimize n st : x z 1 xy xy x y Res(a,ft, ) z x x1 [0;1]; x {0,1}; y 0 ∈ ∈ − + ∈ ∈ • • ∈ < ×ρ + = += + += • ρ ≥ + −ρ ≤ ρ ∈ ∈≥ ∑ ∑ ∑ ∑ ∑ ∑ ¾ Objective: Minimize sum of disrupted passengers ¾ Flight coverage constraints ¾ Aircraft balance for each sub fleet type ¾ Initial and end of the day aircraft resource constraints ¾ Passenger cancellation constraints ¾ Missed connected passengers constraints ¾ Only flight copy variables, x, have to be binary Minimizing Sum of Disrupted Passengers
Minimizing passenger delay Need to consider all potential copies of Min∑∑b recovery itineraries for each passenger Large scale problem: 500,000 integer x+z=1Vf∈F variables; 12 hours CPU using B&B deep te first search methodology ∑x+y=∑x2+y (, tEIn( (f, t EOut() ,xF+you ∑Σ8C×x q202x∈{0}yr20
Minimizing passenger delay • Need to consider all potential copies of recovery itineraries for each passenger • Large scale problem: 500,000 integer variables; 12 hours CPU using B&B deep first search methodology i i p p p Pi I p t f f t Tf tt tt ff ff (f ,t) In( j) (f ,t) Out( j) 0 0 f f i p p i I p ti t p ff fi p Pi I p it t pf f b q x z 1 fF xy xy xy j q n q Cx q 0;x {0,1};y 0 Min ∈ ∈ ∈ − + ∈ ∈ + • ∈ ∈ ∈ + = ∀∈ += + + = = δ ≤× ≥∈ ≥ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
Summary Lecture #2 Cont Approximate models to minimize sum of passenger delay From Model #1, estimate delay if itinerary is disrupted From Model #2, limit the number of itinerary copy to include only good ones Objective function: minimizing estimated passenger dissatisfaction Fine grained down to Passenger Name Record Assign a cost(expected future revenue loss of delay d for PNr p) based on: Fare class Disruption history Loyalty( FFP) Same objective can be used in sorting passengers for recovery priority
Summary Lecture #2 (Cont.) Approximate models to minimize sum of passenger delay • From Model #1, estimate delay if itinerary is disrupted. • From Model #2, limit the number of itinerary copy to include only good ones. Objective function: minimizing estimated passenger dissatisfaction • Fine grained down to Passenger Name Record • Assign a cost (expected future revenue loss of delay d for PNR p) based on: Fare class Disruption history Loyalty (FFP) • Same objective can be used in sorting passengers for recovery priority
Lecture #3 Outline Airline schedule recovery framework Aircraft routing feasibility Disrupted passenger re-routing under seat uncertainty: Heuristics Optimal Optimal with bumping control
Lecture #3 Outline • Airline schedule recovery framework • Aircraft routing feasibility • Disrupted passenger re-routing under seat uncertainty: ¾ Heuristics ¾ Optimal ¾ Optimal with bumping control