lec10_schedule_design_2003

lec10_schedule_design_2003 - 1.206J/16.77J/ESD.215J Airline...

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Unformatted text preview: 1.206J/16.77J/ESD.215J Airline Schedule Planning Cynthia Barnhart Spring 2003 1.963/1.206J/16.77J/ESD.215J The Schedule Design Problem • Outline – Problem Definition and Objective – Schedule Design with Constant Market Share – Schedule Design with Variable Market Share – Schedule Design Solution Algorithm – Results – Next Steps – A Look to the Future in Airline Schedule Optimization Airline Schedule Planning Schedule Design Select optimal set of flight legs in a schedule Fleet Assignment Assign aircraft types to flight legs such that contribution is maximized Aircraft Routing Crew Scheduling Objectives • Given origin­destination demands and fares, fleet composition and size, fleet operating characteristics and costs • Find the revenue maximizing flight schedule Schedule Design: Fixed Flight Network, Flexible Schedule Approach • Fleet assignment model with time windows – Allows flights to be re­timed slightly (plus/ minus 10 minutes) to allow for improved utilization of aircraft and improved capacity assignments Initial step in integrating flight schedule design and fleet assignment decisions Schedule Design: Optional Flights, Flexible Schedule Approach • Fleet assignment with “optional” flight legs – Additional flight legs representing varying flight departure times – Additional flight legs representing new flights – Option to eliminate existing flights from future flight network Incremental Schedule Design Integrated, Incremental Schedule Design and Fleet Assignment Models Base Schedule Deletion Candidates Mandatory Flight List Addition Candidates Optional Flight List Master Flight List Select optimal set of flight legs from master flight list Assign fleet types to flight legs Demand and Supply Interactions 100 Market Share 450 Market Share 410 Market Share 300 A 150 100 100 B 100 190 A 120 40 B 100 200 A 150 B Non-Linear Interactions Schedule Design: Constant Market Share Model • Constant market share model – Integrated Schedule Design and Fleet Assignment Model (ISD­ FAM) – Utilize recapture mechanism to adjust demand approximately ISD­FAM: Example Market Share 450 Market Share 450 A A 100 150 100 100 100 150 100 100 B B 100 + recap1 150 + recap2 A 100 + recap3 B ISD­FAM Formulation ~ ∑ ck ,i f k ,i + Min ∑ k∈ K i∈ L r r ∑ ( fare p − b p farer )t p ∑ p∈ P r∈ P Subject to: ∑ f k ,i = 1 ∀ i ∈ LF ∑ f k ,i ≤ 1 ∀ i ∈ LO f k ,i = 0 ∀ k , o, t f k ,i ≤ N k ∀ k∈ K k∈ K k∈ K yk , o , t − + ∑ i∈ I ( k , o ,t ) f k , i − yk , o , t + − ∑ o∈ O ∑ f k ,i SEATS k + ∑ k ∑δ r∈ P p∈ P i i∈ O ( k , o ,t ) yk , o ,t n + pr tp ∑ ∑ i∈ CL ( k ) −∑ ∑δ r∈ P p∈ P i prr b pt p ≥ Qi r ∑ t p ≤ Dp r∈ P tr ≥ 0 p f k ,i ∈ { 0,1} ∀ i∈ L ∀ p∈ P yk , o , t ≥ 0 ISD­FAM Formulation ~ ∑ ck ,i f k ,i + Min ∑ k∈ K i∈ L r r ∑ ( fare p − b p farer )t p ∑ p∈ P r∈ P Subject to: ∑ k∈ K f k ,i = 1 ∑f Flight Selection≤ k ,i k∈ K yk , o , t − + ∑ i∈ I ( k , o ,t ) f k , i − yk , o , t + − FAM PMM ∑ o∈ O ∑ f k ,i SEATS k + ∑ k ∑δ r∈ P p∈ P i i∈ O ( k , o ,t ) yk , o ,t n + pr tp ∑ ∑ i∈ CL ( k ) −∑ ∑δ r∈ P p∈ P tr ≥ 0 p i 1 ∀ i ∈ LF ∀ i ∈ LO f k ,i = 0 ∀ k , o, t f k ,i ≤ N k ∀ k∈ K prr b pt p ≥ Qi r ∑ t p ≤ Dp r∈ P f k ,i ∈ { 0,1} ∀ i∈ L ∀ p∈ P yk , o , t ≥ 0 ISD­FAM Formulation ~ ∑ ck ,i f k ,i + Min ∑ k∈ K i∈ L r r ∑ ( fare p − b p farer )t p ∑ p∈ P r∈ P Subject to: f k ,i = 1 ∀ i ∈ LF ∑f Flight Selection≤ Schedule Design 1 ∀ i ∈ LO ∑ k∈ K k ,i k∈ K yk , o , t − + ∑ f k , i − yk , o , t + − f k ,i = 0 ∀ k , o, t f k ,i ≤ N k ∀ k∈ K FAM Fleet Assignment Spill + Recapture PMM i∈ I ( k , o ,t ) ∑ o∈ O ∑ f k ,i SEATS k + ∑ k ∑ ∑δ r∈ P p∈ P i i∈ O ( k , o ,t ) yk , o ,t n + pr tp ∑ i∈ CL ( k ) −∑ ∑δ r∈ P p∈ P i prr b pt p ≥ Qi r ∑ t p ≤ Dp r∈ P tr ≥ 0 p f k ,i ∈ { 0,1} ∀ i∈ L ∀ p∈ P yk , o , t ≥ 0 Schedule Design: Variable Market Share Model • Variable market share model – Extended Schedule Design and Fleet Assignment Model (ESD­ FAM) – Utilize demand correction term to adjust demand explicitly ESD­FAM: Demand Correction 100 Market Share 450 Market Share 410 Demand Correction Terms Data Quality Issue A 150 100 100 B 100 + 0 100 150 + 40 190 A 100 + 20 120 40 B 100 150+40+40 -30 A B 2nd degree correction 150 80 ESD­FAM Formulation r % Min ∑ ck ,i f k ,i + ∑ p − p farer )t p +∑ fareq Dq − ∑ fare p ∆ qp (1 − q ) ( fare b r DgZ ∑ ∑P k∈ i∈ KL p∈ r∈ P p∈: p ≠ P q q∈O P f ∑ = 1 ∀∈ F iL f ∑ Subject to: ≤ 1 ∀ LO i∈ = 0 ∀, o, t k k ,i k∈ K k ,i k∈ K yk , o , t − + ∑f i∈( k , o , t ) I k ,i − k , o ,t + − y i∈ ( k , o ,t ) O y ∑ k , o ,tn o∈ O Z f ∑ δ ∆ (1 − ) +∑ ∑D p p∈ q∈O P P i p q q k∈ K k ,i ∑f k ,i + ∑f k ,i ≤N k i∈ ( k ) CL SEATS k + ∑p t p − ∑p bp t p ≥ i ∑δ r ∑δ rr Q i i r∈ p∈ P P r∈ p∈ P P ∆ t ∑D (1 −Z ) +∑ ≤D p q q∈ P O ∀∈ kK q r∈ P r p Z q − f k ,i ≤ ∑0 k∈ K p ∀∈ iL ∀∈ pP ∀ L (q ) i∈ Z q −∑ f k ,i ≥ − q ∀∈ ∑ 1 N q PO i∈( q ) k∈ L K { f k ,i ∈0,1} Z q ∈0,1} { tr ≥ p0 yk , o ,t ≥ 0 ESD­FAM Formulation r % Min ∑ ck ,i f k ,i + ∑ p − p farer )t p +∑ fareq Dq − ∑ fare p ∆ qp (1 − q ) ( fare b r DgZ ∑ ∑P k∈ i∈ KL p∈ r∈ P p∈: p ≠ P q q∈O P f ∑ = 1 ∀∈ F iL f ∑ Subject to: ≤ 1 ∀ LO i∈ = 0 ∀, o, t k k ,i k∈ K ISD-FAM k ,i k∈ K yk , o , t − + ∑f i∈( k , o , t ) I k ,i − k , o ,t + − y i∈ ( k , o ,t ) O y ∑ k , o ,tn o∈ O Z f ∑ δ ∆ (1 − ) +∑ ∑D p p∈ q∈O P P i p q q k∈ K k ,i ∑f k ,i + ∑f k ,i ≤N k i∈ ( k ) CL SEATS k + ∑p t p − ∑p bp t p ≥ i ∑δ r ∑δ rr Q i i r∈ p∈ P P r∈ p∈ P P ∆ t ∑D (1 −Z ) +∑ ≤D p q q∈ P ∀∈ kK q O r∈ P r p Z q − f k ,i ≤ ∑0 p ∀∈ iL ∀∈ pP ∀ L (q ) i∈ Market Share Adjustment ∑ ∑ k∈ K Zq − i∈( q ) k∈ L K { f k ,i ∈0,1} Z q ∈0,1} { tr ≥ p0 q PO f k ,i ≥ − q ∀∈ 1N yk , o ,t ≥ 0 ESD­FAM Formulation ∑ ∑ ∑ ∑ ∑ ∑ Constant Constant ∑ Market Share Market ∑ Min k∈ i∈ KL % ck ,i f k ,i + p∈ r∈ PP fareq Dq − fare p ∆ qp (1 − q ) DgZ p∈: p ≠ P q q∈O P r ( fare p − p farer )t p + br Subject to: f k ,i = 1 ∀∈ F iL f k ,i ≤ 1 ∀ LO i∈ f k ,i = 0 ∀, o, t k f k ,i ≤N k ∀∈ kK k∈ K ∑ ∑ Schedule Design ISD-FAM ∑ ∑ & Fleet Assgn. Fleet k∈ K yk , o , t − + i∈( k , o , t ) I f k ,i − k , o , t + − y i∈ ( k , o ,t ) O o∈ O Z f ∑ δ ∆ (1 − ) +∑ ∑D p p∈ q∈O P P i p q q k∈ K k ,i yk , o , tn + i∈ ( k ) CL SEATS k + ∑p t p − ∑p bp t p ≥ i ∑δ r ∑δ rr Q i i r∈ p∈ P P r∈ p∈ P P ∆ t ∑D (1 −Z ) +∑ ≤D p q q∈ P q O r∈ P r p Z q − f k ,i ≤ ∑0 p ∀∈ iL ∀∈ pP ∀ L (q ) i∈ Market Share Adjustment ∑ ∑ Market Share Adjustment k∈ K Zq − i∈( q ) k∈ L K { f k ,i ∈0,1} Z q ∈0,1} { tr ≥ p0 q PO f k ,i ≥ − q ∀∈ 1N yk , o ,t ≥ 0 Solution Algorithm START Update modifiers Solve I/ESD-FAM Identify itineraries that cause discrepancies Contribution 1 Calculate new demand for the resulting schedule Obtain revenue estimates from PMM Contribution 2 NO Has the stopping criteria been met? YES STOP State Of The Practice/ Theory Practice: Theory: • Most schedule decisions made without optimization • At least one major airline uses Fleet Assignment with Time Windows • Implementation of Incremental Schedule Design approach underway at a major airline • Models and algorithms for incremental schedule design have been developed and prototyped • Validation in progress Computational Experiences • ISD­FAM requires long runtimes and large amounts of memory – ~ 40 minutes on a workstation class computer for medium size (800 legs) schedules – ~ 20 hours on a 6­processor workstation, running parallel CPLEX for full size (2,000 legs) schedules • ESD­FAM takes even longer runtimes and exhausts the memory in some cases – 40 mins (ISD­FAM) vs. 12 hrs (ESD­FAM) on same medium size schedule Schedule Design: Results • Demand and supply interactions – ESD­FAM captures interactions more accurately • Resulting schedules operate fewer flights – Lower operating costs – Fewer aircraft required • ~$100 ­ $350 million improvement annually – Compared to planners’ schedules – Exclude benefits from saved aircraft Schedule Design Results • Results are subject to several caveats – Plans are often disrupted – Competitors’ responses – Underlying assumptions • • • • Deterministic demand Optimal control of passengers Demand forecast Recapture rates/Demand correction terms Nonetheless, significant improvements are achievable Potential for Improved Results • Replace IFAM with SFAM m M S ηΠ S m Min∑ ∑ ( CΠ S ) m=1 n=1 n (f ) m ΠS n m M S ηΠ S ∑ ∑ (δ ) ( f ) Subject to: m =1 n =1 yk , o , t − + m M S ηΠ S ∑ ∑ ∑ (κ ) ( f ) i∈ I ( k ,o ,t ) m = 1 n = 1 m k ,i ΠS n m ΠS n − y k , o ,t + − ∑ o∈ A m M S ηΠ S mi ΠS n m ΠS n ∑ ∑ ∑ (κ ) ( f ) i∈ O ( k ,o ,t ) m = 1 n = 1 yk , o ,t n + ∑ m M S ηΠ S ∑ ∑ ( γ ΠmS ) i∈ CL ( k ) m = 1 n = 1 ( f ) ∈ { 0,1} m ΠS n m k ,i ΠS n k n m ΠS n (f ) m ΠS n yk , o ,t ≥ 0 ≤1 = 1 ∀i∈ L = 0 ∀ k , o, t ≤ Nk ∀ k ∈ K SFAM Basic Concept • Isolate network effects – Spill occurs only on constrained legs 5 Potentially Constrained Flight Leg 3 Unconstrained Flight Leg Potentially Binding Itinerary Non- Binding Itinerary 6 1 9 7 4 2 SFAM IFAM 8 FAM A Look to the Future: Airline Schedule Planning Integration Schedule Design Fleet Assignment Aircraft Routing Crew Scheduling Integrating crew scheduling and fleet assignment models yields: • Additional 3% savings in total operating, spill and crew costs •Fleeting costs increase by about 1% •Crew costs decrease by about 7% A Look to the Future: Real­time Decision Making • For a typical airline, about 10% of scheduled revenue flights are affected by irregularities (like inclement weather, maintenance problems, etc.) • According to the New York Times, irregular operations (due mostly to weather) result in more than $440 million per year in lost revenue, crew overtime pay, and passenger hospitality costs Increasing use and acceptance of optimization­ based decision support tools for operations recovery A Look to the Future: Robust Scheduling • Issue: Optimizing “plans” results in minimized planned costs, not realized costs – Optimized plans have little slack, resulting in • Increased likelihood of plan “breakage” during operations • Fewer recovery options • Challenge: Building “robust” plans that achieve minimal realized costs ...
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This note was uploaded on 11/08/2011 for the course AERO 16.72 taught by Professor Hansman during the Fall '06 term at MIT.

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