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M I T I n t e r n a t i o n a l C e n t e r f o r A i r T r a n s p o r t a t i o n New Approaches to Improving the Robustness of Airline Schedules Prof. John-Paul Clarke Department of Aeronautics & Astronautics Massachusetts Institute of Technology

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Outline Background & Motivation Robust Maintenance Routing Flight Schedule Re-Timing Degradable Airline Schedule Conclusions

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Schedule Design Crew Scheduling Fleet Assignment Maintenance Routing Airline Schedule Planning Process Most existing airline schedule planning methods assume that aircraft, crews, and passengers will operate as planned

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Airline Operations Bad weather reduces airport capacity Airlines cancel or delay flights to reduce demand Delays propagate through the network Airlines must reschedule aircraft/crew and re- accommodate passengers Passengers are not satisfied They are delayed They have no control over their delay All passengers on a given aircraft are delayed equally regardless of fare class

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Delays & Cancellations Trend (1995-1999) Significant increase (100%) in flights delayed more than 45 min Significant increase (500%) in the number of cancelled flights Year 2000 30% of flights delayed 3.5% of flights (approx. 140,000) cancelled Future: Delays and cancellations may increase dramatically more frequent and serious schedule disruptions and revenue loss

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Passenger Disruptions Flight delays and cancellations often cause passenger schedule disruptions 26 million passengers (4% of passengers) disrupted 65% of disruptions caused by missed connections Very long delays for disrupted passengers Average delay for disrupted passengers is approx. 4 hours (versus 15 min delay for non-disrupted passengers) Significant revenue loss - approx. $4 Billion /year

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Robustness Need schedules that are robust (insensitive) to delays and cancellations Definitions of robustness Minimize cost (expected/worst case deviations from optimal) Minimize aircraft/passenger delays and disruptions Easy to recover (aircraft, crew, passenger) Isolate disruptions and reduce the downstream impact Two ways to provide robustness Re-optimize schedule after disruptions occur (operation stage) Build robustness into the schedules (planning stage)

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Outline Background & Motivation Robust Maintenance Routing Graduate Student: Shan Lan Joint work with Prof. Cindy Barnhart Flight Schedule Re-Timing Degradable Airline Schedule Conclusions

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Robust Maintenance Routing Objective Reduce the propagation of delays by combining flight segments in optimal (from the point of view of follow-on delays) maintenance routings Total delay for a route is uniquely determined by routing Solution Approach Derive distributions from historical data for delay introduced into a route by an airport Formulate and solve maintenance routing model that minimizes the propagation of delays subject to maintenance feasibility

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Delay Propagation Arrival delay may cause departure delay for the next flight that is using the same aircraft if there is not enough slack between these two flights Delay propagation may cause schedule, passenger and crew disruptions for downstream flights (especially at hubs) f1 MTT f2 f1’ f2’

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Propagated v. Independent Delay Flight delay may be divided into two categories: Propagated delay Caused by inbound aircraft delay – function of routing 20-30% of total delay (Continental Airlines) Independent delay Caused by other factors – not a function of routing Appropriately allocated slack can reduce propagated delay Add slack where advantageous Reduce slack where less needed

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Definitions i j SlackMin Turn Time PDT PAT ADT AAT PDIAD TAD j’ i’ i’’ PDIDD TDD Planned Turn Time

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Illustration of the Idea f1 MTT f2 f3 f1’ f4 MTT Original routing f3’ New routing f1 MTT f2 f3 f1’ f4 MTT

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Modeling Issues Difficult to use leg-based models to track the delay propagation One variable (string) for each aircraft route between two maintenance events (Barnhart, et al. 1998) A string: a sequence of connected flights that begins and ends at maintenance stations Delay propagation for each route can be determined Need to determine delays for each feasible route Most of the feasible routes haven’t been realized yet PD and TAD are a function of routing PD and TAD for these routes can’t be found in the historical data IAD is not a function of routing and can be calculated by tracking the route of each individual aircraft in the historical data

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String Based Formulation

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Solution Approach Random variables (PD) can be replaced by their mean Distribution of Total Arrival Delay Possible distributions analyzed: Normal, Exponential, Gamma, Weibull, Lognormal, etc. lognormal distribution is the best fit A closed form of expected value function Mixed-integer program with a huge number of 0-1 variables Branch-and-price Branch-and-Bound with a linear programming relaxation solved at each node of the branch- and-bound tree using column generation IP solution A special branching strategy: branching on follow-ons (Ryan and Foster 1981, Barnhart et al. 1998)

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Computational Results Test Networks July 2000 dataModelRoutesAug 2000 data Propagated delays (August 2000) Model Building and Validation

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Results - Delays Total delays and on-time performance Passenger misconnects

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Outline Background & Motivation Robust Maintenance Routing Flight Schedule Re-Timing Graduate Student: Shan Lan Joint work with Prof. Cindy Barnhart Degradable Airline Schedule Conclusions

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Flight Schedule Re-Timing Objective Reduce the number of passenger misconnections by adjusting departure times so that passenger connection times are correlated with the likelihood of a missed connection (disruption) Add connection slack where it is need most Solution Approach Derive distributions from historical data for number of passengers disrupted for each connection Formulate and solve re-timing model that minimizes the number of disrupted passengers

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Definitions AAT = Actual Arrival Time ACT = Actual Connection Time ADT = Actual Departure Time MCT = Minimum Connection Time PAT = Planned Arrival Time PCT = Planned Connection Time PDT = Planned Departure Time Slack MCT PCT PDTAATPATADT ACT

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Illustration of the Idea Airport A Airport B Airport C Airport D Suppose 100 passengers in flight f 2 will connect to f 3 P (misconnect)= 0.3, E(disrupted pax) = 30 P(misconnect)=0.1, E(disrupted pax) =10 Expected disrupted passengers reduced: 20

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Implementation Options Passenger disruption depends on flight delays, a function of fleeting and routing Before maintenance routing problem Delay propagation not considered New fleeting and routing solution may cause delay to propagate in a different way change the number of disrupted passengers After maintenance routing problem Delay propagation considered Need to enable the current fleeting and routing solution Schedule Design Crew Scheduling Fleet Assignment Maintenance Routing

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Connection-Based Formulation Objective minimize the expected total number of passenger misconnects Constraints: For each flight, exactly one copy will be selected. For each connection, exactly one copy will be selected and this selected copy must connect the selected flight-leg copies. The current fleeting and routing solution cannot be altered.

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Connection-Based Formulations Theorem 1: The second set of constraints are redundant and can be relaxed Theorem 2: The integrality of the connection variables can be relaxed Formulation I: CFSR

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Alternative Formulations Formulation II: ACFSR Formulation III: DCFSR

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More Model Properties Theorem 3: ACFSR model is equivalent to CFSR model Theorem 4: DCFSR model is equivalent to CFSR model Theorem 5: The LP relaxation of CFSR model is at least as strong as that of ACFSR, and can be strictly stronger. Theorem 6: The LP relaxation of CFSR model is at least as strong as that of DCFSR, and can be strictly stronger.

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Solution Approach Random variables can be replaced by their mean Distribution of Branch-and-Price

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July 2000 dataRAMRRoutes Aug 2000 dataFSRSchedule CFSR ACFSR Computational Results Network We use the same four networks, but add all flights together and form one network with total 278 flights. Model Building and Validation Strength of the formulations

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Computational Results Assume 30 minute minimum connecting time Assume 25 minute minimum connecting time Assume 20 minute minimum connecting time

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Computational Results Number of copies Estimated reduction in total passenger delays: (30 minutes MCT) 20% (30 minute time window), 16% (20 minute time window), 10% (10 minute time window)

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Outline Background & Motivation Robust Maintenance Routing Flight Schedule Re-Timing Degradable Airline Schedule Graduate Student: Laura Kang Conclusions

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Degradable Airline Schedule Objective Develop airline schedule that is robust, i.e. delays are isolated Provide priority (and thus reliability) for each flight Improve customer satisfaction by giving passengers an accurate expectation of the level of service Provide basis for revenue management and ATC auctions Solution Approach Partition schedule into smaller independent prioritized schedules (layers) subject to operational feasibility

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Implementation Options fleet assignment aircraft routing crew scheduling schedule design DAS D-ARM (Route-based Formulation) DAS D-FAM D-SPM (Flight-based Formulation) DAS

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IP Model Prioritize layers based on revenue (e.g. group highest revenue flights together in most reliable layer) Revenue is “protected” if all flight legs in an itinerary are in a “protected” layer IP model maximizes the total protected revenue subject to feasibility constraints Prototype 2 layers implementation Layer 1: 60% (protected layer) Layer 2: 40%

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Model Statistics 1,134 flight legs 274 aircraft 1,744 itineraries (8% of total) Single flight leg: 1,130 2 flight legs: 613 3 flight legs: 1 53,091 passengers (80% of total) $10,839,340 revenue (84% of total)

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Notation Indices rroute fitinerary ijflight klayer (k=1 … K) γ ij f 1 if flight ij is in itinerary f, 0 otherwise Decision variables y r k 1 if route r is in layer k, 0 otherwise z f k 1 if itinerary f is in layer k, 0 otherwise x ij k 1 if flight ij is in layer k, 0 otherwise Parameters v f k revenue for itinerary f is placed in layer k C h capacity at hub h in bad weather S k fraction of layer k a r number of flights in route r a r h number of flights departing at hub h in route r ACNnumber of aircraft

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Flight-based Formulation

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Route-based Formulation

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Greedy Flight-Leg Pairing STEP 0: Fix connections for non-hub to non-hub flights STEP 1: Pair flight segments at spoke airports using the revenue paring with aircraft utilization heuristic STEP 2: Combine paired flight segments from step 1 at hub airports using the revenue paring with aircraft utilization heuristic STEP 3: Partition very long routes into several shorter routes

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Greedy Flight-Leg Pairing 100 10 100

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Swapping Search Check swapping feasibility Check constraints satisfaction Check objective function improvement Assume revenue is protected proportionally to the number of flight legs in the protected layer Swap route i route j i1i2i3i4i5i6 j1j2j3j4j5j6 i1i2i3i4i5i6 j1j2j3j4j5j6 i1i2i3i4i5i6 j1j2j3j4j5j6 i1i2 i3i4 i5i6 j1j2 j3j4j5 j6

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Tabu Search STEP 0: start with initial solution x* from revenue paring heuristics WHILE( number of iteration is less than N ) STEP 1: Swapping Search. If f(x) > f(x*), x* x STEP 2: Update Tabu list If a pair was in a tabu list for Y iterations, remove it from the tabu list Set X pairs which were swapped in the search in the tabu list Tabu search is sensitive to its parameters X, Y, N State-of-art decision for X, Y, N

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D-ARM w/Heuristics 8,123,060 D-SPM 8,667,632 IP Objective Function Value Current routing 6,492,895 Upper bound for route-based DAS Lower bound for route-based DAS

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D-ARM w/Heuristics 9,057,750 D-SPM 9,624,460 Protected Revenue Current routing 7,302,040 74.5% 70.1% 56.6%

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D-ARM w/Heuristics 43,051 D-SPM 44,984 Protected Passengers Current routing 37,587 67.5% 64.6% 56.4%

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Simulation Results - Good Weather Pr(delay > 15) Pr(delay >0) Average delay Layer 1 6 min 0.37 0.14 Layer 2 6 min 0.48 0.17 Current Routing 6 min 0.42 0.16

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Simulation Results - Bad Weather Pr(delay > 15) Pr(delay >0) Average delay Layer 1 13 min 0.52 0.30 Layer 2 25 min 0.69 0.48 Current Routing 17 min 0.61 0.37

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Outline Background & Motivation Robust Maintenance Routing Flight Schedule Re-Timing Degradable Airline Schedule Conclusions

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Robust Maintenance Routings provide: Airline schedule with reduced delay propagation Flight Schedule Re-Timing provides: Airline schedule with fewer passenger disruptions or missed connections Degradable Airline Schedules provide: Airline schedule that isolates delays Tool for managing passengers’ expectation Potential revenue enhancement

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