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Airline Optimization Problems. Constraint Technologies International www.contecint.com.au. Strategic Planning Years to months. Scenario based / what if? / resource planning etc. Can use operational planning tools. Airline Management Timeframes. Operational Planning Months to weeks.

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Airline optimization problems l.jpg
Airline Optimization Problems

Constraint Technologies International

www.contecint.com.au


Airline management timeframes l.jpg

Strategic Planning

Years to months.

Scenario based / what if? / resource planning etc.

Can use operational planning tools.

Airline Management Timeframes

  • Operational Planning

  • Months to weeks.

  • e.g. aircraft schedule development, crew scheduling, rostering, maintenance planning etc.

  • Operations

  • Days to real-time

  • e.g. situation awareness, tracking, disruption management, maintenance etc.


The crew scheduling problem l.jpg
The Crew Scheduling Problem

  • Given : an aircraft schedule that specifies a couple of months worth of flying at some point in the future...

  • Problem: what is the most efficient way to crew all the planes?

  • Must abide by statutory and union regulations.


Crew scheduling pairings l.jpg

Mon

Tues

Wed

Crew Scheduling - Pairings

  • An aircraft schedule is a list of plane legs to be crewed

  • A crew schedule partitions these legs into pairings:

AKL

AKL

FLT17

FLT13

BNE

BNE

FLT19

FLT714

SYD

SYD


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Set Covering Formulation

  • How do we handle the often complicated and messy cost and legality rules for pairings?

  • Choose a subset of all* possible pairings that forms an optimal† complete crew schedule.

    Translations for the pragmatist:

    * (some)

    † (good)


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Set Covering Formulation

Cost of ith pairing

= 1 for all selected pairings, else 0

= 1 if leg i is in pairing j, else 0

i indexes plane legs, j indexes pairings


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Pairing cost

Set Covering Formulation

x

Legs

Pairings


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Crew Scheduling : Computational Challenges

  • Tens of thousands of legs in a schedule.

  • Number of possible pairings is almost unlimited.

  • Two (related) problems :

    1: Too many legal pairings to even begin to solve LP, let alone MIP.

    2: Even if we reduce number of pairings, still have to be able to solve large MIP problems efficiently (tens of thousands of constraints, hundreds of thousands of variables).


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Column Generation Techniques

  • First solve a restricted crew scheduling problem that includes a small subset of the total possible pairings.

  • Use dual LP solution to generate extra pairings to add to the LP in order to improve the cost function. Extra pairings are generated by solving column generation subproblem.

  • Iterate.

  • Integrality constraints require special techniques - branch and price etc.

  • Column generation subproblem : can use constrained shortest path / k-shortest path / stochastic methods / constraint programming etc.


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Pairing Recombination (k-opt)

  • Start with a feasible crew schedule.

  • Choose a limited subset of the pairings in this schedule, and re-optimize the “mini aircraft schedule” defined by the legs in these pairings.

  • Gets around the scaling problem.

  • Need to decide which pairings to re-optimize at each iteration.


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Systemic Challenges

  • How do we handle the complicated legality and costing rules in a flexible yet efficient manner? -- e.g. CTI “Common Rules” system.

  • “Human factors” make this all the more important.

  • Solution should be robust and efficient within the wider airline context. e.g. robustness with respect to disruptions, “rosterability” problem, non-independence of separate pairings etc.

  • How do we handle the data interface between various systems in an airline e.g. operations, crew tracking systems etc.?


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Other Airline Optimization Problems

  • Rostering (given a crew schedule, assign actual crew members to the pairings so as to satisfy crew preferences and legality requirements)

  • Aircraft scheduling (develop an aircraft schedule that efficiently matches the fleet with passenger demand, maintenance requirements, airport slot restrictions etc.)

  • Other e.g. problems arising from warehousing, maintenance scheduling etc.


Integration l.jpg
Integration

  • Can get into trouble viewing optimization problems as idealized problems in isolation.

  • Improvements can come from moving to a more holistic approach.

  • e.g. we would like to be able to do robust scheduling over the entire cycle from initial planning to flying.

  • A very important area requiring a holistic approach is disruption management...


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Disruption Management

  • Requires integration of several domains:

  • Aircraft routing problem.

  • Crew disruptions.

  • Passenger disruption problem (connections etc.).

  • Slot management, aircraft maintenance, catering etc. etc.

  • There is always a degree of incompleteness and uncertainty in the data and the model : thus it is more important to be able to choose from a range of feasible solutions, rather than having one “best” solution.

  • Need to be fast!

  • Heuristic exploration of solution space.

  • Optimization possibilities?


Questions l.jpg
Questions?

Constraint Technologies International

www.contecint.com.au

[email protected]

[email protected]


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