Airline Optimization Problems Constraint Technologies International

Airline Management Timeframes Strategic Planning Years to months. Scenario based / what if? / resource planning etc. Can use operational planning tools. 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 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 SYD BNE AKL MonWedTues BNE AKL SYD FLT714 FLT13 FLT17 FLT19 An aircraft schedule is a list of plane legs to be crewed A crew schedule partitions these legs into pairings:

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)

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

Set Covering Formulation Pairing cost Legs Pairings x

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).

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.

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.

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.?

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 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...

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? Constraint Technologies International