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Building a Customized Pairing Optimizer at Spirit Airlines with Minimal Cost

Ciyou Zhuat

AGIFORS Crew Management Study Group Conference, May 2003

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Back ground

• Cost cutting: a matter of paramount importance.

• Pairings affect crew soft time, hotel expense, fixed cost etc.

• Existing system: Sabre (Bornemann) CrewPlan for pairings.

• Other modules in use: OASIS, CrewTrac, CrewQual, FilteTrac.

• Experience: in building a network optimizer for revenue management.

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Network Opt vs Pairing Opt

Network Optimization Pairing Optimization

Objective max revenue min cost

Variables O&D demand legal pairings (O=D)

# of variables Large Large

Constraints <= capacity >= 1 (set covering)

Characteristic Stochastic LP Integer LP

Solver LP solver M ILP solver

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First Step: Search for Cost Saving Opportunities

• An optimal set of pairing: key to minimize the crew cost.

• Check sub-optimality: start with a manual approach.– Swap the flight legs (~100) in the pairings to reduce soft time.

– Reassemble pairings with big soft time.

– Keep all the flight legs being covered -- a feasible method.

– One example with less cost: enough to confirm sub-optimality.

• Sub-optimality detected.

Min Connection Block Soft Hotel Total Cost Saving DaysSystem 120 271.2 32.4 37 368.4 59Manual 1 120 271.2 15.9 40 357.1 3.1% 55Manual 2 120 271.2 19.3 38 357.0 3.1% 56

– Total Cost = Block + Soft + 1.75*Hotel.

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Possible Source of Sub-optimality

• Defects in system pairing generator.

• Defects in optimization algorithms.

• Improperly set parameters by the user.

• Inaccuracy in formulation of work rules and contract terms.

• Post optimization adjustment on the system output.

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Second Step: Optimization on NEOS-- network enabled optimization server @ nwu & anl

• Put all pairings (system & manual) in one pool.

• Add more pairings generated in spread sheet.

• Formulate an IP (a set covering problem).

• Generate MPS file in spread sheet.

• Submit the MPS file to NEOS solvers (in next few slides).

• Receive solutions from multiple MILP solvers.– BONSAIG / FortMP / GLPK / Xpress-MP.

– All get the same optimal value, but possibly different parings.

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Cost Saving Results

– Total Cost = Block + Soft + 1.75*Hotel– 528 basic pairings from spread sheet added to the pool for GLPK 1&2.

Min Connection Block Soft Hotel Total Cost Saving DaysSystem 120 271.2 32.4 37 368.4 59Manual 1 120 271.2 15.9 40 357.1 3.1% 55Manual 2 120 271.2 19.3 38 357.0 3.1% 56Manual 3 55 271.2 17.3 37 353.3 4.1% 56

GLPK 1 120 271.2 16.1 37 352.1 4.4% 56GLPK 2 55 271.2 14.4 36 348.6 5.4% 55

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Composition of Optimized Pairing Sets

from GLPK 1 GLPK 2 Total SelectedSystem 0 1 1Manual 1 6 0 6Manual 2 2 5 7Manual 3 0 3 3SpreadSheet 15 12 27Total 23 21 44

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Generate More Pairings in Spread Sheet

• Generate daily (flight leg) groups with connection rules.

• Assemble daily groups, under the layover rules, to get multi day pairings.

• Key issue: converting two dimensional data to one dimensional array in spread sheet.

• Examples (in next two slides).

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Pairings Outgrown the Capacity of Spreadsheet & E-mail

duty/calender days # of Pairings size of MPS1/2 21 7,4682/3 506 110,5463/4 12,598 1,007,8404/4 275,633 89,550,7604/5 289,651 93,991,445

– For a typical month.– Size of MPS in bytes.

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Third Step: Install MILP Solvers

• Download, install and test MILP solvers– BonsaiG, GLPK ... (in next two slides)

• Free software from GNU FSF (free software foundation)– no support and maintenance. (Is this a problem?)

• Free access to source code– a BIG advantage in customizing the optimizer!

• Products of latest research project.– Works extremely well (compared with some commercial software)

• Prompt responses from authors.

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Forth Step: Building a Stand-alone Pairing Optimizer

• Convert the spreadsheet logic to c code.

• Formulate all the work rules and contract terms accurately.

• Design and develop pre/post processors.

• Optimize pairings to reach zero soft time, reduced hotel stay and limited duty days.

• Example of results (under new contract with duty rig.)

Soft Time Hotel Stay Lengh of PairingOld System 3.5% more up to 5 daysNew Optimizer 0% less 3 duty days

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What We’ve Learned

• Monitor the system performance with a stand-alone approach.• Catch cost saving opportunities by a customized pairing generator and

optimizer.• Make incremental movements and reap cost savings in every stage of the

project.• Take full advantage of free software and new research results. • Feed the existing system with optimized pairings without replacing the

whole system -- keep the cost minimal.

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Thank You

Any Questions ?