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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 ?