MATHEMATICAL OPTIMIZATION FOR GATE SCHEDULING
They spent weeks trying to solve it with ChatGPT and spreadsheets. The real answer was a constraint optimization model — built in 4 days, saving $800K per quarter.
A growing regional airport in Quebec handles commercial flights across 9 gates, each requiring a dedicated 6-person ground crew for arrivals, departures, and turnarounds.
Scheduling those crews across a full quarter — 90+ days, multiple shifts, variable flight volumes — had become a serious operational headache. The operations team was building schedules manually in Excel, spending 2 to 3 weeks per cycle juggling labor regulations, crew availability, gate assignments, and budget constraints.
The result was always the same: schedules that were technically valid but financially bloated. Ground crew staffing was running at $1.7 million per quarter — and leadership suspected there was significant waste baked into the process.
Each quarterly schedule took 2–3 weeks to build manually in Excel — a fragile, error-prone process.
Ground crew staffing costs were running well above what the flight volume actually required.
Coordinating coverage across gates, shifts, and labor rules created exponential scheduling complexity.
Before engaging Leap AI, the airport's operations team spent several weeks trying to solve the problem with ChatGPT and Excel macros. The logic seemed sound: describe the constraints, ask the model to generate an optimized schedule.
It didn't work. Not because the team lacked effort — but because this wasn't a language problem.
Large language models are extraordinary at understanding context, generating text, and reasoning through ambiguity. But crew scheduling is a constraint satisfaction problem — a mathematical challenge with hard boundaries: labor laws, minimum rest periods, gate coverage requirements, budget ceilings, and shift-length limits.
An LLM can describe the problem eloquently. It cannot solve it optimally. That requires a fundamentally different class of tool.
AI is a toolbox, not a single tool. The organizations that get the most value from AI are the ones that match the right technique to the right problem.
Language models for language problems. Optimization solvers for optimization problems. Knowing the difference — and having access to both — is the competitive advantage.
Leap AI built a Mixed Integer Linear Programming (MILP) model using Google OR-Tools CP-SAT solver — one of the most powerful open-source constraint optimization engines available.
The model was designed to minimize total staffing cost while respecting every operational and regulatory constraint the airport faces. It doesn't guess. It doesn't approximate. It finds the mathematically optimal solution across the entire scheduling horizon.
From first conversation to working model: 4 days.
The optimization model enforces every real-world constraint simultaneously:
Flight schedules, gate assignments, crew rules, and labor regulations are encoded as mathematical constraints.
A MILP model structures the problem as binary decision variables with a cost-minimization objective.
Google OR-Tools CP-SAT solver explores the solution space and finds the mathematically optimal schedule.
The optimized schedule is delivered in a format ready for operations — no new systems or training required.
The impact was immediate and dramatic.
Quarterly ground crew staffing costs dropped from $1.7 million to $0.9 million — a 47% reduction. The savings came not from cutting corners, but from eliminating the inefficiencies that manual scheduling inevitably creates: overstaffing during low-volume periods, suboptimal shift distributions, and redundant overlap.
The scheduling process itself went from 2–3 weeks of manual work to minutes of compute time. The operations team now runs the model, reviews the output, and makes any manual adjustments they want — a process that takes hours, not weeks.
In the first year alone, the projected savings exceed $3.2 million. Against the cost of building the model, that represents a return on investment above 20,000%.
The financial impact tells only part of the story.
Before the optimization model, the operations team dreaded the quarterly scheduling cycle. It was tedious, high-stakes work where a single error could cascade into coverage gaps or compliance violations. The cognitive load was enormous.
Now, the team focuses on oversight and refinement rather than construction. They review an optimal baseline and adjust for human factors — vacation preferences, team dynamics, training rotations — that the model intentionally leaves room for.
The model didn't replace the operations team. It gave them a foundation they can trust and the time to focus on the decisions that actually require human judgment.
Not every problem is a language problem. Not every AI solution needs a large language model.
The organizations that will lead in the next decade aren't just the ones adopting AI — they're the ones that know which kind of AI to apply. When the problem is ambiguity and context, reach for an LLM. When the problem is constraints and optimization, reach for a solver.
This airport didn't need a chatbot. They needed a mathematician. And the difference between the two saved them $3.2 million in year one.
Speed doesn't come from rushing. It comes from knowing which tool to pick up first.
Not every problem needs a language model. Book a call to find out which AI approach fits yours.
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