Aircraft Maintenance Planning

[mathstream]

Hi,

I'm investigating solvers for an aircraft maintenance problem and would like to try a quick prototype in Timefold. Not sure of the best way to do the formulation for Timefold, so thoughts and hints would be nice:

1. Aircraft have regular checks, of varying complexities, such as an "A check" every 400-600 hours of flying time, takes a day or two to complete. Heavier checks on a less frequent basis.
2. Airlines may have more than one maintenance base, can sometimes outsource to third parties as well as pay overtime. Need to have constraints and costs on all of these, but would start with simple capacity constraints (daily) that apply to various task categories (avionics, airframe, powerplant, etc)
3. Aircraft may not "overfly" a check, as it would be grounded. Can do some maintenance tasks early, but this also has a cost as the airplane is flying less. So, the cost function is not linear and has a "sweet spot" a few days before a check must be done (hours / landings / days).

Some formulation questions:

• Can I have an objective function that is evaluated for each potential solution? This would make the non-linear penalties easier to handle, also allow it to optionally move checks forward, etc. i.e. In additional to all the mandatory checks
• Each visit to a maintenance base has a series of tasks, almost like a subproblem to solve.
• A 1/0 matrix, such as x[aircraft, station, date] would explode in size quite quickly. It would also remind me of a MIP approach, which I want to avoid, even though I have experience with these models. As we add constraints, they can rapidly become very fractional and take a long time to get to the first feasible solution.
• Getting to a good solution fast is better than an "optimal" solution, as the users will likely do scenario analysis and tweak constraints and costs.

Regards,
Alan

[TomCools]

Hi Alan, welcome and sorry for the delay in answer.

• Typically, we don't have a single objective function you need to define. You define business constraints in code and give those a weight. That sort of makes up your "objective function" only the solver can be smarter in which parts to re-calculate (aka, only change the constraints which may have been impacted based on the change the solver made).
• The "visit to maintenance base and series of tasks", while you could model this in 1 model (using a mixed model approach, see this blog post), I would make a first attempt without that.
• I read a performance concern here, do you have any indication on how large your dataset will be?
• Getting to a good solution fast is something Timefold with it's Metaheuristic approach is well suited for.

You might want to check out some of our quickstarts: https://github.com/TimefoldAI/timefold-quickstarts/tree/stable/java/maintenance-scheduling.