Any alternative approach for multi list variables？

[kentbill]

Hello, Teams.

In my scenario, when a job is assigned to a machine for processing, it also requires an additional equipment (such as a mold) to work with the machine in order to complete the job. Both the machine and the equipment have their own work calendars. I would like the job to appear in two lists simultaneously (the machine’s job list and the equipment’s job list), so that the job can comply with both resources’ calendars.
Unfortunately, Timefold currently does not support multiple list planning variables appearing in the same model at the same time. Is there any way to achieve this?

[TomCools]

Hi Kent, i think this can work with shadow variables and a single list.
So you would have your Machine with a PlanningListVariable of Jobs. Then, each job can also have "equipment", which can either be a Fact, or another planning variable in case multiple equipment options are available. This would match with https://timefold.ai/blog/mixed-models-timefold-solver (Pattern 3).

If you need multiple forms of equipment for a single job, that gets a bit more tricky to maintain. Else you could investigate a Shadow Variable route.

[kentbill]

Thank you for your reply, Tom @TomCools

I'm using the Mixed Modes​ now.

However, unlike the food‑packaging example in the Quickstart, in my scenario, different jobs on the same machine may require different equipment. For instance, on Machine A, Job 1 uses Equipment X from 9:00 to 10:00, and then another job - Job 2, requires Equipment Y from 10:00 to 11:00. Therefore, I must use Pattern 3​ in Mixed Modes.

I added an equipmentConflict​ constraint to prevent time conflicts for the same equipment. Yet, the start time of jobs is derived from the job list and their order on the machine, which only depends on the machine and the position in the job list. This could result in the equipmentConflict​ constraint never being satisfied.

To work around this, I introduced a slack variable for job, named delay, an integer planning variable. The start time of a job is: startTime = previousJob.endTime + delay (another constraint keeps the delay as small as possible, with 0 being optimal). This allows the solver to find a solution that satisfies the equipmentConflict constraint.

Although, this approache significantly expands the search space. Especially when job durations vary greatly, the range of delay values must be very large to potentially find a feasible solution. I would greatly appreciate any better approaches to prevent equipment conflicts.

Furthermore, if equipment, like machines, requires a strict and independent calendar, the problem seems even more challenging to implement.

Thank you for your suggestions!