Managing gaps

[Jack_Pk]

Hello everybody!

I am struggling with a very complex school timetable due to a large number of non-negotiable constraints.
My school has a daily timetable of six blocks, five days a week, but teachers can never work more than four hours. Normally, there is the possibility of having a gap. Therefore, schedules such as four consecutive hours, or 3-gap-1, 2-gap-2, etc. are acceptable.
Unable to finalize the schedule in any way, I obtained a small additional margin of freedom: I am allowed to give all teachers two gaps once a week.

I thought I had solved my problems this way: max 2 gaps per day + max 6 gaps per week. I assumed that this way, even if there was a day with 2 gaps, I would have at most one gap on the remaining 4 days.
Unfortunately, I hadn't counted on FET deciding to eliminate gaps altogether on some days and put two on others.  So I have teachers who have no gaps for two days a week (which is fine), but then have two gaps on three days a week (very bad).

My question is: is it possible to impose a maximum of two gaps once a week and a maximum of one gap for all other days?

Thank you in advance.



Translated with DeepL.com (free version)

[Liviu Lalescu]

Hello, Jack!

You could add a dummy activity for each teacher, A1,A2,A3,A4,A5,A6 (durations 1+1+1+1+1+1), min 1 days (A1,A2,A3,A4,A5), 100% (notice A6 is not constrained). Then max 0 gaps for each teacher.

[xtzetzias]

I was about to suggest the same as Liviu, but with 1+1+1+1+2 hours (if you don't mind 2 consecutive gaps) or the dummy activity with 1+1+1+1+1 and a second dummy activity, with only one hour. Of course, 0 gaps for everyone. I use the extra hour, because i think you mean that 5 gaps are not enough.

[Liviu Lalescu]

Thank you, xtzetzias! I corrected my post above (should be 6 activities, duration 1 each, and only 5 of them in a constraint min 1 days between activities 100%).

It is best not to have an activity with duration 2, because this would constrain the timetable more than necessary.

[xtzetzias]

Ok, now it's better than my solution with two activities. I'm not sure i understand how A6 is not constrained, but i will look into it (it probably has to do with the min 1 constraint, which i do not know)

[Liviu Lalescu]

A constraint min days between activities can be edited in its list of constraints dialog.

[xtzetzias]

Thanks! Yes, i just found it. Guess i haven't got familiar enough with activities' constaints...

[Jack_Pk]

Thank you for the replies. Your suggestions didn't fully meet my needs: creating six dummies would have forced all teachers to have the same number of free hours, whereas I wanted FET to use those only when strictly necessary.
 
The dummy-based approach was still the right one, though it needed refinement: I labeled all school activities as "regular" (max 4 hours per day), assigned one dummy hour to each teacher, and set a maximum of one free hour per day. This way, FET used the dummy as a wildcard, leaving only a few "unlucky" teachers with a double free hour, while for the others the dummy was placed at the start or end of the day, effectively disappearing.

Thanks for the help!
Bye bye.

[xtzetzias]

A suggestion I've made could solve your problem. If there was a constraint "Min gaps per day" you could just set min gaps per day to 1, max gaps per day to 2 and max gaps per week to 6.
Liviu says it's difficult to impliment. I hope he will be able to do it :-)

[Vangelis Karafillidis]

Hello.

There are some "indirect" ways that result in min gaps per day = 1. For example you could use a combination of pseudo-activities and a combination of constraints in order to "force" FET to generate a timetable with min gaps per day = 1 for a teacher. But, the user needs accuracy and of course much time and effort in order to add all these pseudo-activities and constraints even just for one single teacher.

Vangelis.