Optimization problem (using operations research)

[lucid crown]

We don't know if all the students from one school travel together to another school or if they can split up, right?

Something you haven't spelled out but that I think is sensible is one teacher per classroom

I would start with saying the binary decision variables have three indices - student name, classroom location
classroom location has two indices for school and room number
This determines how many students are in each room, what year they are in, and from which school they are from

This is valid for the case where the students can split up

You can then simplify this a bit by not having one variable per student that is binary but groups and integer variables with the size of the group

the groups are based on the criterium that year and traveling cost are the same

since your traveling cost table does not contain the same number twice, the groups are built based on the students original school

[silver wolf]

That is right, maybe i can make an assumption that they can split up? Or will that not make any make sense

[silver wolf]

Yeah i have that too thanks

[silver wolf]

Why? This doesn’t make sense to me

cs why would you only group people together with the sams traveling time

will that not make unnecessary amount of classrooms open

[lucid crown]

You group the students together into one variable..you can still put people from multiple groups into the same room
Like X_A,B,1 : People from school A in classroom school B room 1
Like X_B,B,1 : People from school B in classroom school B room 1
and so on...

Oh i forgot you have to add year:

You group the students together into one variable..you can still put people from multiple groups into the same room
Like X_A,1,B,1 : People from school A year 1 in classroom school B room 1
Like X_B,1,B,1 : People from school B year 1 in classroom school B room 1
and so on...

This is to reduce number of variables compared to 1 variable per student

[silver wolf]

Yeah okay so only one decision variable? Cs i was thinking about adding one binary variable that takes
1 if classroom is used at school j for Year y
0 otherwise.
So that it indictes whether a classroom is used and for the use of teacher cost

[silver wolf]

Okay okay thx

[lucid crown]

True, you need a variable for the classroom too. It doesn't need a year index though, I think. Because you have the same cost whether it's used by year 1 or year 2

Idk if it's better to add a constraint like so to make sure a lesson for a specific year is thought in the classroom
X_school,year=1,school,room != X_school,year=2,school,room

Or to add the year index to the classroom variable

[silver wolf]

I had also in mind to add classroom max, because i know that an optimal solution is to put all the 54 students of year 1 in 1 classroom

[silver wolf]

But for the objective, how should that one look like?

Cs im quite lost there

[lucid crown]

I'll let you think and come back another day

[silver wolf]

i had some in mind, but that uses the z{jr} variable, which indicates if classroom r at school j is used