Minimax problem

[SiL588]

Hi everybody,

I'm trying to solve a minimax problem and i have to put down a model to plan a weekly time schedule of a class. Every subject is characterized by a load, and the objective is to minimize the maximum workload every day. Plus, every teacher (=course) has a table (teachers_availability) in which he can indicate, every period of every day, if he's available (1) or not (0).

I know that in a minimax problem I have to put the non-linear relation in the constraints and use a "support variable" (called y in this case).

But when i run it it gives me a syntax error.

What is that I'm doing wrong? I'm attaching the code so you can take a quick look, it's very short I promise :)
Thank you very much!

Silvia

[SiL588]

Sorry, the objective was: minimize daily_loads : sum {i in DAYS}  y[i] ;

[Victor]

There are at least two errors in your code (maybe more):

1. Missing ':' after the indexing expression {i in DAYS} in constraint daily_load.

2. Missing subscript [i] (or something else?) after the reference to variable y.

  subject to daily_load {i in DAYS}: y[i]>=sum {j in PERIODS, k in COURSES} load[k]*x[i,j,k];

It would be easier, if you posted the exact error message and context it refers to.

HTH,

Victor

[SiL588]

Thank you very much, now it works!

Can i ask you something else? I just discovered that my solution to the problem is not right, I should have minimized the maximum value of y[i].  How can i do that? 

Thank you!

[victor.z...@gmail.com]

You can minimize the maximum of y[i] by using an extra variable to represent the maximum, e.g.

  minimize o: max_y;

  s.t. c{i in I}: max_y >= y[i];

HTH,

Victor

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[SiL588]

I'm sorry, I didn't understand. I actually used y[i] as the extra variable to minimize. Do I need to add a second variable?

And what "s.t." means?

Thank you for your help, I really appreciate it.

[victor.z...@gmail.com]

The additional variable max_y is needed to compute the maximum of y[i]. You can use max{i in I} y[i] instead but it is a nonlinear expression and will not work with all solvers.

"s.t." is a keyword to introduce a constraint, same as "subject to".

HTH,

Victor

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[SiL588]

Of course it's subject to, i didn't think about it! :) 

But is it normal that the output is the same as before?

[victor.z...@gmail.com]

I'm not sure what output you are referring to.

Victor