In CS3997 this year, I have decided to have "debates" instead of presentations. This means that I need to make sure that each student has has exactly one topic, and every topic is assigned to an even number of students.

Another constraint is that I asked the students to list in order their top 3 preferences. I wanted to maximize (within reason) "student happiness", so I give weight 4 for their first choice, 2 for the second, and 1 for their third.

Finally, the students are numbered 1...26 in the order they sent me their preferences. I decided to enforce "first-come first-serve" in the objective function, so the happiness of student 1 has more weight than student 26. How much more is a bit of a subjective choice.

If you don't want to look at the solution yet, the students preferences are available separately. 'happy[i,j]' measures how happy student i is being assigned topic j

Almost the real solution is available. In actuallity, I first solved the problem for the first 18 students (so they didn't have to wait), and use the following

 printf { i in students, j in topics : x[i,j]=1 } "s.t. fix_%d_%d: x[%d,%d]=1;\n",i,j,i,j; 

to print out some constraints, which I then cut and past into the model, and resolved a week or so later when I had all of the data.

Here is the Paper roll cutting example from section 2.7.

Here is the icecream production planner we discussed in class.

Here is an expanded version of the diet example we discussed in class. It is taken from the glpk distribution.

Here is the simple flow example we discussed in class.