Originally posted by: SystemAdmin

Hi all,

I have a 2-dimension array of decision variable. I would like to find the max and min of the sum of columns per row and then minimize the difference between the max and min. How do I do that in ILOG?

so to further elaborate, the 2-D array are dvar int of 0..1, so it might look like,
0 0 0 0 1 0
0 0 1 0 0 0
0 1 1 0 1 0
1 0 0 0 0 0
0 0 0 1 0 0
0 0 0 0 0 1

therefore, summing across the columns, each row will sum to,
0 0 0 0 1 0 = 1
0 0 1 0 0 0 = 1
0 1 1 0 1 0 = 3
1 0 0 0 0 0 = 1
0 0 0 1 0 0 = 1
0 0 0 0 0 1 = 1

Hence, the max = 3 and min = 1. I would like to minimize the difference between the max and min.

How do I do it in ILOG?

Thanks.
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Originally posted by: SystemAdmin

If s_i is the sum of row i, you want to introduce a new decision variable z (the maximum difference) and minimize z subject to the constraints s_i - s_j <= z for all i != j. (Note that each (i,j) pair will occur in two constraints, such as s_3 - s_7 <= z and s_7 - s_3 <= z.)

Paul

Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
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