Function optimizing matrix under the constraints (vector)

I'm having problem with finding a function that optimizes a matrix under specific constraints. In my task I have two matrices (K and C) of the same dimensions (SxP).The K matrix has test results in the range of 0 to 10 while Matrix c is a zero-one matrix, selecting the best result in the matrix K. The C matrix has two constraints:

a)

Where SP is the vector representing the maximum number of selected results in a given row

b)

My main task is to choose the best results in the matrix:

Answer 1

[Matt J]

Once you have your objective and constraints expressed as matrix-vector multiplications, the problem is a straightforward application of intlinprog().

Summation along columns of C can be expressed as a matrix-vector multiplication A*C(:) where A=kron(eye(S),ones(1,P)). Summation along rows can be expressed the same way with A=kron(ones(1,S),eye(P)). The double summation for Q can be epxressed can be expressed K(:).'(C(:)).

[Jan Dzban]

I don't understand the second part. Maybe on the example I will explain what I meant.

I have two matrices: The matrix K

and the matrix C:

and vector SP:

The C matrix has following constraints:

X11 + X12 + X13 <=1

X21 + X22 + X23 <=2

X11 + X21 <=1

X12 + X22 <=1

X13 + X23 <=1

x11 to x23 are binary

Now if i use a function intlinprog() i have

min (5x11 + 4x12 + 3x13 + 2x21 + 3x22 + 5x23)

f = [5 ;4 ;3 ;2 ;3 ;5]

intcon = 6

A = [1 1 1; 1 1 1]

b = [1;2]

And here is the problem because the number of columns in the matrix A doesn't match the number of elements in the vector f

[Torsten]

A = [1 1 1 0 0 0 ; 0 0 0 1 1 1]

Best wishes

Torsten.