# Assignment problem, minization of the Standard Deviation

I have an assignment problem. So typically I need to find the optimal combination between two sets of parameters P, M. I know that the Hungarian Algorithm is often privileged for this kind of problem but there is few key points making this technique probably not well appropriated.

• My matrix is not really a cost matrix. It contains values evaluated for each combination of my two parameters. It does not represent a cost but a normalized distance. The minimal or maximal distance does not represent an optimal value.

• My objective is the minimization of the standard deviation. So I want to find the combination of Pi,mi minimizing the standard deviation of their values. i.e. the minimal standard deviation of the distances.

• Hungarian algorithm work with squared matrix and I would like a technique working on m*n matrix. ( it is not a strong constraint for me)

• The matrix size will not exceed 10*10 and most of the pairs can be already associated. (i.e. other criteria indicates that distance value is 0 or out of bounds leading to a single P,M combination). But I would like the find the solution in the worst case: None of the pairs are formed.

What kind of technique could you recommend ?

Thank you very much for your help.