Due to inevitable nondifferentiabilities, the minisum multifacility location problem is regarded as hard to solve. We propose a new chararacterization of points at which nondifferentiabilities occur. By this chararacterization it is possible to check if several variables can be identified with each other, thereby reducing the dimension of the problem and the number of nondifferentiable terms in the objective function.

Key Words. facility location, coincidence conditions, dimension reduction, nondifferentiability detection