Sufficient conditions for coincidence in ℓ₁-minisum multifacility location problems

We consider the problem of finding the optimal way of locating a finite number of facilities in a finite dimensional space, in order to minimize a weighted sum of the distances between these and other pre-existent facilities which are already positioned. We study the specific case where distance is measured in the ℓ₁-norm, giving a new sufficient condition for identifying groups of facilities whose position will coincide at optimality.