Tree Network Location Problems With Minimum Separations

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Abstract
We consider the problem of characterizing feasible locations for identical facilities in a tree network when lower bound constraints are imposed on distances between the facilities as well as between each fixed point and the facilities. We first eliminate from the network some fixed points whose associated constraints, are redundant, and then develop a sequential procedure for locating the maximum number of facilities. We relate this maximum number to the consistency of the distance constraints; the resulting information is relevant in solving a certain class of location problems on tree networks.