The Optimal Assignment of Facilities to Locations by Branch and Bound

Abstract

The problem of assigning facilities to locations consists of the following: in the general case there are n fixed locations to which n facilities must be assigned. Each facility may be assigned to one and only one location. There are n ! feasible assignments. The “distance” between any pair of locations is the cost of transporting a unit of material between the locations. The “traffic intensity” is the rate at which units of material are transferred between a given pair of facilities in both directions. An optimal assignment is one in which the sum of the product of distance times traffic intensity for all pairs of facility-location assignments is a minimum. The branch-and-bound technique with modifications is used to give an optimal assignment.