The Optimal Assignment of Facilities to Locations by Branch and Bound

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.