Normative location theory: Placement in continuous space

This paper selectively reviews an area of operations research, refered to as normative location theory, that deals with the placement of objects in continuous space. The computational procedures discussed in this literature require initially that a certain set objects be located a priori; the placement of the objects in a second set is then determined in such a way that the total “interaction” among the fixed and variable objects is minimized. A number of strategies appropriate for different distance functions are surveyed and a numerical example is given illustrating one particular iterative algorithm. Although the current versions of these location methods depend upon more than the nonmetric information contained in the proximity measures defined for all pairs of objects, they can be generalized, and consequently, several possible connections to nonmetric multidimensional scaling are pointed out.