Exploiting Structure in Linear-Programming Formulations for Land-Use Planning

The utility of linear programming for land-use planning is firmly established. It allows realistic models of complex planning situations to be formulated and solved computationally. However, because many objectives are qualitative and conflicting and many of the constraints may not be clearly defined, the actual construction of a linear-programming formulation to model any specific land-use planning problem will not be easy. In addition, even on large computers real problems cannot in general be solved in an acceptable time. As a consequence, the availability and utility of the technique to people responsible for planning is restricted. In fact, in many planning contexts, what the practitioner needs most is the ability to experiment with alternative plans cheaply and easily. This leads naturally to a search for ‘simplifications’ of the linear-programming formulations for land-use planning which yield effective and implementable systems for the practitioner and which allow him to experiment with realistic alternatives relevant to his planning responsibilities. In this paper, we examine how the structure of a particular linear-programming formulation for land-use planning can be exploited to yield such simplifcations. On the one hand, it is shown that linear-programming formulations which allocate uses to the zones that make up a given planning region, can be classified as generalized upper bounding because of their special structure. On the other hand, this special structure is exploited to show how such linear-programming formulations can be solved more simply than by the direct use of the simplex method. In addition, it is used to motivate the use of the LUPLAN procedure and establish its relationship to linear-programming methods.