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The purpose of this paper is to demonstrate the applicability of geometric programming to regional land-use planning models. The regional models are of the type where the criterion is maximum accessibility, and the model is constrained by population limits on each district. After a brief discussion of geometric programming, the relationship of total accessibility models to geometric programs is developed and a method of obtaining numerical solutions is presented. Several models are analyzed using the geometric programming approach, including a game theoretic model which is used to generate decentralized plans.

This paper shows the equivalence of entropy-maximization models to geometric programs. As a result we derive a dual geometric program which consists of the minimization of an unconstrained convex function. We develop the necessary duality equivalencies between the two dual programs and show the computational attractiveness of our approach. We also develop some characterizations of the optimal solution of the entropy model which have important implications with regard to postoptimal or sensitivity analysis.

This paper exploits recent developments in sensitivity (postoptimal) analysis in nonlinear programming and applies them to regional planning models. In particular the geometric programming point of view is used to develop sensitivity analysis procedures for entropy-maximization and accessibility models. As a result of these developments, we analyze changes in the model parameters with respect to changes in the optimal solution without resolving the model. Several examples are used to illustrate the basic procedures and some error reducing refinements.