Modeling to Generate Alternatives: The HSJ Approach and an Illustration Using a Problem in Land Use Planning

Public-sector planning problems are typically complex, and some important planning issues cannot be captured within a mathematical programming model of a problem; such issues may be qualitative in nature, unknown, or unrevealed by decisionmakers. Furthermore, there are often numerous solutions to a mathematical formulation that are nearly the same with respect to modeled issues but that are drastically different from each other in decision space. In such cases, some of these solutions may be significantly better than others with respect to unmodeled issues. Thus, a potentially important role of programming models is to generate a small number of alternative solutions that are feasible, perform well with respect to modeled issues, and are significantly different with respect to the decisions they specify. Such a set of alternatives may aid analysts and decision makers in understanding the problem and may serve as a catalyst for human creativity and invention. The Hop, Skip, and Jump (HSJ) method has been developed for this purpose. It is designed to produce alternative solutions that are very different from previously generated solutions. Each solution generated is good in the sense that it meets targets specified for modeled objectives. The technique is described in this paper, and is illustrated using a multiobjective linear programming model of a land use planning problem provided by a regional planning commission. In this case, the method is shown to be capable of generating alternative solutions that perform well with respect to the modeled objectives and that are drastically different with respect to the land use pattern specified. Differences among solutions are discussed using visual inspection as well as simple quantitative measures. The technique can be used to extend the capabilities of existing mathematical programming packages.