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.mathematical programming, policy analysis, planning
A method is presented for locating wells in a monitoring network under conditions of uncertainty. The method couples the use of a simulation model of contaminant transport and a facility location model. The Monte Carlo technique is used with the simulation model to translate uncertainty in the simulation model parameters into uncertainty in the contaminant concentration distribution. The simulation model determines which well locations would detect a given realization of a contaminant plume with a concentration above a specified limit. The facility location model is then used to select a fixed number of well locations so that a maximum number of such plume realizations are detected. The selected well network maximizes the probability of detection. The method is applied to an example problem. Although the technique is computationally intensive, the results indicate that practical problems are tractable.
When applied to public-sector planning, traditional least-cost optimization models and their offspring, contemporary multiobjective models, have often been developed under the optimistic philosophy of obtaining "the answer." Frequently, such models are not very useful because there is a multitude of local optima, which result from wavy indifference functions, and because important planning elements are not captured in the formulations. Omitted elements, in fact, may imply that an optimal planning solution lies within the inferior region of a multiobjective analysis instead of along the noninferior frontier. The role of optimization methods should be re-thought in full recognition of these limitations and of the relevant planning process. They should be used to generate planning alternatives and to facilitate their evaluation and elaboration; they should also be used to provide insights and serve as catalysts for human creativity. As illustrated by recent examples, these roles may require the use of several models as well as new types of optimization formulations and modified algorithms and computer codes.government, optimization models, planning, policy analysis
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