A Methodology for Environmental Systems Management: Dynamic Application of the Nested Lagrangian Multiplier Method

Seo, F. & Sakawa, M. (1979). A Methodology for Environmental Systems Management: Dynamic Application of the Nested Lagrangian Multiplier Method. IIASA Research Report (Reprint). IIASA, Laxenburg, Austria: RR-80-012. Reprinted from IEEE Transactions on Systems, Man, and Cybernetics, SMC-9(12) [1979].

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Abstract

In this paper an alternative method for solving multiobjective optimization problems is presented. We are especially concerned with bridging a gap between procedures for obtaining the Pareto-optimal solutions and the "best compromised" preferred solution for the decisionmaker. First, the main concepts of the utility approach are briefly reviewed from the point of view of multiobjective systems analysis, and some shortages of this approach are examined. Second, a new method which we call the nested Lagrangian multiplier method (or NLM method) is introduced and compared with precedent devices for the utility approach. The theoretical background is also scrutinized. Third, the use of the NLM method for environmental systems management in the greater Osaka area is demonstrated, providing an example of dynamic application of this method. Finally, it is recalled that utilization of a mathematical optimization method for integrated plannings would simultaneously provide optimal solutions for allocation as well as evaluation problems, based on duality of mathematical programming. A stress is placed on the utilization of dual optimal solutions as a base of evaluation factors.

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