This paper is concerned with constructing a comprehensive standard for evaluating regional environmental systems. Because such systems are composed of complex natural, economic, and social systems, conventional engineering and economic methods are virtually ineffective for this purpose. Systems-analysis methods appear suited to providing proper evaluation as well as effective control of environmental systems. But, in applying systems analysis to environmental evaluation, we are faced with the problem of measuring numerically the level of satisfaction of the region's residents. Environmental systems are very large in scale, and the components (attributes) which contribute to quality of life are not only many and various but often conflict with each other. In addition they are not commensurable. Therefore new methodologies for evaluating environmental systems must be developed. In such complex large-scale systems analyses, it is necessary, whatever the method used, to structure objectives by means of decomposition and ordering, and the construction of a preference hierarchy is an effective way to perform this structuring. The utility approach to decision analysis is employed to choose the best solutions under this interactive procedure. However, environmental systems also permit, to some extent, the possibility of mathematical formulation in a more rigorous form. Shadow prices (dual optimal variables) are good criteria for evaluating a constrained system's performance. We provide some devices (1) to utilize dual variables obtained in mathematical programming, (2) to nest them into multiattribute utility functions in a hierarchical system, (3) to articulate value trade-offs, and (4) to clarify priorities among objectives. These four procedures constitute the nested Lagrangian-multiplier method.
A Unified Framework for Aerocapture Systems Analysis
