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Show WJ: < 0, when AH marginal units of fj (•) are not preferred over one marginal unit f; (•) given the satisfaction of the other objectives at a given level, and WJ: = 0, when Aij marginal units of fj (•) are equivalent to one marginal unit of fj('), given the satisfaction of the other objectives at a given level ( for WJ: = 0 the decision- maker is said to be indifferent with respect to the trade- offs between the two objective functions). The decision- maker is asked for his position on such trade- offs. His preference whether WJ; is negative, positive, or zero can be made on an ordinal scale of + 10 to - 10. Note that the decision- maker is responding to the various trade- offs with regard to a marginal improvement of one objective at the expense of a marginal degradation of the other. This fact, which is fundamental to the SWT method, gives him invaluable information, since his preferences are not made on the basis of the absolute value of the various objectives alorte, but rather on the basis of the additional information from the marginal increments. Once such an interaction with the decision- maker takes place, the An corresponding to WJ; = 0 can be interpolated. Subsequently, a nonlinear programming problem can be solved in order to determine the optimal decision vector u_* ( based on Everett [ 1963].) The ultimate optimal decision vector, u*, is associated with the policies to which the decision- maker is indifferent ( Wjj = 0) with regard to trade- offs among all resultant values of the objectives being considered. Sub- objective Decomposition Each of the major six identified objectives can be further decomposed into sub- objectives ( or into social indicators, Peterson et al., 1971). The importance of this decomposition is twofold: ( i) It enables the planner to study and ana- lize each social indicator in more specific detail. ( ii) It avoids the need for comparing the trade- offs between major objectives and sub- objectives. This distinction is especially important during comprehensive planning where a major objective may be to enhance the regional economic development ( in units of million dollars) and a sub- objective may be to reduce the dissolved oxygen deficiency in a specific stream's reach ( in units of ppm). The inherent order of magnitude that is associated with a sub- objective and a major objective makes the distinction between them essential. Note that although the decision- maker will ultimately choose between trade- offs among a number of marginal units of one objective vs. one marginal unit of another objective ( as is the case in the SWT method), the order of magnitude and the characteristics of these non- commensurable units should not be overlooked ( e. g. the regional economic development vs. the number of visitors/ day in a local recreation area). In developing a management model for the Great Salt Lake, six major objectives were selected. It would have been possible, of course, to choose the four major ones advocated by the water resources council, namely the enhancement of: ( 1) national economic development, ( 2) regional economic development, ( 3) environmental quality, and ( 4) social well- being, and then associate the six presently identified major objectives as sub- objectives. Alternatively, one might have chosen the nine major goals identified by Peterson et al. ( 1971), and associated the six objectives of the Great Salt Lake study with them. These nine general goals are divided into two major groups: ( a) Maintenance of Security ( i) environmental security ( ii) collective security ( Hi) individual security ( b) Enhancement ( iv) economic opportun- of ity Opportunity ( v) recreational opportunity ( vi) aesthetic opportunity ( vii) cultural and community opportunity ( vui) educational opportunity ( ix) individual freedom and variety Since a decision as to whether an objective is a major objective or a sub- objective may be somewhat arbitrary, it is important that a quantitative coordination procedure be developed that relates trade- offs between the major objectives and the sub- objectives. This section addresses itself to the higher level coordination procedures between a major objective and its associated sub- objectives in a sub- hierarchy on the one hand, and the coordination among all the major objectives in the overall hierarchy on the other. The sub- objectives can be viewed as a lower hierarchical echelon. Furthermore, it is conceivable that additional decomposition of the sub- objectives may be needed and thus the identification of sub- sub- objectives may be required. 50 |
