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Show PART III: MANAGEMENT MODEL DEVELOPMENT CHAPTER V MULTIOBJECTIVE ANALYSES Introduction Construction of Objective Functions The Great Salt Lake will be modeled in the hierarchical structure in Figure 7, where six major societal and economic goals and considerations have been identified at the second layer. These six goals and considerations, ( i) recreation and tourism, ( ii) mineral extraction, ( iii) oil drilling, ( iv) brine shrimp harvesting, ( v) transportation, and ( vi) water supply, represent conflicting and noncommensurable objectives and goals. In particular, present strong societal and environmental preferences make any cost- effectiveness analysis which is solely based on economic considerations obsolete and unacceptable. The hierarchical- multilevel approach ( Haimes, 1973a, b) recognizes the inherent nature of conflicting and often competing objectives that characterizes most physical systems. In the hierarchy of models used to analyze the Great Salt Lake ( Figure 7), the higher level coordination provides the means and ways for analyzing the interactions among all lower level subsystems. There are several methods for developing the higher level coordination and control ( Haimes and Macko, 1973). Particularly worth noting with regard to this study are the multiobjective function analyses and the Surrogate Worth Trade- off ( SWT) Method ( Haimes and Hall, 1974). As noted previously, the economic and societal goals modeled at the first level- second layer of the hierarchical structure are very likely to be both non- commensurable and in competition and conflict. The decisionmaker ( who may be at the level of the Utah State government, the state legislature, a regional commission, a local government, or a federal agency) will need to determine the kind and level of control measures that should be enacted to achieve specific societal objectives. For this purpose, he will need a means of evaluating quantitatively the trade- offs possible among all the goals and objectives as represented by the various objective functions. The SWT method recognizes and answers this need. A major task under Phase II of this study will be to quantify all objective functions, constraints, and system's input- output relationships. The task is both essential and critical, since the ultimate goal of this study is to analyze the Great Salt Lake system as a whole and to recommend a planning policy which takes into consideration quantitatively all the trade- offs among the various objectives. Before detailing how the Surrogate Worth Trade- off Method works, a brief discussion on constructing of the objective functions is in order. A gigantic modeling effort which is responsive to all societal goals was initiated in a study known as the " Straw Man" ( Peterson et al., 1971). They proposed a " structured hierarchical array of elements, beginning at the top with nine general goals successively described by expanding strata of subgoals which are eventually linked to potential water policy action variables through social indicators." We have adopted here methodologies and approaches from the " Straw Man" project which are applicable to the development of a management model of the Great Salt Lake. In particular, the concept of subgoals within a major goal is adopted in this study's hierarchical structure ( Figure 7) where the SWT method plays the coordinating role between a major goal and its various subgoals. The subgoal formulation will be discussed later in this chapter. A fundamental step in constructing the various objective functions is to identify the decision variables ( control measures), state variables, exogeneous variables ( also known as parameters), outputs, and input- output relationships. Let: x_ = n- dimensional state vector. The state vector describes the state of the system at any time. u_ = N- dimensional decision ( control measures) vector a_ = k- dimensional vector of ex ogeneous variables ( parameters) 45 |