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If by varying a slack or decision variable a state is driven to *ero, a decision variable must be selected to trade rv positions With the state to avoid zero valued state variables. ao In addition, when a loose constraint is tightened, a new state ~ variable must be selected from the rest of the decision variables. ~ The exception to this is when a loose constraint is tightened by loosening a currently active constraint. APPLICATION TO REGIONAL SALINITY PROBLEMS On a basin-wide scale, a salinity problem is the combined effect of many irrigated areas, saline springs, diffuse natural inflows, and other miscellaneous sources. These salinity sources not only occur sequentially due to the geographic structure of an hydrologic area, but are also often governed by differing administrative formulas. Consequently, the problem of deter- mining an ",optimal" strategy for a large area like the river basin rapidly becomes too large and too complex for direct analysis. One of the various mathematical techniques for optimizing :complicated systems is to decompose the problem into a series of subproblems whose solutions are coordinated in a manner that produces the solution to the larger problem. One method app~ied to analysis of water quality improvements in the Utah Lake D~ainage basin of central Utah provides both a simple and effective decomposition (Walker, et al. 1973). The structure of the decomposition methodology referred to above is shown schematically in Figure 1. Individual levels of modeling are delineated to define water quality cost-effectiveness analyses at different stages of development enroute to a single repre- sentation at the ultimate basin-wide scale. Conceptual Salinity Control Model The conceptual model illustrated in Figure 1 represents an additive approach for determining the minimal cost salinity control strategy in a river basin. A number of levels or subdivisions having similar characteristics can be defined to correspond to various levels of hydrologic or administrative boundaries in a region. Within each level, the alternative measures for salinity management are characterized by cost- effectiveness relationshiDS. A more detailed review of the structure of cost-effecti~eness functions and their inter- dependence will assist the reader in understanding the appli- cation of the conceptual model in later sections. Description of Cost-Effectiveness Functions -- The alternatives for managing salinty on a basin-wide scale fall into two categories: (1) those that reduce salinity concentrations by dilution or minimizing the loss of pure water from the system by evaporation; and (2) those that improve water quality by reducing the mass emission of salt. l7 "'-