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<br /> <br />;1i), '-j <br /> <br />~ <br /> <br /> <br />'. <br />-.' <br /> <br />. <br /> <br />~ <br />N <br />~ <br />co <br /> <br />",' <br /> <br />.'.... ~ . <br /> <br />Consider the analysis to begin at "Level 2" with four basic alternatives <br />whose cost-effectiveness function is given and the allocation among "Levell" <br />alternatives is known. Two "Level 3" cost-effectiveness functions are <br />developecl by sdding "Level 2" functions in an optimization analysis. The <br />aclclition of incliviclual cost-effectiveness functions becomes the objective <br />function for the next level of eggregation. Constraints consist of limita- <br />tions on the total effectiveness of each individual alternative ancl aggregate <br />effectiveness at the level being developed. Detailecl mathematical descriptions <br />of these procedures are given by Walker et al. (1979). <br /> <br />Optimization Proceclure <br /> <br />',., <br /> <br />The relationships bet"Ween costs and salinity recluctions are generally <br />nonlinear. Aggregating tha level to level cost-effectiveness function, there- <br />f.ore, requires an unclers'tancling of the various tec!miques for nonlinear opti- <br />mization. Most,water quality planners c10 not have sufficient backgrouncl in <br />the~e subj ects for s technique Iike. originaU;y us.ell by Walker (1973) and <br />Walker et al. (1973) to be Widely useful. As a result, a very simple optimi- <br />zation procedure was developecl for application and demonstration in this <br />writing. In fact, the entire basin-wide optimization was accomplished on an <br />HP9825A desktop computer with only a total of 24K bytes of capacity. <br /> <br />For purposes of illustration, consider an irrigated valley which is <br />supplied water through canals. Each canal has a totel length of LJ: meters, an <br />inlet wetted perimeter of W meters ancl an inlet capacity of ~ cUDic meters <br />per second. Walker (1978) ~eviewecl canal lining cost-effectiveness for salin- <br />ity control ancl derived the following relationship: <br /> <br />i <br /> <br />, <br /> <br />Cc = K' 1 1(1 - bf~:1\l+K21 + K3f(51) <br /> <br />(1) <br /> <br />in which, <br /> <br />C = capitsl construction cost necessary to impact the mass emission of <br />0. salts due to eeepage by Sl Mgm/yr; <br /> <br />K!' K2' K3 = empirical constraints relating canal size ancl lining costs; <br /> <br />b = empirical function c1escribing the spatial distribution of canal <br />deliveries to individual farm turnouts; <br /> <br />K' <br /> <br />RJ~2 Lt/(l + K2)b; <br /> <br />(2) <br /> <br />f(5l) <br /> <br />Lt <br />= b- <br /> <br />I (~t)2 <br /> <br />(3) <br /> <br />10.5 <br />Sl <br /> <br />-~ <br />K' b <br />2 <br /> <br />41 <br /> <br />"J, ~... <br /> <br />" . <br />