Determine the monthly water allocation to domestic, industrial, agricultural, and recreation demands in a river system shown in Figure 9. 39 The average monthly river discharges upstream of the system, in a 2-year time horizon, are presented in Table 9. 21.

The return flow of domestic and industrial sectors is assumed to be 20% of allocated water, and the initial volume of the lake is 30 million cubic meters. The utility functions of different sectors are presented in Table 9. 21 and Figure 9. 40. The values of utilities have been normalized between 0 and 1, and the higher utility shows the higher priority of a decision maker or a sector. The shape of utilities is considered to be trapezoidal, and the array (a, b, c, and d) in Table 9. 21 shows the values of water allocated to the agricultural sector, corresponding to utilities of 0, 1, 1, and 0, respectively.

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TABLE 9.21 Monthly River Discharge and Utility Functions of Agricultural Sector Agriculture Demand (MCM/Month) (0, 10, 15, 25)* River Discharge Upstream of the System (MCM) 31 Month (0, 8, 12, 20) 31 (0, 10, 15, 25) (0, 10, 15, 25) 31 40 123 + 4 (0, 10, 15, 25) (0, 5, 10, 15) 45 60 5 (5, 10, 25, 50) 75 69 (15, 30, 60, 90) 100 8 (20, 35, 55, 90) 90 9 (25, 35, 60, 90) 51 (30, 40, 60, 90) 31 (25, 35, 60, 10) 31 10 11 12 The entries in the parentheses are a, b, c, and d in the utility function, respectively.