OCR Text |
Show foot, the unit recreation benefits to be $ 200/ Acre, the unit energy benefits to be $ 50/ Mega watt- hour and flood storage was not considered. The first two examples took between 2 to 8 minutes of central processor time to solve using PSLP on a GOULD 9080 minicomputer. The applications on the 7 reservoir system ( example # 3) took between 5 to 17 minutes of central processor time on the same computer. The GOULD 9080 is roughly comparable to a DEC 8600 in processing speed. The total computer memory requirements ( double precision arithmetic) for these problems varied from approximately 524 Kilobytes to 656 Kilobytes. Of this the SLP compiled code is estimated to account for about 400 Kilobytes. Reservoirs in Series Example - ONEIDA and AMALGA Figure 5.2 illustrates the relative configuration of the 2 reservoirs and the demand areas. No M& I or irrigation demands are posed on Oneida, while 1 M& I and 1 Irrigation demand area is supplied by Amalga. Firm releases for Hydropower are considered for each reservoir, as is Hydropower generation. The Bear River gaged upstream of Oneida is used for the natural inflows to Oneida, while the Cub River is used for the unregulated natural inflow into Amalga. The output from PSLP for the example is presented in Table 5.4, and represents the optimal solution to the problem. Values of the objective function ( Net Annual Benefits) and the constraints are presented, followed by the values of the decision variables at optimality. The units are Millions of Dollars for the objective function, and Thousands of Acre- feet for the yields and storages. The objective function representing net annual benefits, is $ 23,712 million at the optimum. The total storage capacity TSC01, of Oneida is 140,000 Acre- feet, while TSC02, the total storage capacity of Amalga is 138,183 Acre-feet. The indicated final active storages FAS01 and FAS02 of the two reservoirs are zero, indicating that the reservoirs were full at the end of the critical period. The ratios of Dead Storage to Total Storage, DSC01 and DSC02 for the two reservoirs are .697 and .20 respectively. The total M& I annual yield ( TOTM& I01) from is 219,469 Acre- feet, while the total Irrigation annual yield ( TOTIRR01) is 113,768 Acre- feet. Values for the decision variables are next presented. The dead storages DS01 and DS02 are 97,564 and 27,655 Acre- feet respectively. MI0201 and IR0201 are the M& I and Irrigation annual yields respectively, from Amalga. Since only 1 demand area for each use is supplied from only 1 reservoir ( Amalga), these value are identical to those for the corresponding constraints. An annual firm release for hydroenergy HOI of 103,337 Acre-feet is provided from Oneida, while the corresponding release H02 from Amalga is zero. A generator size G01 of 22.135 MW is selected for Oneida, while the corresponding value G02 for Amalga is 2.226 MW. For each decision variable and each constraint, applicable lower and upper bounds are also presented. The column under DUAL ACTIVITY, shows the potential change in the objective function per unit relaxation of the " tight" bound at optimality. For a variable/ constraint strictly within its bounds, this should be 0. For constraints/ variables at a bound the objective function change is the negative of the value in this column for a constraint/ variable at its upper/ lower bound respectively. For example a unit increase in the upper bound on TSC01 increases the objective function by 0.00696, while a unit decrease in the lower bound for H02 increases the objective function by 0.01479. 124 |