| OCR Text |
Show ir. . sf. si, mm si si, max i - i„ O0is r ~ looooK, ( 5.18) H . < H s , min s s , mix ( 5.19) D . < D s , nun s < D s , max ( 5.20) F £ F S , 1 1 0 S < F s smax ( 5.21) Objective Function: The objective of the model is to maximize expected net annual revenue for the reservoir system. It is expressed as the difference between total annual revenue/ benefits realized from the sale of M& I water, Irrigation water, hydro- energy, recreation and flood control, and the total annual cost of reservoir storage and hydropower plants. It is mathematically represented as: Max OBJ = TAR - TAC ( 5.22) where TAC is the total annual cost and TAR the total annual revenue. Presented below are the functional relationships between TAR, TAC and the decision variables of the model, that were used for the example applications reported. Because of the nonlinear nature of the formulation, it would be relatively easy to accommodate more complex relations for the objective function terms. The total annual cost TAC is expressed as the sum of the annual storage cost and the annual cost of M& I water treated. c 2 M R , < 10s TAC - clg T$ s + X S c9s\ PmlKm) ( 5- 23) m= lr= l where cls , c2s represent the coefficient and exponent for the storage cost function, c9s, clOs, represent the coefficient and exponent for the treatment cost function, and pr mi is the average reliability ( expressed as a probability) of M& I yield m at reliability level r, for the operation period, of duration T The total expected annual revenue TAR is expressed in terms of its components for the sake of clarity. Term 1 : Expected Annual Revenue from M& I water supply M R Y Y R' pr . M* ( 5.24) m= l r* l where Rim r is the unit revenue from M& I water supplied to area m at reliability level r. 112 |
