# Decomposition techniques in mathematical programming : by Antonio J. Conejo

By Antonio J. Conejo

This textbook for college kids and practitioners provides a pragmatic method of decomposition suggestions in optimization. It offers a suitable combination of theoretical heritage and functional functions in engineering and technology, which makes the e-book attention-grabbing for practitioners, in addition to engineering, operations examine and utilized economics graduate and postgraduate scholars. "Decomposition suggestions inRead more...

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**Sample text**

Such decomposition techniques are explained in the following chapters. 1 Two-Year Coal and Gas Procurement Consider the problem of the procurement of coal and natural gas (expressed in energy units) in a factory to supply the energy demand of the present year and next year. The demand for energy this year is known with certainty and it is equal to 750 MWh. 1 $/MWh, respectively. 2. 5, and 4 $/MWh. Note that we have converted the units to their equivalent units in terms of electricity production.

M; i = 1, . . 27) 4. the allowed discharge bounds ; t = 1, . . , m; i = 1, . . , n . 28) Function to Be Optimized. , m maximize dti , rti ; t = 1, 2, . . , m; i = 1, 2, . . , n z= n ki dti − et λt t=1 i=1 . 4 Energy Production Model Consider the triangular energy demand depicted in Fig. 6. In this ﬁgure, the vertical axis represents power and the horizontal axis time; therefore, the area Power d Energy 1 Time Fig. 6. Electricity demand curve for the energy production model 24 1 Motivating Examples Power 14 13 12 11 xi : Energy 10 p4 = 7 9 8 d=7 x4 = 6 1 14 5 4 x3 = p3 = 3 15 14 3 2 1 x2 = 10 7 p2 = 2 x 1 = 13/14 p1 = 1 1 Time Fig.

8) s = 1, . . , n . 9) Constraints. The constraints of this problem are 1. water balance constraints rts = rt−1,s − dts + wts ; t = 1, . . , m; s = 1, . . 10) s = 1, . . 11) 2. allowable reservoir level constraint rmin ≤ rts ≤ rmax ; t = 1, . . , m; 3. allowable discharge constraint dts ≤ dmax ; t = 1, . . , m; s = 1, . . 12) 4. nonanticipativity constraint dt1 s1 = dt1 s2 rt1 s1 = rt1 s2 if Ots1 = Ots2 if Ots1 = Ots2 ∀t ≤ t1 ∀t ≤ t1 . 10) are the balance of water input and output for period t and scenario s.