By Antonio J. Conejo

This textbook for college students and practitioners provides a pragmatic method of decomposition concepts in optimization. It presents a suitable mixture of theoretical history and sensible functions in engineering and technological know-how, which makes the ebook fascinating for practitioners, in addition to engineering, operations learn and utilized economics graduate and postgraduate scholars. "Decomposition ideas inRead more...

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**Extra info for Decomposition techniques in mathematical programming : engineering and science applications**

**Example text**

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.

Solution for the hydroelectric river basin example Period t Discharge plant 1 (m3 ) Discharge plant 2 (m3 ) Electricity production (MWh) Electricity demand (MWh) Energy sold (MWh) 1 2 43 42 70 70 530 525 490 525 40 0 In summary, the main elements of the hydroelectric proﬁt maximization problem for a river system of n reservoirs during m time periods, are: Data. n: the number of reservoirs m: the number of time periods considered λt : the electricity price for period t ki : electric energy production to water volume discharge factor for reservoir i wti : the water inﬂow in reservoir i during period t r0i : initial water content in reservoir i rimax : maximum allowed water content in reservoir i rimin : minimum allowed water content in reservoir i : maximum allowed water discharge during a time period for reservoir i dmax i et : electricity demand during period t Ωi : the set of reservoirs above reservoir i and connected to it.

A good design requires minimizing the cost while satisfying some geometric and reliability constraints of the work being designed. Consider the wall in Fig. 14, where a and b are the width and the height of the wall, w is its weight per unit length, t is the horizontal force acting on its right-hand side, h is the corresponding oﬀset with respect to the soil level, and γ is the unit weight of the wall. In this example we assume that a, b, and γ are deterministic constants, and t ∼ N (µt , σt ) and h ∼ N (µh , σh ) are independent normal random variables with the indicated mean and standard deviations.