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By B. D. Craven (auth.)

ISBN-10: 0412558904

ISBN-13: 9780412558900

ISBN-10: 1489972269

ISBN-13: 9781489972262

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Extra resources for Control and Optimization

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For (usually) many products, a set proportion of overheads (comprising setup costs, together with other costs not directly related to level of production) is commonly combined with a marginal cost to give a 'cost per unit'. However, an optimization model still requires instead a marginal cost for each product. 1 fory 1 81 for U1 marginal costs for raw materials and energy transport costs, but not material costs, which have already been included in r 1 maintenance costs, but not energy costs wages and 'fringe benefits' less unemployment payments penalty cost for demand unfulfilled Here maintenance means, more generally, the cost of keeping the process running, except for material costs, which have been already charged against production.

Is a closed convex cone (Ben-Israel, 1969). ), it follows that the image of a polyhedral cone by a matrix is another polyhedral cone, hence closed. Example A system of constraints g;(x):::;; 0 (i = 1, 2, ... m), h1 (x) = 0 (j = l, 2, ... , r) may be expressed as- G(x) E S, where G(x) is the vector function with components g 1(x), ... , gm(x), h 1(x), ... ' X {0} = {y E Rm+r: YI;;:: 0,. , Ym;;:: 0, Ym+l = 0, ... , Ym+r =OJ where here {0} means the zero cone in R'. Consider now a modified constraint system, given by -MG(x)e S, where M is some k x (m + r) matrix.

Since the demand for these outputs generally exceeds what is available, there is an optimization problem here how best to use the the limited resources? Consider then a network, consisting of nodes (points) and arcs (lines, which need not be straight, connecting various of the nodes). The nodes will represent reservoirs and hydroelectric power stations, and the arcs will represent streams and channels and pipelines. 3 shows a very simplified example, with two reservoirs and one hydroelectric power station.

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Control and Optimization by B. D. Craven (auth.)

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