D is the accumulated measure variationstolerances v

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Unformatted text preview: denote the available tolerance choices tij together with associated costs cij. The assignment of a tolerance tij to a dimension i is represented by the binary variable xij. Furthermore, let aik be the sensitivity coefficients with respect to the critical measure k. We also assume that there is a function Lk for each measure k that somehow measures the quality loss a deviation of k from target induces (Sec. 2.3). The problem becomes to min ∑ cij xij + ∑ E [Lk ] (a ) k = 1,..., m i = 1,..., n i = 1,..., n, j = 1,..., ni (b) (11) (c) (d ) ∑ (a ∑x i, j j i, j k ik ij t ) 2 xij ≤ Vk2 ij =1 xij ∈ {0,1} (11b) is a budget constraint. It insures that the limit on the variation of each of the measures is not violated. (11c) is called an assignment constraint. It guarantees that exactly one tolerance is assigned to each dimension. Note that restricting the loss functions to polynomials together with (11d) preserves (11) as an ILP. Ostwald and Huang solved the problem without loss function using an additive algorithm by Balas [Ostwa...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.

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