Each configuration will yield a different duality gap

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Unformatted text preview: ction. In this paper, we will not restrict ourselves to a specific loss function. We will accept general loss functions in the sense that they can be described by an arbitrary polynomial of a certain degree. It is worth noting, however, that an implicit expression of the expected quality loss of (4) is trivial to derive: E[L( y )] = E [z( y − T ) 2 ] = zE[( y − µ ) 2 + ( µ − T ) 2 + 2( y − µ )( µ − T )] = zσ 2 + z ( µ − T ) 2 + 2 z ( µ − T )( E[ y ] − µ ) = zσ 2 + z( µ − T ) 2 . ( 7) Otherwise, these calculations can be carried out with an appropriate quadrature rule, a method for approximating integral calculations [Heath, 1997]. Solution methods used on the continuous allocation problem are, among others, SQP (Sequential Quadratic Programming), simulated annealing, genetic algorithms, and iterations on Lagrangian multipliers [Hong and Chang, 2002]. So far in this paper, tolerances may be chosen from within an enclosed region. However, it is more likely that the manufacturer may only choose between a finite number of machines and/or manufacturers. The optimal solu...
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