S x is called the feasible set and an object x s is

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Unformatted text preview: C (t ) i i τ j ≤ Vj l i ≤ t i ≤ ui , i (3) where a cost function Ci has to be available for each tolerance i. Note that we have not yet in this model restricted us to considering only discrete tolerance values; rather, we allow tolerances to be allocated within a whole tolerance band (li,ui). Vj is the upper bound on the variation on measure j that must not be exceeded. Many different cost functions have been suggested to use together with the continuous tolerance optimization problem (3). Table 1 lists a selection of cost functions that have occurred in literature. Cost Model A − B⋅ t B A+ t B A+ 2 t A ⋅ e -B ⋅t Name Linear Reciprocal Author Edel & Auer Chase & Greenwood Parkinson Spotts Reciprocal squared Exponential Speckhart Table 1; A Selection of Cost Models [Chase and Parkinson, 1991] The coefficient A represents a fixed cost, such as machine set-up, material, etc. If one of these functions describes the true manufacturing cost correctly, solving the optimizat...
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