Platform Selection under Performance Loss Constraints in Optimal Design of Product Families

Designing a family of product variants that share some components usually entails a performance loss relative to the individually optimized variants due to the commonality constraints. Choosing components for sharing may depend on what performance losses can be tolerated. This article presents a methodology for making commonality decisions while controlling individual performance losses. Previous work focused on evaluating individual performance losses due to pre-specified sharing. Trade-offs were identified for different platforms (i.e., the sets of components shared among products) by means of Pareto sets. In the present work an optimal design problem is formulated to choose product components to be shared without exceeding a user-specified performance loss tolerance. This enables the designer to control trade-offs and obtain optimal product family designs for different levels of performance losses in an attempt to maximize commonality. A family of automotive side frames is used to demonstrate the approach. NOMENCLATURE P Set of products. m Number of products in set P . p,q Superscripts denoting products. C p Set of components in product p. c i Component i in product p. ∗Corresponding author, Phone/Fax: (734) 647-8401/8403 1 n Number of design variables. d Number of model responses. x Vector of design variables. η Sharing decision variable. R Vector of responses. f Objective function representing product performance. f ◦ Optimal objective function value for null platform f ∗ Optimal objective function value for a platform-based product. g Vector of inequality constraints. h Vector of equality constraints. Ŝ pq Set of pairs of indices describing candidate platform between two products. Ŝ Set of all sets Ŝ pq with p, q ∈ P . S pq Set of pairs of indices describing platform between two products. S Set of all sets S pq with p, q ∈ P . L Performance loss tolerance. D Distance function. ω Preference on sharing component. b Width of rectangular cross section. h Height of rectangular cross section. t Thickness of rectangular cross section. Copyright  2002 by ASME