PLATFORM SELECTION UNDER PERFORMANCE LOSS CONSTRAINTS IN OPTIMAL DESIGN OF PRODUCT FAMILIES Ryan Fellini, Michael Kokkolaras, Panos Y. Papalambros ∗ {rfellini,mk,pyp}@umich.edu Department of Mechanical Engineering University of Michigan Ann Arbor, Michigan 48109 Alexis Perez-Duarte alexispz@umich.edu Department of Aerospace Engineering University of Michigan Ann Arbor, Michigan 48109 ABSTRACT Designing a family of product variants that share some com- ponents usually entails a performance loss relative to the indi- vidually optimized variants due to the commonality constraints. Choosing components for sharing may depend on what perfor- mance losses can be tolerated. This article presents a method- ology for making commonality decisions while controlling indi- vidual performance losses. Previous work focused on evaluat- ing 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 de- signer 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 p i Component i in product p. ∗ Corresponding author, Phone/Fax: (734) 647-8401/8403 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 prod- uct. g Vector of inequality constraints. h Vector of equality constraints. ˆ S pq Set of pairs of indices describing candidate platform be- tween two products. ˆ S Set of all sets ˆ S 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. 1 Copyright  2002 by ASME Proceedings of DETC02 ASME 2002 Design Engineering Technical Conferences and Computer and Information in Engineering Conference Montreal, Canada, September 29-October 2, 2002 DETC2002/DAC-34099