Bicriteria Product Design Optimization

Competitive imperatives are causing manufacturing firms to consider multiple criteria when designing products. However, current methods to deal with multiple criteria in product design are ad hoc in nature. In this paper we present a systematic procedure to efficiently solve bicriteria product design optimization problems. We first present a modeling framework, the AND/OR tree, that permits a simplified representation of product design optimization problems. We then show how product design optimization problems on AND/OR trees can be framed as network design problems on a special graph— a directed series-parallel graph. We develop a solution algorithm for the bicriteria problem that requires as a subroutine the solution of the parametric shortest path problem. Although this problem is hard on general graphs, we show that it is polynomially solvable on the series-parallel graph. As a result we develop an efficient solution algorithm for the product design optimization problem that does not require the use of complex and expensive linear/integer programming solvers. Using software tools based on the results described in this paper, product managers can efficiently explore and optimize over the entire universe of choices available to them at the design stage itself. This should significantly reduce product development costs, as the expensive design-build-test-redesign loop is virtually eliminated. As a byproduct of the solution algorithm, sensitivity analysis for product design optimization is also efficiently performed under this framework. We illustrate our model and solution algorithm on a complex design problem at a FORTUNE 100 company. ∗The Robert H. Smith School of Business, Van Munching Hall, University of Maryland, College Park, MD 20742; e-mail: sr141@umail.umd.edu †The Robert H. Smith School of Business and the Institute for Systems Research, Van Munching Hall, University of Maryland, College Park, MD 20742; e-mail: mball@rhsmith.umd.edu ‡I2 Technologies, One Cambridge Center, Cambridge, MA 02142; e-mail: Vinai Trichur@i2.com