Bicriteria Product Design Optimization

Abstract

Competitive imperatives are causing manufacturing firms toconsider multiple criteria when designing products. However,current methods to deal with multiple criteria in product designare ad hoc in nature. In this paper we present a systematicprocedure to efficiently solve bicriteria product designoptimization problems. <p>We first present a modeling framework, theAND/OR tree, that permits a simplified representation of productdesign optimization problems. We then show how product designoptimization problems on AND/OR trees can be framed as networkdesign problems on a special graph---a directed series-parallelgraph. <p>We develop a solution algorithm for the bicriteria problemthat requires as a subroutine the solution of the parametricshortest path problem. Although this problem is hard on generalgraphs, we show that it is polynomially solvable on theseries-parallel graph. As a result we develop an efficientsolution algorithm for the product design optimization problemthat does not require the use of complex and expensivelinear/integer programming solvers. <p>As a byproduct of thesolution algorithm, sensitivity analysis for product designoptimization is also efficiently performed under this framework.We illustrate our model and solution algorithm on a complexdesign problem at a FORTUNE 100 company.