Research Papers: Design Theory and Methodology

A Decomposed Gradient-Based Approach for Generalized Platform Selection and Variant Design in Product Family Optimization

[+] Author and Article Information
Aida Khajavirad

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213aida@cmu.edu

Jeremy J. Michalek

Department of Mechanical Engineering, and Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213jmichalek@cmu.edu

If more information is known about the production volume of each variant and the life of the tooling, a more accurate prediction can be made; however, commonality metrics are generally applied at a higher level of abstraction so that they do not require excessive data to compute.

If anything, the first alternative would probably be preferred over the second because the sharing appears to be more balanced (again, this depends on production volume).

If data are available on relative cost savings for commonality of each component, appropriate weights can be included as well.

The proposed decomposition improves scalability by (1) separating platform selection from variant design and (2) optimizing each product separately. However, the size of the remaining platform selection subproblem constrains the degree of scalability for large problems.

Following the bulk of the product family literature, we have treated performance targets as exogenous and introduced a generic penalty function for deviation from those targets. If data are available, quantification of differentiation in terms of the market responses of a heterogeneous consumer population would more completely describe the product family trade-off (30-31); however, we do not pursue this here.

The complete mathematical formulation is available in Ref. 29 or from the authors. Details were not included here due to space limitations.

J. Mech. Des 130(7), 071101 (May 19, 2008) (8 pages) doi:10.1115/1.2918906 History: Received July 18, 2007; Revised October 19, 2007; Published May 19, 2008

A core challenge in product family optimization is to jointly determine (1) the optimal selection of components to be shared across product variants and (2) the optimal values for design variables that define those components. Each of these subtasks depends on the other; however, due to the combinatorial nature and high computational cost of the joint problem, prior methods have forgone optimality of the full problem by fixing the platform a priori, restricting the platform configuration to all-or-none component sharing, or optimizing the joint problem in multiple stages. In this paper, we address these restrictions by (1) introducing an extended metric to account for generalized commonality, (2) relaxing the metric to the continuous space to enable gradient-based optimization, and (3) proposing a decomposed single-stage method for optimizing the joint problem. The approach is demonstrated on a family of ten bathroom scales. Results indicate that generalized commonality dramatically improves the quality of optimal solutions, and the decomposed single-stage approach offers substantial improvement in scalability and tractability of the joint problem, providing a practical tool for optimizing families consisting of many variants.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

The double-counting property of Fellini’s metric; (left) case 1: η=2; (right) case 2: η=3

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Figure 2

Commonality level change for two basic cases

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Figure 3

First derivative of the approximating functions with respect to α

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Figure 4

ECI using three approximating functions; (left) Fellini's curve; (middle) Half Logistic; (right) Hubbert curve

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Figure 5

ATC framework for optimizing the joint product family problem

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Figure 6

Decomposition algorithm for optimizing the joint product family problem

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Figure 7

Design variables shown on the disassembled analog scale (29)

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Figure 8

Pareto curves for family of ten bathroom scales




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