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Multicriteria Optimization inProduct Platform Design

Sigurd A. Nelson IIMatthew Parkinson

Panos Y. Papalambros

Optimal DesignLaboratory

University of Michiganhttp://ode.engin.umich.edu

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Product Platforms: What Are They?

A set of common components from which astream of derivative products can be created

• Honda’s “World Car”• A single platform that is used for “customized” Accords for the U.S.,

Europe, and Asia

• Black & Decker• Cordless tool product line has many parts and assembly processes

in common

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The Problem:

• Without the Product PlatformDesigns are optimized for individual performance

• In a Product PlatformSome performance is sacrificed to allow aspects of the design tobe common across products

In other words

We have competing objectives:

Commonality and Performance

What are the trade-offs?

craMethodology

• Pick a product line• Select candidate parts or design

variables that can be sharedacross the line

• Create performance metrics(quantifying the design space)

• Optimize individual designs• Add “commonality” constraint• Perform multicriteria optimization

• determine the performance “cost”of commonality

• Identify the “amount” ofcooperation desired

Nail Gun Product Line

Goal: Use same spring-loadingmechanism during assembly

craQuantify the Desired Performanceof Models within the Product Line

Professional

• Industrial Strength

maximize nail length

Weekend Warrior

• Inexpensive

minimize energy(cost of spring,loading mechanism)

• Performance-based objective functions• speed, weight, strength, etc• cost• time to market• market demand

craOptimize the Designs Individually

Professional

Minimize: - nail length,Subject to:

energy required ≤ energy availabledistance driven ≥ minimum depthmax. shear stress ≤ allowable stresssolid height spring ≥ space for spring

Design Variables:starting height of hammernail lengthpreload length

Resulting Optimal Design:

nail length = -2.566 cm

Weekend Warrior

Minimize: spring energy,Subject to:

nail length ≥ minimum nail sizedistance driven ≥ minimum depthmax. shear stress ≤ allowable stresssolid height spring ≥ space for spring

Design Variables:starting height of hammernail lengthpreload length

Resulting Optimal Design:

energy = 7.66 kJ

Af Bf

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-0.027 -0.025 -0.023 -0.021 -0.019

Nail Length - Professional Model

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- Wee

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The Individual Optima

• The solution pair can be plotted on a two-dimensionalplot.

• This design is the Null Platform

),( οοBA ff

),( οοBA ff

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Minimize joint problem

starting height A = starting height B

Pose Multicriteria Problem andAdd the Commonality Constraint

ProfessionalSubject to:

energy required ≤ energy availabledistance driven ≥ minimum depthmax. shear stress ≤ allowable stresssolid height spring ≥ space for spring

Design Variables:starting height of hammernail lengthpreload length

Weekend WarriorSubject to:

nail length ≥ minimum nail sizedistance driven ≥ minimum depthmax. shear stress ≤ allowable stresssolid height spring ≥ space for spring

Design Variables:starting height of hammernail lengthpreload length

),( Af Bf

cra Re-Optimize to Determine the Effectof the Additional ConstraintProfessional

• Minimize:

Weekend Warrior

• Minimize:

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-0.027 -0.025 -0.023 -0.021 -0.019

Nail Length - Professional Model

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),( BfAf ),( Af Bf

Null Platform

craInitial Approximation of Sacrifices

Required by Sharing

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-0.027 -0.025 -0.023 -0.021 -0.019

Nail Length - Professional Model

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Utopia Point

Increase in Spring Energy

Decrease in Nail Length

All optimal design pairs (the Pareto set)reside within this space

Null Platform

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-0.027 -0.025 -0.023 -0.021 -0.019

Nail Length - Professional Model

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Calculate the Pareto Set andSelect Desired Performance

Null Platform

Utopia Point

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Summary and Conclusions

• Multicriteria optimization can be used as a Product PlatformDesign tool

• Comparing the Null Platform and Utopia Point designs gives anestimation of the “cost” of using a platform

• If this cost is acceptable, a more detailed approximation of thetrade-offs (the Pareto set) can be obtained

• This can then be used as a resource when making designdecisions