An Extension of the Commonality Index for Product Family Optimization

2007 ◽  
Author(s):  
Aida Khajavirad ◽  
Jeremy J. Michalek
Keyword(s):  
Product Family ◽  
Companion Paper ◽  
Manufacturing Cost ◽  
Discrete Problem ◽  
Product Lines ◽  
Product Families ◽  
Continuous Space ◽  
Product Family Optimization ◽  
Gradient Based ◽  
Commonality Index

One critical aim of product family design is to offer distinct variants that attract a variety of market segments while maximizing the number of common parts to reduce manufacturing cost. Several indices have been developed for measuring the degree of commonality in existing product lines to compare product families or assess improvement of a redesign. In the product family optimization literature, commonality metrics are used to define the multi-objective tradeoff between commonality and individual variant performance. These metrics for optimization differ from indices in the first group: While the optimization metrics provide desirable computational properties, they generally lack the desirable properties of indices intended to act as appropriate proxies for the benefits of commonality, such as reduced tooling and supply chain costs. In this paper, we propose a method for computing the commonality index introduced by Martin and Ishii using the available input data for any product family without predefined configuration. The proposed method for computing the commonality index, which was originally defined for binary formulations (common / not common), is relaxed to the continuous space in order to solve the discrete problem with a series of continuous relaxations, and the effect of relaxation on the metric behavior is investigated. Several relaxation formulations are examined, and a new function with desirable properties is introduced and compared with prior formulations. The new properties of the proposed metric enable development of an efficient and robust single-stage gradient-based optimization of the joint product family platform selection and design problem, which is examined in a companion paper.

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

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
Aida Khajavirad ◽  
Jeremy J. Michalek
Keyword(s):  
A Priori ◽  
Computational Cost ◽  
Product Family ◽  
Substantial Improvement ◽  
Single Stage ◽  
Continuous Space ◽  
Design Variables ◽  
Joint Problem ◽  
Product Family Optimization ◽  
Gradient Based

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.

A Single-Stage Gradient-Based Approach for Solving the Joint Product Family Platform Selection and Design Problem Using Decomposition

2007 ◽  
Author(s):  
Aida Khajavirad ◽  
Jeremy J. Michalek
Keyword(s):  
Design Problem ◽  
Optimization Problem ◽  
Computational Cost ◽  
Product Family ◽  
Single Stage ◽  
System Level ◽  
Continuous Space ◽  
Joint Product ◽  
Product Family Optimization ◽  
Gradient Based

A core challenge in product family optimization is to develop a single-stage approach that can optimally select the set of variables to be shared in the platform(s) while simultaneously designing the platform(s) and variants within an algorithm that is efficient and scalable. However, solving the joint product family platform selection and design problem involves significant complexity and computational cost, so most prior methods have narrowed the scope by treating the platform as fixed or have relied on stochastic algorithms or heuristic two-stage approaches that may sacrifice optimality. In this paper, we propose a single-stage approach for optimizing the joint problem using gradient-based methods. The combinatorial platform-selection variables are relaxed to the continuous space by applying the commonality index and consistency relaxation function introduced in a companion paper. In order to improve scalability properties, we exploit the structure of the product family problem and decompose the joint product family optimization problem into a two-level optimization problem using analytical target cascading so that the system-level problem determines the optimal platform configuration while each subsystem optimizes a single product in the family. Finally, we demonstrate the approach through optimization of a family of ten bathroom scales; Results indicate encouraging success with scalability and computational expense.

A Product Dissection-Based Methodology to Benchmark Product Family Design Alternatives

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Henri J. Thevenot ◽  
Timothy W. Simpson
Keyword(s):  
Product Family ◽  
Cost Savings ◽  
Production Costs ◽  
Manufacturing Cost ◽  
Successful Implementation ◽  
Product Family Design ◽  
Potential Cost ◽  
Product Families ◽  
Product Platforms ◽  
Design Alternatives

Today’s companies are pressured to develop platform-based product families to increase variety, while keeping production costs low. Determining why a platform works, and alternatively why it does not, is an important step in the successful implementation of product families and product platforms in any industry. Internal and competitive benchmarking is essential to obtain knowledge of how successful product families are implemented, thus avoiding potential pitfalls of a poor product platform design strategy. While the two fields of product family design and benchmarking have been growing rapidly lately, we have found few tools that combine the two for product family benchmarking. To address this emerging need, we introduce the product family benchmarking method (PFbenchmark) to assess product family design alternatives (PFDAs) based on commonality/variety tradeoff and cost analysis. The proposed method is based on product family dissection, and utilizes the Comprehensive Metric for Commonality developed in previous work to assess the level of commonality and variety in each PFDA, as well as the corresponding manufacturing cost. The method compares not only (1) existing PFDAs but also (2) the potential cost savings and commonality/variety improvement after redesign using two plots—the commonality/variety plot and the cost plot—enabling more effective comparisons across PFDAs. An example of benchmarking of two families of valves is presented to demonstrate the proposed method.

A Methodology to Support Product Family Redesign Using Genetic Algorithm and Commonality Indices

2005 ◽  
Author(s):  
Henri J. Thevenot ◽  
Jyotirmaya Nanda ◽  
Timothy W. Simpson
Keyword(s):  
Genetic Algorithm ◽  
Product Family ◽  
Product Line ◽  
Manufacturing Companies ◽  
Component Level ◽  
Product Families ◽  
Overall Design ◽  
Family Level ◽  
Systematic Methodology ◽  
Commonality Index

Many of today’s manufacturing companies are using platform-based product development to realize families of products with sufficient variety to meet customers’ demands while keeping costs relatively low. The challenge when designing or redesigning a product family is in resolving the tradeoff between product commonality and distinctiveness. Several methodologies have been proposed to redesign existing product families; however, a problem with most of these methods is that they require a considerable amount of information that is not often readily available, and hence their use has been limited. In this research, we propose a methodology to help designers during product family redesign. This methodology is based on the use of a genetic algorithm and commonality indices - metrics to assess the level of commonality within a product family. Unlike most other research in which the redesign of a product family is the result of many human computations, the proposed methodology reduces human intervention and improves accuracy, repeatability, and robustness of the results. Moreover, it is based on data that is relatively easy to acquire. As an example, a family of computer mice is analyzed using the Product Line Commonality Index. Recommendations are given at the product family level (assessment of the overall design of the product family), and at the component level (which components to redesign and how to redesign them). The methodology provides a systematic methodology for product family redesign.

A Method for Benchmarking Product Family Design Alternatives

2007 ◽  
Author(s):  
Henri J. Thevenot ◽  
Timothy W. Simpson
Keyword(s):  
Product Family ◽  
Cost Savings ◽  
Production Costs ◽  
Manufacturing Cost ◽  
Successful Implementation ◽  
Product Family Design ◽  
Potential Cost ◽  
Product Families ◽  
Product Platforms ◽  
Design Alternatives

Today’s companies are pressured to develop platform-based product families to increase variety while keeping production costs low. Determining why a platform works, and alternatively why it does not, is an important step in the successful implementation of product families and product platforms in any industry. Internal and competitive benchmarking is essential to obtain knowledge of how successful product families are implemented, thus avoiding potential pitfalls of a poor product platform design strategy. While the two fields of product family design and benchmarking have been growing rapidly lately, we have found few tools that combine the two for product family benchmarking. To address this emerging need, we introduce the Product Family Benchmarking Method (PFBenchmark) to assess product family design alternatives (PFDAs) based on commonality/variety tradeoff and cost analysis. The proposed method utilizes the Comprehensive Metric for Commonality developed in previous work to assess the level of commonality and variety in each PFDA, as well as the corresponding manufacturing cost. The method compares not only (1) existing PFDAs but also (2) the potential cost savings and commonality/variety improvement after redesign using two plots — the Commonality/Variety Plot and the Cost Plot — enabling more effective comparisons across PFDAs. An example of benchmarking two families of valves is presented to demonstrate the proposed method.

An Approach to Product Family Positioning Based on Shared Surplus

2005 ◽  
Author(s):  
Yiyang Zhang ◽  
Jianxin Jiao
Keyword(s):  
Product Family ◽  
Target Market ◽  
Product Lines ◽  
Market Segments ◽  
Product Families ◽  
Notebook Computer ◽  
Customer Preferences ◽  
Engineering Costs

To compete in the marketplace, manufacturers have been seeking for expansion of their product lines by providing product families. Product family positioning aims at planning the appropriate products to be provided to the target market segments. Due to the involved complexity such as diverse customer preferences, engineering costs, competition among similar products, etc, positioning the product family is very difficult. This paper proposes a shared surplus model for product family positioning. A comprehensive methodology for product family positioning is developed. An application of the proposed methodology for the notebook computer family positioning is reported.

Multidisciplinary Analysis and Product Family Optimization of Front-Loading Washing Machines

2016 ◽  
Author(s):  
Sangjin Jung ◽  
Timothy W. Simpson
Keyword(s):  
Product Family ◽  
The United States ◽  
Strength Analysis ◽  
Product Families ◽  
Washing Machines ◽  
Multi Objective Genetic Algorithm ◽  
Multidisciplinary Analysis ◽  
Surface Models ◽  
Product Family Optimization ◽  
Deviation Functions

In the past decade, the market share of front-loading washing machines has seen explosive growth in the United States. As a result, many companies are now offering families of front-loading washing machines with a variety of features and options. Understanding the tradeoffs within these product families is challenging as existing research has focused primarily on a single disciplinary analysis (e.g., dynamic analysis, strength analysis); few models exist for cleanliness, reliability, energy efficiency, etc. In this paper, we introduce a new integrated multidisciplinary analysis using simulations, mathematical models, and response surface models based on the ratings of product attributes. In order to determine feasible design solutions for a front-loading washer family, we formulate a product family design problem using deviation functions and a product family penalty function. A multi-objective genetic algorithm is applied to solve the proposed formulation, and the results indicate that designers can successfully determine solutions for the best performance, most common, and compromise families of front-loading washers.

Robust Product Family Consolidation and Selection Using the Hypothetical Equivalents and Inequivalents Method

2007 ◽  
Author(s):  
Bryan R. Dolan ◽  
Kemper E. Lewis
Keyword(s):  
Utility Theory ◽  
Product Family ◽  
Value Functions ◽  
Product Lines ◽  
Product Families ◽  
Robust Solution ◽  
Advantages And Disadvantages ◽  
Multi Attribute Utility Theory ◽  
Similar Materials ◽  
Effective Product

The design and development of effective product lines is a challenge in modern industry. Companies must balance diverse product families that satisfy wide ranging customer demands with practical business needs such as combining manufacturing processes and using similar materials, for example. In this paper, the issue of consolidating an existing product family is addressed. Specifically, the Hypothetical Equivalents and Inequivalents Method (HEIM) is utilized in order to select an optimal product family configuration. In previous uses, HEIM has been shown to assist a decision maker in selecting one concept from a set when concept attributes conflict with each other. In this extension of HEIM, the optimization problem’s constraints are formulated using two different value functions, and common solutions are identified in order to select an optimal family of staplers. The result is then compared with the result found using a multi-attribute utility theory (MAUT) based approach. While each method has its advantages and disadvantages, and MAUT provides a necessary first step for product family consolidation and selection, a robust solution is achieved through HEIM.

A Comparison of Commonality Indices for Product Family Design

2004 ◽  
Author(s):  
Henri J. Thevenot ◽  
Timothy W. Simpson
Keyword(s):  
Product Family ◽  
Individual Performance ◽  
The Other ◽  
Product Family Design ◽  
Global Marketplace ◽  
Manufacturing Costs ◽  
Product Families ◽  
The Relationship ◽  
Compare And Contrast ◽  
Commonality Index

Today’s highly competitive and global marketplace is redefining the way companies do business: many companies are being faced with the challenge of providing as much variety as possible for the market with as little variety as possible between products. In order to achieve this, product families have been developed, allowing the realization of a sufficient variety of products to meet the customers’ demands while keeping costs relatively low. The challenge when designing a family of products is in resolving the tradeoff between product commonality and distinctiveness: if commonality is too high, products lack distinctiveness, and their individual performance is not optimized; on the other hand, if commonality is too low, manufacturing costs will increase dramatically. Toward this end, several commonality indices have been proposed to assess the amount of commonality within a product family. In this paper, we compare and contrast six of the commonality indices from the literature based on their ease of data collection, repeatability and consistency. Eight families of products are dissected and analyzed, and the commonality of each product family is computed using each commonality index. The results are then analyzed and compared, and recommendations are given on their usefulness for product family design. This study lays a foundation for understanding the relationship between different platform leveraging strategies and the resulting degree of commonality within a product family.

Stable and Supported Semantics in Continuous Vector Spaces

2020 ◽  
Author(s):  
Yaniv Aspis ◽  
Krysia Broda ◽  
Alessandra Russo ◽  
Jorge Lobo
Keyword(s):  
Logic Program ◽  
Matrix Multiplication ◽  
Vector Spaces ◽  
Continuous Space ◽  
Continuous Vector ◽  
Novel Approach ◽  
Gradient Based ◽  
Normal Logic ◽  
Parameter Values ◽  
Normal Logic Program

We introduce a novel approach for the computation of stable and supported models of normal logic programs in continuous vector spaces by a gradient-based search method. Specifically, the application of the immediate consequence operator of a program reduct can be computed in a vector space. To do this, Herbrand interpretations of a propositional program are embedded as 0-1 vectors in $\mathbb{R}^N$ and program reducts are represented as matrices in $\mathbb{R}^{N \times N}$. Using these representations we prove that the underlying semantics of a normal logic program is captured through matrix multiplication and a differentiable operation. As supported and stable models of a normal logic program can now be seen as fixed points in a continuous space, non-monotonic deduction can be performed using an optimisation process such as Newton's method. We report the results of several experiments using synthetically generated programs that demonstrate the feasibility of the approach and highlight how different parameter values can affect the behaviour of the system.

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