Exhibit 2001
`Exhibit 2001
`
`

`
`CONCURRENT ENGINEERING: Research and Applications
`
`Designing Platforms for Customizable Products and Processes in Markets
`of Non-Uniform Demand
`
`Christopher B. Williams, Janet K. Allen, David W. Rosen and Farrokh Mistree*
`
`Systems Realization Laboratory, G. W. Woodruff School of Mechanical Engineering
`Georgia Institute of Technology, Atlanta, GA, USA
`
`Abstract: The foremost difficulty in making the transition to mass customization is how to offer product variety affordably. The answer to this
`quandary lies in the successful management of modularity and commonality in the development of products and their production processes.
`While several platform design techniques have emerged as a means to offer modularity and commonality, they are limited by an inability to
`handle multiple modes of offering variety for multiple design specifications. The Product Platform Constructal Theory Method (PPCTM) is a
`technique that enables a designer to develop platforms for customizable products while handling issues of multiple levels of commonality,
`multiple product specifications, and the inherent tradeoffs between platform extent and performance. The method is limited, however, by its
`inability to handle multiple design objectives and its reliance on the assumption that demand in the market is uniform for each product variant.
`The authors address these limitations in this study by infusing the utility-based compromise decision support problem and demand modeling
`techniques. The authors further augment the PPCTM by extending its use to a new domain: the design of process parameter platforms.
`The augmented approach is illustrated through a tutorial example: the design of a product and a process parameter platform for the realization
`of a line of customizable cantilever beams.
`
`Key Words: mass customization, product platforms, process parameter platforms, constructal theory.
`
`1. Offering Affordable Variety through
`Platform Design
`
`As manufacturing enterprises have struggled to meet
`demands for customized products through traditional
`economies of scale strategies, mass customization has
`emerged as a manufacturing paradigm for enterprises to
`efficiently and effectively satisfy customers’ require-
`ments for variety. Offering product variety affordably,
`the crux of mass customization, is the foremost difficulty
`that enterprises face in making the transition to this
`paradigm.
`It is not feasible or effective to cope with customers’
`demands for product variety through a simple increase
`in inventory, a reaction commonly found in mass
`production. Manufacturing enterprises are recognizing
`that product design presents the best control over
`offering such variety [1]. Similarly, as a result of the
`shift
`to mass customization,
`the complexity of
`the
`production process design problem is dramatically
`increased – enterprises are forced to manufacture more
`
`*Author to whom correspondence should be addressed.
`E-mail: farrokh.mistree@me.gatech.edu
`Figures 2 and 5 appear in color online: http://cer.sagepub.com
`
`complex products (multiple features, multiple variants)
`with reduced product
`life cycles, reduced time-to-
`market, and volatile demand [2]. As such, current
`manufacturing approaches must enable the quick
`launch of new product models, rapid adjustment of the
`manufacturing system capacity to market demands, and
`integration of new process technologies into existing
`systems [3].
`One manner in which enterprises can efficiently
`handle product and production capacity
`variety
`is through the development of platforms – a set
`of common components, modules, or parts
`from
`which a stream of variants can be created [4].
`The design of platforms enables the manufacturer
`to maintain
`the
`economic
`benefits
`of
`having
`common parts and processes (reduced system complex-
`ity,
`reduced development
`time and costs) while
`still being able to offer variety to customers [5]. In
`this
`study the authors present augmentations
`to
`an existing platform design approach (the Product
`Platform Constructal Theory Method, PPCTM)
`that
`enable a designer
`to systematically manage
`modularity and commonality in the development
`of both customizable products
`and production
`processes
`in the presence of non-uniform market
`demand.
`
`June 2007
`Volume 15 Number 2
`1063-293X/07/02 0201–16 $10.00/0
`DOI: 10.1177/1063293X07079328
`ß 2007 SAGE Publications
`
`
`
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`201
`
`

`
`202
`
`C. B. WILLIAMS ET AL.
`
`1.1 Offering Product Variety through
`Platform Development
`
`Consider the following illustrative example: a manu-
`facturing enterprise wishes to offer a line of customiz-
`able cantilever beams. The company wants to offer
`product variety in multiple design specifications; speci-
`fically, they wish to provide customers the ability to
`specify a beam of any desired length and of any loading
`condition (within certain ranges). The manufacturer and
`designer have decided to offer variety via three methods:
`(i) to change the beam cross-section, (ii) to change the
`beam material, and (iii) to cut the beams to customized
`lengths from standardized pieces. In order to efficiently
`offer product variety, the designer must determine the
`proper organization and extent of application of these
`different methods of offering variety (i.e., the architec-
`ture of a product family). This decision must be made
`in the presence of a market with non-uniform demand
`(i.e., the manufacturer must produce more of some
`product variants than others) and two conflicting design
`goals: to provide the lowest average cost across the
`volatile market, and to provide the lowest average
`maximum beam deflection (essentially a quality metric)
`across the family.
`In order to address the problem described above, a
`designer requires a platform design method that can
`consider non-uniform demand, multiple customizable
`specifications, multiple modes of managing product
`variety, and the tradeoff between commonality and
`product performance. At first glance, this illustrative
`example seems fairly simple; however, none of the
`various product platform design approaches that have
`been proposed in the literature are able to tackle all of
`the facets of this problem.
`Bottom-up platform approaches such as Kalpakjian’s
`group technology [6], Ericsson and Erixon’s modular
`functional deployment [7], and Siddique and Rosen’s
`product family reasoning system [8] provide a means for
`a designer to consolidate existing products to create
`product families. Such approaches are not appropriate
`for the illustrative example since they offer strategies for
`product rationalization after a number of products have
`been designed and manufactured.
`Top-down platform design methods are more relevant
`to this problem as they are characterized by an up-front
`decision to simultaneously develop a product family
`based on a common core and to reduce redesign cost.
`Examples include Nayak and coauthors’ variation-based
`platform design methodology [9], and Simpson and
`coauthors’ product platform concept
`exploration
`method [10,11]. Such techniques provide a designer the
`ability to develop a product platform based upon a scaled
`variable and a series of commonalized design parameters.
`Unfortunately, as
`seen in Simpson’s
`review of
`32
`‘optimization-based’
`product
`platform design
`
`that
`limitations
`there are several
`[12],
`approaches
`prevent a designer using existing top-down techniques
`from satisfactorily solving the seemingly simple canti-
`lever beam example posed at the beginning of this
`section.
`
`– Synthesis of multiple techniques for managing variety
`for multiple design specifications: A common limita-
`tion of existing top-down approaches is that variety is
`only considered in only one product specification.
`Typically, products are customized for multiple
`specifications (e.g., the torque and the power of a
`motor, the length and loading of a beam, etc.).
`Furthermore, products are customized by using
`multiple approaches for managing product variety
`(e.g., modular design, adjustable features, dimen-
`sional customization, etc.). Of those surveyed by
`Simpson, only two existing methods are capable of
`handling multiple methods for managing variety
`(namely modularity and product scaling): that of
`Fujita and Yoshida [13], and Hernandez and coau-
`thors [14].
`– Determination of platform extent: In the majority of
`top-down techniques, all features or components must
`be either common to all products or to none of them,
`typically resulting in dramatic tradeoffs between
`commonality and performance [10, 15–17]. In order
`to reduce the impact of commonality on performance,
`a designer should be able to specify different levels of
`commonality of the various features and components
`of the product family.
`– Determination of the number of product variants: In the
`beam example described above, it is not initially clear
`as to how many product variants should be offered
`given the complexity of the market demand. Two-
`thirds of the techniques surveyed by Simpson require
`specification of the platform a priori to optimization.
`Ideally, the determination of the number of product
`variants in a platform should be a decision variable
`that is influenced by both the demand present in the
`market and the resulting determination of platform
`extent.
`– Modeling manufacturing costs and market demand:
`Half of
`those techniques surveyed assume that
`maximizing product performance maximizes
`demand, maximizing commonality minimizes produc-
`tion costs, and that resolving the tradeoff between the
`two yields the most profitable product family. Since
`manufacturing costs and market demand greatly
`influence decisions relating to platform extent and
`the number of product variants in the family, these
`assumptions can lead to sub-optimal product families.
`Specifically, only half of
`the methods surveyed
`integrate manufacturing costs directly, and less than
`one-third of
`the methods incorporate market
`demand or sales into the problem. Of the techniques
`
`
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`
`Designing Platforms in Markets of Non-uniform Demand
`
`203
`
`(a)
`
`S
`
`
`
`yy
`
`
`
`xx
`
`P2
`
` ∆P2
`
`Pn
`
` ∆Pn
`
`P1
`
` ∆P1
`
`O
`
`(a)
`
`S
`
`P1
`
`P2
`
`Pn
`
` ∆Px,1
`
` ∆Px,2
`
`
`
`yy
`
` ∆Py
`
`x
`x
`
`O
`
`Figure 1. Product platform design as a problem of optimal access.
`
`surveyed that incorporate market modeling in the
`formulation of the method, several use traditional
`market-based analysis to determine the most effective
`location for a product family in a market space, but
`do not relate this information to the actual product
`architecture [18–20]. Those techniques that use a
`quantitative approach for incorporating customer
`demand into the formulation of the product archi-
`tecture [13,21–23], only model customer demand as
`uniform across the market. This is not adequate since
`markets of mass-customized products are character-
`ized as niche and heterogeneous.
`
`these limitations, designers using
`As a result of
`existing ‘optimization-based’ top-down approaches are
`unable to systematically design a satisfactory platform
`for the cantilever beam example problem, let alone the
`complex product platforms that are typical of those
`realized in industry.
`
`1.2 Context
`
`In response to these limitations, Hernandez proposes
`the PPCTM: a novel top-down approach for developing
`product platforms that facilitates the realization of a
`stream of customized product variants, and which
`accommodates the issues of multiple levels of common-
`ality and multiple customizable specifications [24]. The
`result of
`the use of
`the PPCTM is a hierarchical
`organization of several approaches of commonality, as
`well as the specification of their range of application
`across the product platform.
`While it has several advantages over current platform
`design techniques, the PPCTM does have its limitations.
`Specifically,
`it
`is unable to handle the markets of
`fragmented demand and heterogeneous niches that are
`inherent in customized products. In addition, a designer
`using the PPCTM is unable to model multiple design
`objectives. In this study, the authors present a series of
`augmentations to the PPCTM in order to address
`these limitations. Specifically, the authors integrate the
`utility-based compromise decision support problem and
`
`into the PPCTM.
`non-uniform demand strategies
`Furthermore, the authors abstract the principles of the
`PPCTM to apply it in a new domain: the creation of
`platforms for process parameters.
`The PPCTM and its underlying theoretical founda-
`tion are described in Section 2. The authors close
`Section 2 with a discussion of the tools and concepts
`used in their augmentation of
`the PPCTM. The
`augmented method is presented in Section 3. The ability
`to use the augmented PPCTM for the development of
`both a product platform (Section 4) and a process
`parameter platform (Section 5) is shown by revisiting the
`cantilever beam illustrative example problem. Section 6
`concludes the study.
`
`2. Augmenting the Product Platform
`Constructal Theory
`
`2.1 The Product Platform Constructal
`Theory Method
`
`The PPCTM was developed in order to provide
`designers a methodical approach for synthesizing multi-
`ple methods of offering product variety in the develop-
`ment of product platforms for customized products [14].
`As a result of the PPCTM’s theoretical foundations in
`both hierarchical systems theory [25] and constructal
`theory [26–28], Hernandez represents the design of
`platforms for customizable products as a problem of
`optimal access in a geometric space (a detailed descrip-
`tion of the theoretical constructs of the PPCTM can be
`found in [23,29]).
`An optimal access problem is characterized by the
`need to determine the optimal ‘bouquet of paths’ that
`link all points of an area, S, with a common destination,
`O (Figure 1(a)). Bejan proposes to solve access problems
`through constructal theory, which is centered on a
`hierarchic process of optimization. A shape that
`optimizes
`‘access’ at
`the most elementary volume
`occurs first, followed by an assembly of these innermost
`‘volumes’ into a second, larger-shapes, which in turn are
`
`
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`
`204
`
`C. B. WILLIAMS ET AL.
`
`Non-uniform demand modeling
`techniques
`
`
`
`00
`
`
`
`600600
`
`
`
`500500
`
`
`
`400400
`
`
`
`DemandDemand
`
`
`
`300300
`
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`200200
`
`
`
`100100
`
`
`
`00
`
`
`
`10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3010 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
`
`
`
`Pres sure (MPa)Pres sure (MPa)
`
`
`2828
`
`2525
`
`
`2222
`
`1919
`
`
`
`Volume (m^3)Volume (m^3)
`
`
`
`1616
`
`
`
`1313
`
`
`
`1010
`
`Step 1: Define the market
`space
`
`Step 2: Formulate an
`objective function
`
`Step 3: Identify modes for
`managing product variety
`
`Step 4: Identify mumber of
`stages and define a baseline
`decision for each stage
`
`Step 5: Formulate a
`multistage optimization
`problem
`
`Step 6: Solve the multistage
`optimization problem
`
`Step 1: Define the geometric space
`and the demand scenario
`
`Step 2: Define the objective
`functions
`
`Step 3: Identify the modes for
`managing customization
`
`Step 4: Identify the number of
`stages and define a multi-attribute
`utility function for each stage
`
`Step 5: Formulate a multi-stage
`utility-based compromise decision
`support problem
`
`Step 6: Solve the utility-based
`compromise decision support
`problem
`
`Process parameter
`platform design concepts
`
`u-cDSP
`
`Z=1−E[U(X)]
`n
`=Σ ki(di
`−−di
`
`+
`)
`
`i=1
`
`Figure 2. Augmenting the product platform constructal theory method.
`
`Augmentations
`
`PPCTM [14]
`
`Augmented PPCTM
`
`assembled into a third volume, and so on [26].
`Following the basic tenants of constructal theory, this
`optimization process should proceed in a specific time
`direction: from the optimization of the basic elements to
`the higher-order assemblies of
`the structure. This
`sequential process continues until all relevant volume
`is connected.
`In his abstraction of constructal theory and problems
`of optimal access to product platform development,
`Hernandez identifies the space of customization as the
`set of all feasible combinations of values of product
`specifications that a manufacturing enterprise is willing
`to satisfy (i.e., space S in Figure 1). Each product
`specification for which variety will be offered is
`represented as a dimension in this space (dimensions x
`and y in Figure 1). The magnitude of each dimension
`represents the amount of variety that will be offered.
`Each point in the space of customization represents a
`variant that the manufacturer wishes to offer.
`In the creation of a product family for customized
`products, a designer wishes to link all different feasible
`product variants (P1, P2, . . . Pn in Figure 1) within the
`space of customization from a baseline set of compo-
`nents (the product platform, O in Figure 1). The manner
`in which each product variant is linked is through modes
`for managing variety ( Px,1, Px,2, Py,1 . . . Px/y,n in
`Figure 1(b)). Modes for managing product variety are
`any generic approach in product design or its manu-
`facturing process for achieving a product customization
`(i.e., modular design, platform design and standardiza-
`tion, robust design, dimensional customization, adjus-
`table customization, etc.).
`
`The fundamental problem addressed in the applica-
`tion of the PPCTM to platform design is how to
`systematically organize and determine the extent of
`application of these modes for managing product variety
`across the space of customization. Considering that
`potential for rapid adaptation is higher in complex
`systems when they
`are organized hierarchically,
`Hernandez proposes
`to hierarchically organize the
`multiple of modes for managing product variety. With
`the modes organized effectively, one must determine
`their extent of application. Through the application of
`the tenets of constructal
`theory, each level of
`the
`hierarchy represents a sub-space of
`the space of
`customization; the dimensions of each space represent
`each mode’s range of application (Figure 1(b)).
`In order to determine these dimensions, a multi-stage
`decision is formulated wherein the ranges of application
`of each mode for managing product variety are the
`decision variables. The goal of each decision is to find an
`appropriate compromise among the objective functions
`(e.g., cost, profit, design performance, etc.) so that an
`appropriate balance between commonality and perfor-
`mance is achieved. The six steps of
`the original
`instantiation of the PPCTM are presented in Figure 2.
`
`2.2 Handling Non-uniform Demand
`
`Simpson states that the inability of product platform
`design techniques to model the manufacturing costs and
`the market demand for products in the family can lead
`to the development of sub-optimal product families [12].
`As such, both the market demand and the cost of
`
`
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`
`Designing Platforms in Markets of Non-uniform Demand
`
`205
`
`manufacturing have direct influence on the product
`architecture when
`designing with
`the PPCTM.
`Specifically,
`the objective function that drives
`the
`decision-making process is evaluated as an average
`over the total number of variants produced (as dictated
`by the demand). Furthermore, the cost of manufactur-
`ing the entire product family is evaluated by taking the
`product of the manufacturing cost of each variant and
`its respective demand.
`Unfortunately, the PPCTM example problems pre-
`sented thus far (pressure vessel [14], beverage merchan-
`diser [24], electric motors [23]) have been solved with the
`assumption of uniform demand across the space of
`customization. This approximation does not adequately
`capture the complexity of a traditional market space for
`a customized product. Without accurate knowledge of
`the market demand, a designer is unable to determine
`the appropriate extent of application of each mode for
`managing product variety across the platform.
`In order to alleviate this limitation,
`the authors
`propose two augmentations to the PPCTM. The first
`step of the PPCTM, ‘define the market space,’ will be
`expanded to include the development of a model of the
`demand scenario for the market. The resultant demand
`model (continuous or discrete) should be expressed in
`terms of the dimensions of the space of customization.
`This model will then be carried over into the second step
`of
`the PPCTM wherein the objective function is
`formulated as an average across this varying function
`of demand. An implementation of this augmentation is
`illustrated in Section 4.2.
`The second proposed augmentation is to eliminate
`the PPCTM’s explicit constraint
`that
`the range of
`application of each mode for managing variety must
`be a multiple of the range of application of the mode
`that supercedes it in the platform hierarchy (i.e.,
`in
`Figure 1(b), Px,2¼ n Px,1, where n is an integer).
`Originally intended to make the design space more
`tractable, this constraint prevents a designer from truly
`capturing effect of a non-uniform market demand on the
`architecture of the product family.
`
`2.3 Modeling Multiple Design Objectives
`
`compromise decision support problem (u-cDSP). The
`u-cDSP is a decision support construct that is based on
`utility theory [30] and permits mathematically rigorous
`modeling of designer preferences such that decisions
`can be guided by expected utility in the context of risk
`or uncertainty associated with the outcome of a
`decision [21]. While any appropriate decision formula-
`tion technique is serviceable,
`the authors prefer to
`formulate each decision stage with the u-cDSP since its
`use ‘provides structure and support for including human
`judgment in engineering decisions involving multiple
`attributes, while simultaneously providing an axiomatic
`basis for accurately reflecting the preferences of a
`designer with regard to feasible tradeoffs among these
`attributes under
`conditions of uncertainty’
`[31].
`Furthermore, the u-cDSP has proven useful in previous
`product platform techniques as it provides a decision
`construct
`in which a designer can model multiple,
`conflicting objectives.
`The formulation of each utility-based compromise
`decision support problem follows the four steps pre-
`sented in [21]. A utility function for each of the design
`objectives, u(A(X)), is formulated by qualitatively and
`quantitatively assessing the preferences of the designers.
`These individual utility functions are then combined into
`a multi-attribute utility function, U(X), as a weighted
`average of the individual utilities. Finally, goal and
`deviation functions are developed for each decision
`stage. The deviation function of the u-DSP, Z(X), is
`formulated to minimize deviation from the target
`expected utility (i.e., 1, the most preferable value),
`which is mathematically equivalent
`to maximizing
`expected utility. The goal and deviation functions
`formulated for each u-cDSP inherently consider the
`compromise of the tradeoffs between each objective
`function. With the goal of minimizing the deviation of
`the expected utility from the ideal value, parameters that
`provide the best values for this overall objective are
`chosen while maintaining consistency with the designer’s
`preferences.
`
`2.4 Offering Manufacturing Capacity Variety
`through Platform Design
`
`the PPCTM (Figure 2),
`In the second step of
`a designer defines an objective function that drives the
`mathematical optimization of the product platform. In
`its previous applications, the PPCTM has only shown
`effectiveness for a single design objective (typically, to
`minimize the average cost of the product family). This is
`a cause for concern since multiple, coupled, and
`conflicting goals become more prevalent as systems are
`more complex.
`In order to provide a designer the ability to handle
`multiple design objectives,
`the authors propose to
`augment
`the PPCTM by infusing the utility-based
`
`Aside from making the augmentations mentioned
`above, the authors strive to further expand the PPCTM
`by applying it to a new domain: the development of
`platforms for process parameters for the realization of
`customized products.
`As
`in the realm of product design, effectively
`managing modularity and commonality in production
`process development has been recognized as an impor-
`tant component of producing a large variety of products
`while maintaining low costs. Realizing that improving
`the flexibility and productivity of a manufacturing
`system is the ‘crucial challenge of modern industrial
`
`
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`
`C. B. WILLIAMS ET AL.
`
`[32], many production process design
`management’
`approaches have been developed to enable manu-
`facturing enterprises to affordably produce customized
`products.
`System-level philosophies such as cellular manufac-
`turing [33], flexible manufacturing systems [34], and
`reconfigurable manufacturing systems
`[3]
`focus on
`reducing setup times, reducing in-process inventory,
`improving part quality, shortening lead time, improving
`part quality through grouping similar parts, modules,
`and components into dedicated cells of manufacturing
`processes. These philosophies and their related imple-
`mentation technologies provide general strategic direc-
`tion for various aspects of the production process – from
`sequencing and synchronization of multiple machining
`and assembly operations, to line balancing and capacity
`planning.
`On a lower level of abstraction, Jiao and coauthors
`introduce the concept of process platforms – a set of
`similar production processes that share a common
`process structure – to facilitate coordination in product
`and process variety management [35]. The resultant
`design approach aids
`in the development of
`the
`production process plan and structure by taking
`advantage of the common production processes required
`to manufacture all of the product variants.
`It
`is the authors’ assertion that platform design
`techniques are applicable at an even lower level of
`abstraction in the problem of manufacturing process
`design. In the context of a single workstation of a
`production process,
`frequent changes in production
`capacity requirements force a manufacturing engineer
`to reconfigure its process parameters (e.g., turning speed,
`tool size, laser power, operating temperature, etc.) in
`order to maintain the best compromise between conflict-
`ing process objectives
`(e.g., minimization of cost,
`maximization of throughput, maximization of quality).
`Such reconfiguration requires
`re-evaluation of
`the
`process parameters, and entails a costly and lengthy
`setup of the workstation. In this context, the core concept
`of platform design – offering variety efficiently through
`commonality and/or modularity – can be applied to
`reduce workstation setup penalties. As such, the concept
`of a process parameter platform is introduced:
`
`A process parameter platform is defined as a set of
`common process parameters from which a stream of
`derivative process parameters can generate a customized
`machining process efficiently despite changes in required
`capacity.
`
`The crux of process parameter platform design is the
`commonalization of process parameters such that
`transitions between different workstation setups are
`handled efficiently and effectively. The application of
`the augmented PPCTM to this new domain is illustrated
`in Section 5.
`
`3. The Augmented Product Platform Constructal
`Theory Method
`
`The augmentation of the PPCTM, as described in the
`previous section, is presented graphically in Figure 2.
`The first step of the augmented PPCTM involves the
`space of customization through (i) the identification of
`the design specifications that will be varied according
`to the customer demands (the dimension of the space),
`(ii) the range of variety that will be offered for each
`specification (the bounds of the space), and (iii) the
`analysis and modeling of the demand of the market. The
`choice for best model for demand of a market is context
`based. Although not explicitly illustrated in this study,
`the reader should be assured that this methodology is
`robust
`to any non-uniform demand model
`that a
`designer may choose, as shown in [36].
`For the development of a process parameter platform,
`there is but one design specification in which a
`manufacturer wishes to offer variety: production capa-
`city. Thus the space of customization for process
`parameter platform design is a single dimension,
`bounded by the range of production capacity that the
`manufacturing enterprise wishes to offer.
`In the second step, objective functions are defined.
`In order to handle the tradeoff between platform extent
`and performance, the objective functions are evaluated
`as averages across the space of customization. Typical
`objective functions for product platform design include
`the minimization of cost, or the improvement of a
`product performance metric. For process platform
`design, objective functions can include minimization of
`cost, maximization of throughput, and maximization of
`part quality among others.
`The modes
`for managing variety (defined in
`Section 2.1) are identified in the third step. These
`modes for managing variety are the linking mechanism
`between the variants that compose the product family.
`Graphically,
`they represent a geometric ‘sub-space’
`of the entire space of customization; the size of each
`sub-space represents the extent of application of each
`mode. The determination of these modes is a strategic
`decision that involves decision-making in the context
`of both design and manufacturing.
`The modes are then hierarchically organized in Step 4.
`Modes that are capable of achieving the smallest
`variations in the varied design parameters are typically
`used at the lower levels of the hierarchy (i.e., before
`modes that can only achieve large variations in the
`design parameters). Economical and technological
`considerations place an important role in establishing
`the hierarchic use of the modes for managing variety.
`The determination of the range of application of each
`mode for managing variety is accomplished through the
`formulation and solution of a multi-stage utility-based
`compromise decision support problem (Steps 5 and 6).
`
`
`
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`Designing Platforms in Markets of Non-uniform Demand
`
`207
`
`nth space level
`
`beams in Section 4. The augmented PPCTM is then
`extended through its usage in designing a process
`parameter platform for the manufacture of a line of
`customizable cantilever beams in Section 5.
`
`2nd space level
`
`4. PPCTM Application: Product Platform Design
`
`Z3
`For each nth space
`determine
`common
`parameter, rn
`
`Z2
`
`Dr1, Dr2,…, Drn
`
` Dr2
`
`For each 2nd space
`determine
`common
`parameter, r2
`
`Z1
`
` Dr1
`
`1st space level
`For each 1st space
`determine common
`parameter, r1
`
`
`
`In this section, the authors illustrate the design of a
`product platform using the PPCTM. It should be noted
`that the example is kept fairly simple in order to focus
`the reader’s attention on the method itself. It
`is
`important to keep in mind that the example’s emphasis
`is on illustrating the method rather than the results
`per se. It is assumed that uncertainty and risk are absent
`from this problem. It is also noted that some values used
`in the example are estimates and do not change the
`fundamental results of this study. The model of the
`cantilever beam can easily be modified to suit specific
`situations; however, the authors’ focus is centered on the
`validation of the method itself.
`
`4.1 Example Problem: Customizable
`Cantilever Beams
`
`example posed in Section 1.1,
`Revisiting the
`the following scenario is considered: a manufacturer
`wishes to offer a line of customizable cantilever beams
`(Figure 4). The manufacturer wishes
`to provide
`customers the ability to specify a beam that ranges in
`length (L) from 0.5 to 10 m, and is capable of supporting
`a single end-load (P) from 50 to 500 N.
`The manufacturer has decided to offer variety via
`three methods, (i) by changing the beam cross-section,
`(ii) by changing the beam material, and (iii) by cutting
`the beams
`to customized lengths
`from standard
`pieces. The manufacturer has two conflicting goals: to
`provide the lowest average cost across the volatile
`market and to provide the lowest average maximum
`beam deflection across the family (i.e., to improve
`product quality).
`
`4.2 Step 1: Define the Geometric Space and
`Demand Scenario
`
`For the design of the family of customizable beams,
`there are two independent design specifications that
`characterize the desired product customization – the
`beam length and the applied load. The resulting two-
`dimensional continuous
`space of customization is
`illustrated in Figure 5(a).
`For this problem, the manufacturer has observed that
`there is significantly more demand for the medium-
`ranged cantilever beams. More specifically, the manu-
`facturer has det