Product design in a concurrent engineering environment: an optimization approach

17
This article was downloaded by: [McGill University Library] On: 20 November 2014, At: 11:09 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK International Journal of Production Research Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tprs20 Product design in a concurrent engineering environment: an optimization approach SHAD DOWLATSHAHI Published online: 07 May 2007. To cite this article: SHAD DOWLATSHAHI (1992) Product design in a concurrent engineering environment: an optimization approach, International Journal of Production Research, 30:8, 1803-1818, DOI: 10.1080/00207549208948123 To link to this article: http://dx.doi.org/10.1080/00207549208948123 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

Transcript of Product design in a concurrent engineering environment: an optimization approach

Page 1: Product design in a concurrent engineering environment: an optimization approach

This article was downloaded by: [McGill University Library]On: 20 November 2014, At: 11:09Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

International Journal of Production ResearchPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tprs20

Product design in a concurrent engineeringenvironment: an optimization approachSHAD DOWLATSHAHIPublished online: 07 May 2007.

To cite this article: SHAD DOWLATSHAHI (1992) Product design in a concurrent engineering environment: an optimizationapproach, International Journal of Production Research, 30:8, 1803-1818, DOI: 10.1080/00207549208948123

To link to this article: http://dx.doi.org/10.1080/00207549208948123

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Page 2: Product design in a concurrent engineering environment: an optimization approach

INT. J. PROD. RES., 1992, VOL. 30, No.8, 1803-1818

Product design in a concurrent engineering environment:an optimization approach

SHAD DOWLATSHAHIt

In this paper an optimization approach to the design of products in a concurrentengineering environment is explored. A five-step algorithm containing attribute­based utility values is utilized which allows for the incorporation of concurrentengineeringdesignattributes in the objectivefunction. Two integer programmingmodelsare presented.Modell considersmodule/part interactions;however, it doesnot consider the interactions among various part options making up a product.Model 2 considers both interactions and also results in groups of part options thatcan be designed and manufactured together. In each step of the optimizationprocess, the design of a pad assembly of a braking system is considered andexplained.

1. IntroductionThe optimization of product design in a concurrent engineering environment poses

the greatest challenge to a designer. The natural focal point of concurrent engineering ison product design. A decision concerning product design tends to have a number ofsignificant manufacturing and non-manufacturing impacts upon the life cycle of theproduct. The following examples signify such an importance.

• A study revealed that the product design is responsible for only 5% of aproduction cost of 2000 components (Corbett 1986).

• According to General Motors executives, 70% of the cost of manufacturing trucktransmissions is determined in the design stage (Whitney 1988).

• Ford Motor Company has estimated that among the four manufacturingelements of design, material, labour, and overhead, 70% of all production savingsstem from improvements in design (Cohodas 1988).

• A study revealed that the product design is responsible for only 5% of aproduct's cost; it can, however, determine 75% or more of all manufacturing costsand 80% of a product's quality performance (Huthwaite 1988).

• Yet another study shows that 70% of the life cycle cost of a product is determinedat the design stage. The life cycle cost here refers to cost of materials,manufacture, use, repair, and disposal of a product (Nevins and Whitney 1989).

Concurrent engineering, as it is defined and used in this paper, calls for considerationand inclusion of such design attributes as manufacturability, reliability, maintaina­bility, schedulability, marketability, and the like in the early phases of the designprocess. Dowlatshahi (1992) provides a discussion of concurrent engineering and thevarious approaches to its successful implementation.

Received July 1991.t Address correspondence to: 150 Center Street, Platteville, Wisconsin 53818, USA.

0020-7543/92 $3000© 1992 Taylor & Francis Ltd.

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1.1. Obstacles in the optimization of product design(l) Compiling a set of meaningful objective function and constraints is not always

feasible or practical. The heterogeneous nature of constraints and the conflicting natureof objectives make the formulation and optimization of complex designs by theconventional optimization methods difficult. In addition to formulation of constraintspecifications, there is the problem offunctional uncertainty ofthe constraint contours.

(2) If one is able to construct the objective function and constraints in acomprehensive nature, one has to encounter the problem of measuring and quantifyingthe qualitative nature of concurrent engineering design attributes and incorporatingthem into an optimization model. This problem is further complicated by the domaindependent nature of the design process. Unlike the physical laws of measurement,measuring design attributes such as quality, performance, aesthetics, and the like isalways subject to question and interpretation. Unless and until well-defined principlesof a scientific design theory have been developed, tested, validated, and documented,these problems continue to hamper the efforts of designers to optimize the designprocess.

1.2. Elements and assumption of product design optimizationIn order to provide a general framework in which an optimization of a product

design in a concurrent engineering can take place, the following elements andassumptions are introduced:

(I) The design optimization, in this paper, refers to the design of mechanicalproducts with assemblable parts.

(2) Designing products in a concurrent engineering context has been viewed in twodistinct ways. The first approach attempts to improve existing products by incorporat­ing concurrent engineering design attributes in the product. This approach cansignificantly improve the business, manufacturing, and support aspects of the productlifecycle.There is a growing need for research in this area of product design. The secondapproach to product design in concurrent engineering is the creation of novel or exoticproducts. Cross (1989) states that even though the emphasis of much research in.product design is on the creation of novel products, making variations andimprovements in the existing designs is an important feature of the innovative designprocess. He further elaborates that clients and customers usually seek improvementsrather than novelties in design. He also suggests that a small variation in the number ofdesign parts generates a large number of design options.

The first approach to designing products in a concurrent engineering environmenthas been selected as the theme of this paper. Generating improvements andmodifications to existing products is especially important in the design of commercialproducts with limited resources.

(3) Improper processing of quantifying the intangible and qualitative designcriteria poses a serious threat to the integrity and efficiency of the overall designprocess. There has been a tendency on the part of some designers to arbitrarily selectone design attribute over another based on past experience. The attribute-based utilityvalues presented in this paper attempt to quantify the design attributes with a highdegree of accuracy and efficiency so that they can be incorporated in an objectivefunction. It is generally agreed that an attempt to quantify or prioritize intangiblesprovides an insight concerning the design process and makes the designer more awareof potential problems. The approach of 'quantify whenever possible' has been

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Product design in concurrent engineering 1805

supported by French (1985) as one of the two essential precepts of the mechanicalsystem design.

This element of the optimization process provides designers with the ability tothoroughly analyse and evaluate design options. For further evaluation of some of theadvancements in measurement problems in optimization of concurrent engineering,one may wish to review the white papers produced by a working group of The Institutefor Defense Analyses ULCE DSS Working Group (1988).

The essence of such an approach prevents designers from disregarding someimportant attributes which otherwise might have been omitted.

(4) The design optimization model is developed based on the followingjustifications and assumptions:

(a) design optimization is iterative and interactive in nature;(b) there have to be trade-offs among various design attributes;(c) objective function consists of a set of concurrent engineering design attributes;(d) for ease of application and optimization to the product design, the multiple

objectives pursued by concurrent engineering is combined in a single objectivefunction.

2. Optimization of product design in a concurrent engineering environmentAn algorithm containing five steps for the optimization of product design in a

concurrent engineering environment is proposed. The design of a braking system padassembly is introduced in each step as an example. Table I outlines the steps involved.

2.2. Step 1: Decompose the systemTo increase the efficiency and practicality ofthe design process, a modular product

design is utilized. A module, for defintion purposes, refers to a subsystem, subassembly,part options space, or any other classification depending on the nature and complexityof the product design. The modules need to be cohesive, bounded, or be a self-containedgroup of activities. The decomposition process needs to be hierarchical in natureallowing further breakdown of the modules. Neville (1989) suggests that the 'naturalseparability or modularity' of the design domain should be used as the basis forpartitioning the system into modules. He further elaborates that such a separationrequires that there are clusters of decisions with richer interactions within modules thanbetween modules. Figure 1 represents a decomposition scheme.

The hierarchy in Figure I can be adjusted based upon given system requirements.Simple products can be directly decomposed into their respective part options space.

A hierarchical structure of a braking system is presented in Fig. 2. A typical padassembly consists of linings (pads), shoes (back plates), and special features. The pads

No. Step

I Decompose the system2 Establish feasible parts space3 Reduce the number of part options4 Calculateattribute based utility values5 Model and optimize product design

Table I. Steps in optimization of product design.

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1806 S. Dowiatshahi

....

I------~-------SSl SS2 ..

~ 1_-....-----sall sa12 . . . sa21 sa22 ...

M-~~~plll p1l2... p121 pI22... p2ll p212... p221 p222 ...

Figure 1. Hierarchy of a system decomposition.

Braking system

Figure 2. Hierarchical structure of a braking system.

serve as the friction material and are connected to shoes. This connection can be in theform of riveting, bonding, moulding, or clamping. The lining can also be grooved by itsfull thickness to a shoe.

2.2. Step 2: Establish feasible parts spaceThe end result of the innovative descriptive design process is the optimal design

alternative. In the case of a large or complex product, the optimal design alternativeconsists of several modules. For example, a pad assembly of a braking system is amodule subject to an optimization process.

Once the optimal design alternative is selected, all of its feasible part options shouldbe specified. Note that each part, which becomes an integral part of the final product,consists of several part options. In this paper, whenever applicable, the terms part

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Product design in concurrent engineering

.flit. ,

Figure 3. Six shoe design variations for light to medium-duty trucks.

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options and design variations are used interchangeably. The process of establishingpart options, by itself, is an innovative process and should permit the designer toinclude any feasible part that conceivably meets the specifications of the optimal designalternative. The process requires skill on the part ofthe designer to develop the feasibleparts space.

Figure 3 represents various disc brake shoes (feasible parts space) appropriate forthe design of a braking system pad assembly for light to medium-duty trucks. Fourselection criteria in the design of a pad assembly are considered:

(I) Lining thickness. The thickness oflining has a direct effect on the performanceof the pad assembly and, therefore, on the overall braking effectiveness.

(2) Braking area (size).The size of the braking area also has a determining impacton the overall performance of the caliper assembly. The lining thickness and thesize of the braking area are interrelated and interchangeable. An inadequatesize brake is a major cause of inadequate disc brake performance.

(3) Friction material. The friction material used in the lining not only determinesthe life of the pad assembly, but also affects brake performance, reliability, andmaintainability. The material selected should be wear and temperatureresistant.

(4) Special features. These are features that enhance the performance of the padassembly by providing additional applications that are not ordinarily consi­dered as part of a pad assembly design.

To translate these criteria into part options (design variations), a set of feasible partoptions for the pad assembly is presented in Table 2.

Table 2 provides the designer with 1728 (6 x 6 x 8 x 6) feasible combinations ofdesigning a pad assembly.

2.3. Step 3: Reduce the number of part optionsThe reduction in the number of feasible part options is accomplished by excluding

any inflexible, impractical, or undesirable part option by a screening process. Thehigher the depth of the screening process, the lower the number of part optionsremaining in the feasible parts space.

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Designspecifications

Lining thicknessin inches

Braking size perinch' per 2200lbs

0-030

63-50

0·125

62·00

0·062

69·75

Design variation

0'150

77-5

0·175

73·63

0-118

65·87

00o00

Friction material

Special features

Semimetallicand resinbondedmetallic

In-wheelparking

Carbon-carbon~

NAO· binder NAO· Ceramic NAO· binder Sintered Sintered \::lresin with binder material resin with cooper iron and cfibreglass resin with with organic wollastonite and graphite ~

!?:mineral resin graphite to

wool :>-

'"=.Worn-lining Automatic Anti-squeal Cushion Cushion

indicator lining shim between betweenadjustment shoe and friction

piston materialand shoe

• Non-asbestos organic.

Table 2. Table of feasible part options: pad assembly.

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Product design in concurrent engineering 1809

In order to assure the practicality and efficiency of the optimization model, careshould be taken so that the number of part options is reduced to a minimum. It is alsoessential that at least two part options remain per part category so that different formsof designing a product can be contemplated. The variations or options in a part do notnecessarily have to relate to the size or shape of a part. The variation can be expressed interms of surface roughness, stress levels, geometry, structure, dynamics, materials,space requirements or features. It can also be expressed in terms of manufacturingcriteria such as kinetics, forces, or energy. The use of these variations are dependentupon the nature and complexity of a given product design.

The infeasible, impractical, and undesirable part options of pad assembly may beeliminated based on the following criteria:

• friction level• friction stability• lining strength, stiffness, and toughness• lining wear life• fade resistance• fade recovery• contamination sensitivity• lining mechanical properties

Table 3 presents the set of reduced part options at the completion of the screeningprocess. After completion of Step 3, the number of part options has been reduced to 72(3 x 2 x 4 x 3). This is a considerably lower number than that of Step 2.

2.4. Step 4: Calculate attribute-based utility valuesThe purpose of this step is to incorporate concurrent engineering design attributes

in the objective function of the optimization model in Step 5. This objective isaccomplished by comparing and evaluating all pairwise combinations of module/partoptions until the utility values of all the part options belonging to each module havebeen calculated.

.Designspecification Design variation

Lining thickness 0·125 0'175 0'118in inches

Braking size per 69·75 73-63inch? per 2200lb

Friction material Sernimetallic NAO' with NAO' binder Sintered ironand resin fibreglass resin with and graphitebonded metallic wollastonite

Special features In-wheel parking Worn-lining Automaticindicator lining

adjustment

• Non-asbestos organic.

Table 3. Table or reduced part options: pad assembly.

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1810 S. Dowlatshahi

To determine attribute based utility values, the attribute rating model of Starkey(1988) is modified and expanded. The steps for determining the utility values are asfollows.

2.4.1. Step 4.1: Choose n design attributesChoose n design attributes that are most relevant to a particular combination of

module/part options. This allows for flexibilitysuch that only the most relevant designattributes are taken into consideration. The selection of design attributes may varyfrom one part to another. The parts of an automobile engine are more affected bymanufacturability, reliability, and maintainability attributes than by appearance andergonomic attributes. Then, assign weights to the n design attributes. The total weightmust equal to I.

2.4.2. Step 4.2: Develop a table of pairwise comparison/evaluationsDevelop a table to facilitate the pairwise comparisons/evaluations of design

attributes. In order to assist in developing such a table, a seven-level rating system isdeveloped in Table 4.

Now, one can develop the table of pairwise comparisons/evaluations for variousdesign attributes as shown in Table 5. Note that n, the number of design attributes inTable 5, is assumed to be 5. In constructing Table 5, the following notation is used:

aj=design attribute i

i= 1,2,... ,n

Wj = weight of design attribute a j

•O<wj<1 and Lwj=1

i=l

r,= rating value of design attribute a, in any particular pairwise comparison

InTable 5,column (I) represents the number and types of design attributes selectedfor pairwise comparison/evaluations. The design attributes are listed alphabetically.Column (2) represents the weights assigned to each design attribute based on a

RatingDesign attribute relationship r j

Absolutely superior 7

Especially important 6

Fairly important 5

Ordinarily important 4

Fairly unimportant 3

Generally unimportant 2

Significantly inferior

Table 4. Rating values of design attributes.

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Product design in concurrent engineering 1811

Pairwise comparisons/evaluationsDesign Design

attribute Weight at VS. Q 2 at VS. Q 3 at YS. a4 at vs. as attributea, Wi Wi'i Wli Wi'i W;'i value

a, W, WI't Wt't Wl't WI't 1·000W 2'2

a2 W2 W2'2Wt'lW 3'3

a, W, W3'3WI'tW4'4

a. W. W4'4WI't

Ws'sa, w, Ws's

WI't

Table 5. Table of pairwise comparisons/evaluations for design attributes.

designer's discretion and previous experience. Columns (3-6) represent variouspairwise comparisons/evaluations. Design attribute at> as the base design attribute, iscompared against all other design attributes in sequential order. Namely, compare andevaluate attribute a , against attribute a2 , attribute a , against attribute a3, etc. Eachpairwise comparison consists of the product of weight and the assigned rate for eachdesign attribute (w,r,). The total rating values assigned to any two design attributes foreach pairwise comparison must be equal to 8. For example, r , +r 2 =8, and r , +r 3 =8,etc. Possible combinations of rating values in comparison of any two design attributesare: (7-1, 6-2, 5-3, 4-4, 3-5, 2-6, 1-7).

Note that r 1 in the first row for attribute at may accept a different value as it iscompared to other design attributes (a2, a3 , a4 , a,) in each of the pairwisecomparisons/evaluations columns (columns 3-6). In the last column, the designattribute values are calculated by dividing the value of each design attribute to thevalue of a , as shown in Table 5.

2.4.3. Step 4.3: Determine normalized valuesUse a normalization procedure by dividing the value of each design attribute value

by the sum of all design attribute values to arrive at the normalized value for eachdesign attribute.

2.4.4. Step 4.4: Choose two design attributesChoose two design attributes with the highest normalized values. Add these two

values and consider it a utility value for that particular combination of module/partoption. The utility values are subsequently incorporated in the objective function.Figure 4 represents a flow chart of attribute-based utility values.

Inorder to determine the utility values for the reduced number of part options of thepad assembly, n =5 design attributes and their respective weights are selected. Thetables of pairwise comparisons/evaluations are developed. The normalized and,combined values of the design attributes are subsequently calculated. The predominant

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1812 s. Dowlatshahi

Develop a table of pairwisecomparisons/evaluations. Assign rates.

Calculate normalized values

Calculate utility values

Incorporate utility values

in the objective function

No

Figure 4. Flow chart of attribute-based utility values.

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Designspecification Utility values

Lining thickness 0·605 0·506 0·538in inches

Braking size per 0'794 0·875inch? per 2200lbs

Friction material 0·823 0·913 0·900 0·715

Special features 0·915 0·920 0·875

Table 6. Table of utility values for pad assembly.

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ObjectiveConstraints

function

Design PartIattributes I I options

Figure 5. Solution space in design optimization.

concurrent engineering design attributes selected for the design of the pad assemblyinclude: durability, performance, manufacturability, reliability, and safety. The finalresults are presented in Table 6.

Details of calculations for Table 6 are available upon request from the author.Utility values calculated in Table 6 are subsequently used in the optimization model.

2.5. Step 5: Model and optimize product designAt this step, the objective function and constraints are formulated. Figure 5

illustrates the process of achieving an optimal product design.Two product design optimization models are presented in this step. Step 5.1

presents a model in which the coupling among parts is secondary to the couplingamong modules/parts. Step 5.2 presents a model in which both couplings areconsidered simultaneously.

2.5.1. Step 5.1: ModellUtilize a model where the set of part options belonging to each part is specified. The

model selects the necessary number of a part options from each part for each module.Note that each module may consist of one or more parts.

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1814 S. Dowlatshahi

In this step, an integer programming formulation of the product design is presented.The nomenclature is introduced as follows:

xij=number of part option P, is used in module M,y.=number or product type k k=I,2,oo.,pC. = unit cost or product type k k = 1,2, ... , puij= utility value of part option P, used in module M i

cij=cost of part option P, used in module M;mij=manuracturing cost of part option Pj used in module M,

V= vector of the number of each part making up all the modulesW=vector of the number or each reduced part option for all partsF.=factory cost or product kB = total product budget availableV=[v 1, V2,··"V j, •• "Vm]T

W=[w 1, w2, · · · ,wj , ..• ,w n]

Model M.1. The objective function of model M.I maximizes the utility valuesassociated with the selection of the part option Pjfrom the module M, based onconcurrent engineering design attributes

m •

Max L L uijxijt» 1 j= 1

Subject to

•L X;j=Vi i=I,2,oo.,mj= 1

m

L Xij=Wj j=I,2,oo.,ni= 1

m •

L L CijX,j'o;;;C. k= 1,2,oo.,pi= 1 j=t

Xij-X,,:o;;;o

X'j+X,,:O;;; I

xij~O, integer i= 1,2, ... ,m;j= 1,2, ... ,n

(I)

(2)

(3)

(4)

(5)

(6)

Constraint (I) ensures that vector Vis assigned to module Mi' Constraint (2) ensuresthat vector W is selected from part options Pj' Constraint (3) ensures that the costs ofparts used do not exceed the product unit cost. Constraint (4)ensures that ifpart optionPj of module M, is selected, only then can the part option P, of module M. be selected.The converse of this constraint, however, is not true. Constraint (5) represents theinfeasibility constraint. It ensures that only one or none of the two part options P, andP, of modules M, and M. is selected respectively. Constraints (4) and (5) should be usedwith care with respect to the demand of a particular product design. Constraint (6)imposes non-negativity and integrality.

Note that model M.I does not consider the manufacturing cost of part options P,used in module M; such as assembly and material handling costs. Model M.l.l, as anenhanced version of model M.I, considers the manufacturing cost. Model M.l.1 ispresented next.

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Product design in concurrent engineering 1815

Model M.I.I. The constraint related to the manufacturing cost is formulated as 'follows:

k=I,2, .. ,p (7)

Constraint (7)ensures that the manufacturing cost of parts does not exceed the factorycost of the unit product.

Note that model M.1 and model M.l.I both consider only one product. It isconceivable that a company produces more than one product type. In this case, theproduction of several product types is subjected to the availability of funds. Thisadditional constraint is discussed in model M.l.2.

Model M.I .2. The constraint related to the availability of total budget isformulated as follows:

Yt ~o, integer

k=I,2, ... ,p

k=I,2, ... ,p

(8)

(9)

Constraint (8)ensures that the aggregate cost of product types does not exceed the totalavailable budget. Constraint (9) imposes non-negativity and integrality.

Additional constraints can be added and/or the existing constraints can be deletedfrom the models presented in Step 5.1 based upon the specific demands of a givenproduct design.

2.5.2. Step 5.2: Model 2Utilize a model where not only module/part interaction is considered, but also an

interaction among all part options is present in the problem. This model, as anenhanced version of the model presented in Step 5.1,is also capable of decomposing theselected part options into a predetermined number of manufacturable groups. Thisfeature of the Step 5.2 model can serve as a group technology (GT) scheme for the partoptions selected in the product design (Kusiak 1990).

In this step, a p-median formulation of the product design is presented. In additionto the nomenclature introduced in Step 5.1, the following notation is used:

x,,= {I if part option r, is used in module M i

'J ° otherwise

n= the total number of part options or design variationsG,=set of part options or design variation for part number I,

1= 1,... ,0, such that I~ G,[=n1= 1

p=a predetermined number of manufacturable groups

Model M.2. Objective function of model M.2 maximizes the utility values betweenany two part options i and j.

n n

Max L L uijxiji= 1 j= 1

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Subject to

n

L Xii=Pi= 1

Xij - Xli '" 0

Xij +Xli '" I

s. Dowlatshahi

k= 1,2, ... ,p

for all i= I, ,n, j= 1, ,n

for all j = 1, , n, j = 1, , n

(10)

(II)

(12)

(13)

(14)

(15)

(16)

Constraint (10) ensures that for each part only one part option or design variation isselected. Constraint (11)defines the exact number of manufacturable groups required.Constraint (12)ensures that the costs of parts used do not exceed the product unit cost.Constraints (13)and (14)correspond to constraints (4)and (5)in model M.1. Constraint(I 5)ensures that part option P, belongs to module M, only when this module is formed.Constraint (16) ensures integrality.

Models M.2.1 and M.2.2, enhanced versions of model M.2, are similar to thosepresented in models M.1.1 and M.I.2, and may be used in a similar fashion.

To summarize the steps taken in the optimization of product design, the flow chartof modelling approach to product design is presented in Fig. 6.

The model presented in Step 5.1 uses the Vand Wvectors and cost values to result inthe following solution for the design of pad assembly:

Objective function value = 3·313

X II = I 0·125 inch lining thicknessX2S = I 73·63inch 2 braking size per 2200lbX 3 ? = 1 non-asbestos organic binder resin with fibreglass

X 4 1 1 = I worn lining indicator

The solution is obtained using the LINDO software (Schrage 1984). Detailed solutionprocedures as well as the input file are available upon request from the author.

The model presented.in Step 5.2 considers the interrelationships among variouspart options (design variations) of the pad assembly. In this model, the matrices ofmodule/part/part options, design variation interrelationships, utility values, and costvalues are developed. In addition, tables of pairwise comparisons/evaluations forvarious design variations are developed. Using p=2, and the LINDO software(Schrage 1984), Step 5.2 provides the following solution:

Objective function value = 3·474

X I S = I 0·125 inch lining thicknessX S 1 1 = I 73·63inch? braking size per 2200lbX?II == I Non-asbestos organic binder resin with fibreglassX 1 IS == I Worn lining indicator

The results obtained can be classified in two design variation groups.

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Product design in concurrent engineering 1817

Feasible

parts space

Reduced part

options space

Make pairwise module/part optioncomparisons. Evaluate based on ratingvalues. Calculate utility values

No

No

Stop

Develop objective function andconstraints

c ~,------,------Figure 6. "Flow chart of modelling approach to product design.

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and

Product design in concurrent engineering

DV 1={5, 7}

DV2={1,II}

Each design variation group assists the designer with the simultaneous consideration ofdesign and manufacturing issues pertaining to that particular group. In this example,the design and manufacturing of braking size/friction material and liningthickness/worn lining indicator are considered simultaneously.

The detailed solution procedure as well asthe input file for Step 5.2 are availableupon request from the author.

3. Conclusion and assessmentThis paper has provided a system approach to the design of mechanical products

where the constraints associated with the design attributes of a concurrent engineeringenvironment are represented. This approach allows for a comprehensive treatment ofdesign attributes in a product design. This paper has made no specific attempts toexplore the technical merits as well as the ratings of design-manufacturability, design­safety, and like concerns. This is best left to design experts in specific product designareas. The models presented, however, are capable of reflecting the results in anoptimization model leading to the identification of product configuration.

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Journal of Advanced Manufacturing Technology.FRENCH, M. 1., 1985, Conceptual Designfor Engineers (London: The Design Council, Springer-

Verlag).HUTHWAITE, B., 1988, Designing in quality. Quality, 27 (II), 34-35.KUSIAK, A., 1990, Intelligent Manufacturing Systems (Englewood Cliff, NJ: Prentice-Hall).NEVILLE, JR., G. E., 1989, Conceptual models ofdesign processes. Design Theory '88:Proceedings

of the 1988 NSF Grantee Wiirkshop on Design Theory and Methodology, pp.82-116.NEVINS, J. L.,and WHITNEY, D. E., 1989, Concurrent Design ofProducts and Processes (New York:

McGraw-Hili), pp.2-3.SCHRAGE, L. E., 1984, Linear, Integer, and Quadratic Programming with LINDO (Palo Alto, CA:

Scientific Press).STARKEY, C. V., 1988, Basic Engineering Design (London: Edward Arnold).ULCEDSSWORKING GROUP, 1988, AnEvaluation of PotentialResearch Directions. Technical

Paper IDA Paper P-2064-Vol. I, Institute for Defense Analysis, Alexandria, VA, May.WHITNEY, D. E., 1988, Manufacture by design. Harvard Business Review, July-August, 83-91.

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