A. Kusiak, Engineering Design: Products, Processes, and ...user.engineering.uiowa.edu/~coneng/lectures/Chapter_8.pdf · A. Kusiak, Engineering Design: Products, Processes, and Systems,

A. Kusiak, Engineering Design: Products, Processes, and Systems, Academic Press, San Diego, CA, 1999.

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CHAPTER 8

TEAM FORMATION 1. INTRODUCTION 2. QUALITY FUNCTION DEPLOYMENT 3. ANALYTICAL HIERARCHY PROCESS 4. MATHEMATICAL PROGRAMMING MODEL 5. AUTOMOTIVE CASE STUDY 6. MODEL SOLUTION 7. MODIFIED HIERARCHY 8. SUMMARY

REFERENCES APPENDIX: Eigenvalues and Eigenvectors QUESTIONS PROBLEMS

1. INTRODUCTION The concept of multi-functional teams is one of the key aspects of problem solving in many industries. Specialists from various disciplines, for example, design, manufacturing, quality testing, and marketing work in a group rather than individually in order to solve a manufacturing problem or develop a new product. The concept of multi-functional teams is important in product development. The membership of a team depends on the type of product to be developed, customer requirements, engineering and product characteristics, and so on. The literature does not provide analytical solutions for forming teams. Furthermore, no comprehensive model exists to prioritize team membership based on the characteristics of the problem considered. For example, when a multi-functional team is formed, it is not known how important is the information provided by a team member for a particular characteristic of the product or customer requirement. Askin and Sodhi (1994) presented an approach to organizing teams in concurrent engineering. They developed five different criteria for team formation and discussed team training, leadership, and computer support issues. The labor assignment heuristic was developed for team formation. The deficiency of the approach presented by Askin and Sodhi (1994) is that it considers a single criterion, i.e., time and cannot accommodate multiple criteria. Also, it does not consider customer requirements and product characteristics. Reddy et al. (1993) proposed the notion of virtual teams to overcome the barriers of hierarchical organizational structures. A virtual team consists of geographically scattered team of experts using a computer-supported environment to collaborate over a network. A layered architecture of different types of computer technology has been described, i.e., network layer, enterprise information model layer, collaboration services layer, transformation layer, and activity layer, the integration of which enable a virtual team. Klein (1993) described a design rationale capture system (DRCS) which provides an integrated and generic framework for capturing rationale in a


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team context. DRCS system integrates design-decisions and design-rationale capture in a single tool and allows more effective support for the capture of computer-interpretable rationale from multi-functional design teams. None of the two papers offers a methodology for forming teams. The methodology presented in this chapter is based on Zakarian and Kusiak (1996). It is structured, unified, and capable of dealing with the tangible and intangible aspects of forming multi-functional teams. The analytical hierarchy process (AHP) approach is used to generate data necessary for optimization. The AHP methodology captures the importance of various elements of the problem and suggesting the course of action. Also, the user acceptability and confidence in the data provided by the AHP methodology is high compared with other multiattribute decision approaches (Shoemaker and Ward 1982). A conceptual framework for prioritizing team members based on customer requirements and product characteristics is presented. The mathematical programming model is developed to determine optimal composition of a team. The application of quality function deployment (QFD) and analytical hierarchy process (AHP) methodology to forming multi-functional teams is discussed next. 2. QUALITY FUNCTION DEPLOYMENT

The quality function deployment (QFD) approach was discussed in Chapter 2. The essence of QFD is to convert customer requirements into "quality characteristics" and develop product design of high quality by systematically deploying the relationships between customer requirements and engineering characteristics, beginning with the quality of each functional component and extending the deployment of the quality of each part and process. The QFD objectives are to identify: 1) the customer, 2) the customer wants, and 3) how to meet the customer's requirements. In this chapter, we use the "house of quality" to collect and represent the data for the multi-functional team selection model. The application of QFD to the formation of multi-functional teams is discussed next. The QFD used to collect data required for development of a team formation model. First, project managers, customers, and suppliers develop a QFD planning matrix in which the customer requirements are related to the engineering characteristics (requirements) of the product (see Figure 1(a)). Then, engineering requirements become the rows of an engineering characteristic - team members' deployment matrix (Figure 1(b)). In other words, the planning matrix in Figure 1(b) relates engineering characteristics of the product to the potential team members that are responsible or can provide those characteristics. The matrices in Figure 1 are useful in organizing the factors considered in the team selection problem into a hierarchical structure of the AHP methodology.


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(a)

Cus

tom

er re

quir

emen

ts

Engineering chracteristics Team members

(b)

Eng

inee

ring

cha

ract

eris

tics

Figure 1. The basic planning matrices: (a) customer requirements -

engineering characteristics planning matrix, (b) engineering characteristics - team members planning matrix

3. ANALYTICAL HIERARCHY PROCESS The objective of multicriteria decision making is to select the best available alternative under conflicting criteria. The analytical hierarchy process (AHP) methodology provides a comprehensive framework for solving such a problem. The AHP is a multicriteria decision-making method that uses a hierarchy to represent a decision problem. The method developed by Saaty in 1970's is based on an axiomatic foundation that has established its mathematical viability (Saaty 1986, 1987, and 1981, Harker and Vargas 1990). The diverse applications of the technique are due to its simplicity and ability to cope with complex decision making problems. The AHP methodology has been widely used for solving problems where definite quantitative measures are not available to support correct decisions. Zahedi (1986) provided an extensive list of references on the AHP methodology and its applications. For recent industrial applications of AHP see Madu and Georgatzas (1991) and Armacost et al. (1994). The AHP begins with representing a complex problem as a hierarchy. At the top level of the hierarchy, the goal (objective) upon which the best decision should be made is placed. The next level of the hierarchy contains attributes or criteria that contribute to the quality of the decisions. Each attribute may be decomposed into more detailed attributes. The lowest level of the hierarchy contains decision alternatives. After the hierarchical network is constructed, one can determine the weights (importance measures) of the elements at each level of the decision hierarchy, and synthesize the weights to determine the weights of decision alternatives. First, a comparison matrix, which includes Level 1 elements (criteria) of the hierarchy, is constructed. Then, a ratio scale pairwise comparison of each pair of criteria with respect to the overall goal is performed. The relative importance of each criterion is estimated using an eigenvector approach (Saaty 1981) or other methods. Then, the relative importance of each alternative with respect to each criterion is determined using similar pairwise comparisons. The pairwise comparisons between the criteria as well as between the alternatives are made using the nine point scale proposed by Saaty (1986): 1, 3, 5, 7, and 9 to express the ratio scale preference between the alternatives, 2, 4, 6, and 8 for compromises, and reciprocals for the


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inverse comparisons. Table 1 summarizes Saaty's relative importance scale modified for the team selection problem. Typically, a decision-maker provides the upper triangular of the comparison matrix, while reciprocals are placed in the lower triangular. In other words, if scale factor 3 is assigned to entry (i, j) of the matrix, where i and j is the row and column of the comparison matrix, respectively, then value 1/3 is assigned to the entry (j, i). Also, when compared to itself each criterion or alternative has equal importance. Therefore, the diagonal elements of the matrix always equal to one. The advantage of the pairwise comparison of elements instead of direct assignments of preference values is that the latter results in inaccuracies, since the comparison process is more complex. Table 1. Scale of relative importance (Saaty 1986) modified for team selection

Definition

Explanation 1 3 5 7 9

2, 4, 6, 8

Equal importance Moderate importance of one over another Essential or strong importance Very strong or demonstrated importance Extreme importance Intermediate values between two adjacent judgments Reciprocal

Two views contribute equally to the goal Experience and judgment moderately favors one view over another Strongly favors one view over another A view is very strongly favored and its dominance is demonstrated in practice The evidence of favoring one view over another one is of the highest possible level of affirmation When a compromise is needed For inverse comparisons

The AHP methodology provides an index for measuring inconsistency in each comparison matrix as well as for the entire hierarchy. For example, the consistency meaning in the team selection process is defined as follows. If a respondent moderately prefers team member B over C, and team member C over D, then it is expected that s/he will prefer team member B over D is of the highest possible order of affirmation. The consistency index (CI) and consistency ratio (CR) for comparison matrix A are computed as follows: CI = (λmax - n)/(n - 1) CR = (CI/ACI) 100% where: λmax is the largest eigenvalue of the comparison matrix (see the Appendix for the

definition of eigenvalues), n is the dimension of the matrix, ACI is the average index for randomly generated weights (Saaty 1981). If the calculated value of the consistency ration, CR, for the comparison matrix is less than 10%, the consistency of the pairwise judgment is accepted based on Saaty's rule of thumb. However, when the consistency ratio is greater than 10%, the judgments expressed by the


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experts are considered inconsistent, and decision-makers are given an opportunity to reconsider their judgments. The relative preference throughout the hierarchy is obtained performing pairwise comparisons, where a decision-maker or group of decision-makers expresses their judgments. To aggregate the judgment of a group of individuals, an aggregate relative preference must satisfy the reciprocal property. Aczel and Saaty (1983) demonstrated that the geometric mean of a set of individual judgments satisfies the ratio scale and the reciprocal property. Therefore, if a group of decision-makers is involved in the team formation process and these decision-makers came to a consensus, then the entries in the comparison matrix are the geometric means calculated for each pair of responses. In the team selection problem considered in this chapter, the AHP is applied as follows. The values that the team members contribute to the criteria established by the customer vary. To select a team, one must elicit all possible characteristics or attributes desired, and then develop a method for assessing their importance to the overall goal. Therefore, all the elements, i.e., customer requirements, engineering characteristics, and team members obtained from the planning matrices in Figure 1(a) and 1(b) form together

Goal

1 2 3 4 k

1 2 3 4 n

1 2 mLevel 3Team members

Level 2Engineeringcharacteristics

Level 1Customerrequirements

1

Figure 2. Hierarchical structure of the team selection problem

the structure depicted in Figure 2. In order to derive a matrix containing the weights associated with the team members and the engineering characteristics, systematic process is used. This matrix is used to form the mathematical programming model presented next. 4. MATHEMATICAL PROGRAMMING MODEL The multi-functional teams' formation problem is formulated as an integer programming model. The model is based on the engineering characteristics - team member type priority incidence matrix. Each row of the matrix corresponds to a distinct engineering characteristic of the product. Each column denotes a type of a team member. Each entry wij in the incidence matrix indicates the weight (priority) of a member of functional team of type j with respect to engineering characteristic i. To formulate the model the following notation is introduced: i - index for engineering characteristics j - functional team type n - number of engineering characteristics


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m - number of types of functional teams wij - weight (priority) of a member of functional team of type j with respect to

engineering characteristic i p - number of multifunctional teams mj - number of characteristics that a member of functional team j can undertake. The value of

mj is a function of time, technological and scheduling constraints, and so on. M - an arbitrary large positive number

ijx =1 if a member functional team of of type j belongs to the multidisciplinary team that is responsible for engineering characteristic i

0 otherwise

iy =1 if a multidisciplinary team responsible for

engineering characteristic i is formed0 otherwise

The objective function of the model ((1) - (6)) maximizes the total of priority weights of the multi-functional teams.

max ijwj=1

m∑

i=1

n∑ ijx (1)

s.t. ijx ≤ jm i=1

n∑ j =1, ..., m (2)

iy ≤ pi=1

n∑ (3)

ijx ≤ M iyj=1

m∑ i = 1, ..., n (4)

ijx = 0, 1 i = 1, . .., n j =1, ..., m (5)

i y = 0, 1 i =1, ..., n (6)

Constraint (2) imposes an upper bound on the number of projects that a team member of type j is to undertake. Constraint (3) specifies the required number of teams. Constraint (4) ensures that team member of type j belongs to team i only when team i is formed. Constraint (5) and (6) ensure the integrality. Additional constraints, e.g., a budget constraint, team size, can be easily incorporated into the model ((1) - (6)). Next, the AHP framework and mathematical programming formulation are illustrated with a case study. 5. AUTOMOTIVE CASE STUDY

Consider an automotive company that is to form teams to develop a new model of a car. Therefore, a pairwise comparison of the importance of possible team members with respect to the overall goal (development of a car) is required. Before the AHP is used, planning matrices discussed in Section II are constructed. First, project managers, customers, and suppliers develop a planning matrix in which the customer requirements are related to the engineering characteristics. Then, the desired


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engineering characteristics are related to the potential team members. The two transformations are shown in Figures 3 and 4, respectively.

Automatic transmission

Lighter brake pedal pressure

Normal functioning of the brakes after engine stops running

Easy brake replacement

Easy brake fluid replacement

No erratic shifting

No delay engagement

No transmission overheating

Easy oil replacement

Fuel efficiency

Easy oil check and replacement

Quiet engine operation

Excellent engine performance

Passenger side airbag

Roomy back seats

Roomy trunkDoors easy to open, easy to close, easy to lock

Corrosion protection

Bright driving beam

No lighting troubles

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Engineering Characteristics

Customer Requirements

Even brakingB

rake

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lic s

yste

m

Self

adj

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akes

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uum

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ter c

ylin

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r

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etar

y ge

ars

and

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rols

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ve b

ody

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tch

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ine

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icat

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em

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inde

r blo

ck a

nd h

ead

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cham

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ves

and

port

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stem

Safe

ty c

hara

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s

Mat

eria

l cho

ice

Cir

cuit

brea

kers

Switc

hes

1

1 2 10 11 12 13 14 15 16 17 18 3 4 5 6 7 8 9

Figure 3. Customer requirements - engineering characteristics planning matrix


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Brakes hydraulic systemVacuum

Engineering Characteristics

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 2 3 4 5 6 7

Self adjusting brakesMaster cylinderTorque converterPlanetary gears and controlsValve bodyReverse clutchEngine lubricating systemCylinder block and headCombustion chamberValves and portingInjection systemSafety characteristicsConvenience characteristicsMaterial choiceCircuit breakersSwitches

Mec

hani

cal e

ngin

eer

Rel

iabi

lity

engi

neer

Fina

nce

expe

rt

Ele

ctri

cal e

ngin

eer

Team Members

Man

ufac

turi

ng e

ngin

eer

Des

ign

engi

neer

Qua

lity

engi

neer

Figure 4. Engineering characteristics - functional team planning matrix

Once matrices in Figures 3 and 4 are developed, a hierarchical structure in Figure 5 is constructed. The highest level in the structure is the goal, i.e., build a car. The attributes, i.e., customer requirements and engineering characteristics, which are required to satisfy the goal, are placed on the Level 1 and 2, respectively. At the last level of the hierarchy, the decision alternatives (i.e., team members) are placed. The next step is to prioritize customer requirements using pairwise comparisons and the relative importance scale in Table 1. The comparison matrix for the twenty one customer requirements is shown in Table 2. The resulting weights of the customer requirements are shown in Figure 6.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 2 3 4 9 10 11 12 13 14 15 16 17 185 6 7 8

Mechanical engineer

Manufactur. engineer

Design engineer

Quality engineer

Finance expert

Electrical engineer

Reliability engineer

Build a carGoal



Level 3Team members

Figure 5. Hierarchical structure for the team formation problem in Example 1


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Table 2. Pairwise comparison of customer requirements with respect to the goal

1

2

3

4

5

6

7

8

9

10

11

12

13

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16

17

18

19

20

21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

λmax = 23.6080 CI =0.1304 CR =0.0835

Priority vector (W)0.0237041

0.0106860

0.0339473

0.0182134

0.0124572

0.0554965

0.0156157

0.0198665

0.0464340

0.0162947

0.1213543

0.0242059

0.0634667

0.1619140

0.1512870

0.0667434

0.0301688

0.0366631

0.0270693

0.0130475

0.0513638

1 3

1

1/2

1/5

1

1

1/2

2

1

2

1

2

1

1

1/3

1/6

1/3

1/3

1/6

1

1

1/2

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1

1

4

1

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1

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3

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4

1

1

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1/5

1

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1

1/3

1/3

1

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1

2

1/2

1/2

3

2

1/2

3

1

1/6

1/4

1/4

1/6

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1/5

1/8

1/9

1/6

1/8

1

1

1/3

1/2

1/2

1/2

3

1/2

1/3

1

1

5

1

1/3

1/7

1/3

1/4

1/5

1

1/2

1/6

1/7

1/4

4

1/4

1

1/7

1/9

1/5

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1/8

1/9

1/2

1/7

1/3

1

1/6

1/9

1/5

1/7

1/9

1/4

1/9

1/9

1/2

1/9

1/2

1/8

1/5

1

1

1/5

1/4

1

1/3

1/7

1/2

1/4

1/5

1

1/5

2

1/3

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4

5

1

1

1/2

2

1

1/3

2

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1/3

2

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3

1/2

1

5

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1

1/3

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1/3

3

1/2

1/3

3

1/5

3

1/2

1

5

5

2

1

1

1

1/3

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1/2

1/2

5

1/3

1/2

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1

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1

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1/2

1/4

1


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The matrix Table 2 is upper triangular, while the lower triangular matrix would include reciprocal elements aij = 1/aji, where, aij is entry (i, j) of the matrix. For example, in comparing the fuel efficiency and roomy trunk relative to their importance in the car, a moderate importance for fuel efficiency over roomy trunk is indicated by the entry a11,17 = 3 in the matrix. The priority vector of the customer requirements is determined using the largest eigenvalue λmax of the matrix in Table 2. The eigenvector corresponding to the λmax is the priority vector of the customer requirements. The consistency ratio CR of the matrix in Table 2 is calculated as follows. The computation for the data in Table 2 yields the priority vector W with the largest eigenvalue λmax = 23.6080. The consistency index is CI = 0.1304 and the consistency ratio CR is 0.0835. Note, the value of average consistency index ACI = 1.56 is used which was obtained for randomly generated weights (Saaty 1981).

0.023700.01069

0.03395

0.018210.01246

0.05550

0.015620.01987

0.04643

0.01629

0.12135

0.02421

0.06347

0.161910.15129

0.06674

0.030170.03666

0.027070.01305

0.05136

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Prio

rity

Customer requirement

Figure 6. Weights of customer requirements

At the second level of the hierarchy the engineering characteristics are prioritized with respect to the customer requirements. The engineering characteristics are decomposed, as some of them are not pertinent to the customer requirements. For example, the relationship between engineering characteristics 5, 6, 7, ..., 18 the customer requirements 1, 2, 3, 4, and 5 is not elicited. The prioritization is done using comparison matrices describing the relative impact of the engineering characteristics to the customer requirements. Based on the weights of customer requirements, the normalized weights of engineering characteristics are derived (see Table 3 and Figure 7). Table 3. Normalized weights of engineering characteristics

Engineering characteristics Weight vector (wi)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Brakes hydraulic system Vacuum Self adjusting brakes Master cylinder Torque converter Planetary gears and control Valve body Reverse clutch Engine lubricating system Cylinder block and head Combustion chamber Valves and porting Injection system Safety characteristics Convenience characteristics Material choice Circuit breakers Switches

0.02385 0.02209 0.02416 0.02888 0.05902 0.03689 0.02644 0.03120 0.06640 0.05675 0.07593 0.10071 0.07104 0.11573 0.11791 0.07829 0.02899 0.03572

0.02385 0.02209 0.024160.02888

0.05902

0.036890.02644

0.03120

0.066400.05675

0.07593

0.10071

0.07104

0.11573 0.11791

0.07829

0.028990.03572

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Prio

rity

Engineering characteristic Figure 7. Normalized weights of engineering characteristics

Next, a matrix that includes the elements of the lowest level of hierarchy in Figure 5 is constructed. The issue here is to determine which team member has more impact on an engineering characteristic considered. For example, in the comparison matrix for the first team member the importance of team members in building the brakes hydraulic system is evaluated. Therefore, eighteen comparison matrices A1, A2, ..., A18 are constructed, one for each engineering characteristic at Level 2. The pairwise comparison of team members with respect to each engineering characteristic in Level 2 is important, as the members receive different ratings when using different criteria. Following a prioritization scheme similar to the one described above, one derives weights for each team with respect to each engineering characteristic at Level 2. The resulting priority vectors from eighteen matrices are weighted (multiplied) by the importance wi of engineering characteristic i, i = 1, ..., 18, derived in Table 3. Then, the aggregate priority matrix is constructed which lists the priority measures for each team member with respect to each engineering characteristic of the car, normalized with respect to the overall goal. These priority vectors W1, W2, W3, W4, W5, W6, and W7 are summarized in Table 4. The weights of the team members with respect to each engineering characteristic are summarized in Figure 8.


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Table 4. Normalized weights of each team with respect to the engineering characteristics ME MF DE QE FE EE RE

0.00716 0.00208 0.00117 0.00358 0.00070 0.00164 0.007500.00617 0.00193 0.00108 0.00334 0.00065 0.00188 0.007040.00675 0.00211 0.00119 0.00365 0.00071 0.00206 0.007700.00816 0.00485 0.00232 0.00312 0.00070 0.00366 0.006060.01592 0.00419 0.00316 0.00762 0.00220 0.01742 0.008510.01243 0.00220 0.00220 0.00622 0.00140 0.00622 0.006220.00183 0.00610 0.00951 0.00356 0.00356 0.00074 0.001140.00850 0.00281 0.00469 0.00312 0.00081 0.00412 0.007150.01748 0.00809 0.00612 0.00743 0.00299 0.00943 0.014870.01734 0.01109 0.01238 0.00561 0.00142 0.00754 0.001390.01263 0.00469 0.03822 0.00698 0.00137 0.00889 0.003160.03240 0.02249 0.01733 0.01007 0.00423 0.01249 0.001710.01273 0.00512 0.00255 0.00837 0.00479 0.02206 0.015410.00964 0.00730 0.02095 0.02307 0.01679 0.00876 0.029210.00491 0.02044 0.03658 0.01306 0.01875 0.00778 0.016390.01245 0.00924 0.01890 0.00935 0.01681 0.00433 0.007220.00155 0.00077 0.00693 0.00260 0.00363 0.00831 0.005190.00254 0.00146 0.00508 0.00418 0.00585 0.01194 0.00468

Brakes hydraulic systemVacuumSelf adjusting brakesMaster cylinderTorque converterPlanetary gears and controlsValve bodyReverse clutchEngine lubricating systemCylinder block and headCombustion chamberValves and portingInjection systemSafety characteristicsConvenience characteristicsMaterial choiceCircuit breakersSwitches

W 1 W 2 W 3 W 4 W 5 W 6 W7


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0.00000

0.00200

0.00400

0.00600

0.00800

0.01000

0.01200

0.01400

0.01600

0.01800

Vacuum

Engineering characteristic

Prio

rity

Brakes hydraulic system Self adjusting brakes Master cylinder Torque converter Planetary gears and controls

ME

MF

DE

QE

FE

EE

RE

0.00000

0.00500

0.01000

0.01500

0.02000

0.02500

0.03000

0.03500

0.04000

Prio

rity

Valve body Reverse clutch Engine lubricating system Cylinder block and head Combustion chamber Valves and porting


ME

MF

DE

QE

FE

EE

RE

0.00000

0.00500

0.01000

0.01500

0.02000

0.02500

0.03000

0.03500

0.04000

Injection system Safety characteristics Convenience characteristics Material choice Circuit breakers Switches


Prio

rity

ME

MF

DE

QE

FE

EE

RE

Figure 8. Normalized weights of team members with respect to engineering characteristics

After the matrix in Table 4 is obtained, a mathematical programming model presented in Section 4 determines the optimal composition of teams. VI. MODEL SOLUTION

Consider the engineering characteristics - team member type priority incidence matrix in Table 4. Assume that at most 18 teams are to be formed. Table 5 shows the number of characteristics that each team member type is able to undertake. Table 5. Data

Functional team type

ME MF DE QE FE EE RE


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Number of

characteristics

17 14 17 10 6 14 15

Solving the model ((1) - (6)) for the incidence matrix in Table 4 and p = 18, results in the following solution: x11 = x13 = x17 = 1, x12 = x14 = x15 = x16 = 0, x21 = x27 = 1, x22 = x23 = x24 = x25 = x26 = 0, x31 = x32 = x33 = x37 = 1, x34 = x35 = x36 = 0, x41 = x42 = x43 = x46 = x47 = 1, x44 = x45 = 0, x51 = x52 = x53 = x54 = x56 = x57 = 1, x55 = 0, x61 = x62 = x63 = x64 = x66 = x67 = 1, x65 = 0, x71 = x72 = x73 = x77 = 1, x74 = x75 = x76 = 0, x81 = x82 = x83 = x86 = x87 = 1, x84 = x85 = 0, x91 = x92 = x93 = x94 = x96 = x97 = 1, x95 = 0, x101 = x102 = x103 = x104 = x106 = x107 = 1, x105 = 0, x111 = x112 = x113 = x114 = x116 = x117 = 1, x115 = 0, x121 = x122 = x123 = x124 = x125 = x126 = x127 = 1, x131 = x132 = x133 = x134 = x135 = x136 = x137 = 1, x141 = x142 = x143 = x144 = x145 = x146 = x147 = 1, x151 = x152 = x153 = x154 = x155 = x156 = x157 = 1, x161 = x162 = x163 = x164 = x165 = x166 = x167 = 1, x173 = x176 = x177 = 1, x171 = x172 = x174 = x175 = 0, x181 = x183 = x185 = x186 = x187 = 1, x182 = x184 = 0, Based on definition of xij the following teams are selected: T1 = {ME, DE, RE}, T2 = {ME, RE}, T3 = {ME, MF, DE, RE}, T4 = {ME, MF, DE, EE, RE}, T5 = {ME, MF, DE, QE, EE, RE}, T6 = {ME, MF, DE, QE, EE, RE}, T7 = {ME, MF, DE, RE}, T8 = {ME, MF, DE, EE, RE}, T9 = {ME, MF, DE, QE, EE, RE}, T10 = {ME, MF, DE, QE, EE, RE}, T11 = {ME, MF, DE, QE, EE, RE}, T12 = {ME, MF, DE, QE, FE, EE, RE}, T13 = {ME, MF, DE, QE, FE, EE, RE}, T14 = {ME, MF, DE, QE, FE, EE, RE}, T15 = {ME, MF, DE, QE, FE, EE, RE},


16

T16 = {ME, MF, DE, QE, FE, EE, RE}, T17 = {DE, EE, RE}, T18 = {ME, DE, FE, EE, RE}. 7. MODIFIED HIERARCHY To reduce the number of the AHP comparison matrices and the size of the model, one can extend the hierarchical structure of Figure 5 by adding a new level (Level 3), i.e., components (subsystems) of the car, into the hierarchy (see Figure 9). In this hierarchical structure several engineering characteristics related to a single component (subsystem) of the car. The importance measure of the subsystems of the car can be obtained by summing the importance measures of the engineering characteristics related to the subsystem of the car. Therefore, instead of prioritizing team members with respect to


17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 2 3 4 9 10 11 12 13 14 15 16 17 185 6 7 8

Brakes Transmission Engine Design Lighting system

Mechanical engineer

Manufactur. engineer

Design engineer

Quality engineer

Finance expert

Electrical engineer

Reliability engineer

Build a carGoal



Level 3Components

Level 4Team members Figure 9. Modified hierarchical structure for the team formation problem in Example 1


18

the engineering characteristics of the car, one can prioritize the teams with respect to the components (subsystems) of the car without the need for restructuring the entire model. Such a modification reduces the size of the component (subsystem) - team member type priority incidence matrix (see the matrix in Table 6 of size (5 × 7) compared with the (18 × 7) matrix in Table 4). Moreover, in this case one team for each subsystem is formed. Table 6. Normalized weights of each team with respect to each subsystem

ME MF DE QE FE EE RE W1 W2 W3 W4 W5 W6 W7

Power brakes Transmission Engine Design Lighting system

0.0413 0.0245 0.0158 0.0120 0.0030 0.0185 0.0300 0.0206 0.0081 0.0135 0.0090 0.0020 0.0119 0.0243 0.0804 0.0514 0.0574 0.0260 0.0066 0.0254 0.0574 0.0168 0.0727 0.1302 0.0466 0.0668 0.0277 0.0584 0.0024 0.0014 0.0011 0.0043 0.0060 0.0138 0.0086

For example, if one assumes a team is required for each subsystem of the car and Table 7 shows the number of potential projects each team member type is prepared to undertake, then the model ((1) - (6)) determines optimal teams for the subsystems of the car. Table 7. Data for the modified model

Functional team type

ME MF DE QE FE EE RE Maximum number of

characteristics

4 3 5 3 3 5 4

Solving the model ((1) - (6)) for the incidence matrix in Table 6 and p = 5, results in the following solution: x11 = 1, x12 = 1, x13 = 1, x14 = 1, x15 = 0, x16 = 1, x17 = 1, x21 = 1, x22 = 0, x23 = 1, x24 = 0, x25 = 0, x26 = 1, x27 = 1, x31 = 1, x32 = 1, x33 = 1, x34 = 1, x35 = 1, x36 = 1, x37 = 1, x41 = 1, x42 = 1, x43 = 1, x44 = 1, x45 = 1, x46 = 1, x47 = 1, x51 = 0, x52 = 0, x53 = 1, x54 = 0, x55 = 1, x56 = 1, x57 = 0. Based on definition of xij the following teams are formed: T1 = {ME, MF, DE, QE, EE, RE}, T2 = {ME, DE, EE, RE}, T3 = {ME, MF, DE, QE, FE, EE, RE}, T4 = {ME, MF, DE, QE, FE, EE, RE}, T5 = {DE, FE, EE}. 8. SUMMARY A conceptual framework was presented for the selection of multi-functional teams. The QFD planning matrix was used to collect and represent data for the multi-functional team


19

selection model. The AHP was used for prioritizing team members based on the customer requirements and engineering characteristics of the product. A mathematical programming model was formulated to determine the required composition of teams. The approach presented in this chapter combines different factors (modules) of the team selection problem into a hierarchical structure of the AHP. This modularity permits a great amount of flexibility in the formation of teams, i.e., one can add an additional factor to the team selection hierarchy and perform the analysis without restructuring the entire model. Similarly, the factors can be removed when necessary. The approach presented here is perhaps the first attempt to formalize the team selection process. The methodology discussed in the chapter can be applied to numerous areas of teams' formation, including concurrent engineering. REFERENCES 1. Aczel, J., and Saaty, T. L. (1983), Procedures for Synthesizing Ratio Judgments. Journal

of Mathematical Psychology, 27, 93 - 102. 2. Arbel, A., and Seidmann, A. (1984), Performance Evaluation of Flexible Manufacturing

Systems. IEEE Transactions on Systems, Man, and Cybernetics, 14, 606 - 617. 3. Armacost, R. L. Componation, P. J., Mullens, M. A., and Swart, W., (1994), An AHP

Framework for Prioritizing Customer Requirements in QFD: An Industrial Housing Application. IIE Transactions, 26, 72 - 79.

4. Askin, R. G., and Sodhi, M. (1994), Organization of Teams in Concurrent Engineering. In Handbook of Design, Manufacturing, and Automation, Dorf, R. D., and Kusiak, A., (Eds.), John Wiley & Sons, Inc., New York, NY, 85 - 105.

5. Carter, D. E., and Baker, B. S. (1992), Concurrent Engineering: The Product Development Environment for the 1990s. Addison-Wesley, Reading, Mass.

6. Harker, D. T., (1990), Theory of Ratio Scale Estimation: Saaty's Analytical Hierarchy Process. Management Science, 36, 269 - 273.

7. Hauser, J. R., and Clausing, D. (1988), The House of Quality. Harvard Business Review, May-June, 63 - 73.

8. Handfield, R. B. (1994), Effects of Concurrent Engineering on Make-to-Order Products. IEEE Transactions on Engineering Management, 41 (4), 384 - 394.

9. Klein, M. (1993), Capturing Design Rationale in Concurrent Engineering Teams. Computer, January, 39 - 47.

10. Kusiak, A., and Belhe, U. (1992), Concurrent Engineering: A Design Process Perspective. Proceedings of American Society of Mechanical Engineers, 59, 387 - 401.

11. Kusiak, A., and Wang, J. (1993), Decomposition in Concurrent Design. In Concurrent Engineering: Automation, Tools, and Techniques, Kusiak, A. (Ed.), John Wiley & Sons, Inc., New York, NY, 481 - 507.

12. Maddux, G. A., Amos, R. W., and Wyskida, A. R. (1991), Organization Can Apply Quality Function Deployment as Strategic Planning Tool. Industrial Engineering, 23 (9), 33 - 37.

13. Madu, C. N., and Georgatzas, N. C. (1991), Strategic Thrust of Manufacturing Automation Decision: A Conceptual Framework. IIE Transactions, 23, 138 - 147.

14. Reddy, Y. V., Srinivas, K., Jagannathan, V., Karinthi, R. (1993), Computer Support for Concurrent Engineering. Computer, 1, 12 - 16.

15. Saaty, T. L. (1981), The Analytical Hierarchy Process. McGraw Hill, New York.


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16. Saaty, T. L. (1986), Axiomatic Foundation of the Analytical Hierarchy Process. Management Science, 32, 841 - 855.

17. Saaty, T. L. (1990), An Exposition of the AHP in Reply to the Paper 'Remarks on the Analytical Hierarchy Process'. Management Science, 36, 259 - 268.

18. Shoemaker, P. J., and Ward, C. C. (1982), An Experimental Comparison of Different Approaches to Determining Weights in Additivity Utility Models. Management Science, 28, 128 - 196.

19. Zahedi, F., (1986), The Analytical Hierarchy Process - A Survey of the Method and its Applications. Interfaces, 16 (4), 96 - 108.

19. Zakarian, A. and A. Kusiak (1996), An Analytical Approach to Forming Teams, Working Paper ISL-9612, Department of Industrial Engineering, The University of Iowa, Iowa City, IA.

APPENDIX: Eigenvalues and Eigenvectors Consider matrix A and identity matrix I.

A = 1 2

3 4

I = 1 0

0 1 Multiplying the identity matrix by the eigenvalue vector results in the following matrix.

λI = λ 0

0 λ To obtain eigenvalues

A-λI = 1-λ 2

3 4-λ

= (1- λ)(4 - λ) - 6 = (λ - 5λ −2) = 02

The eigenvalues are shown next.

λ 1 =5 + 33

2

λ 2 =5 − 33

2 To obtain eigenvector corresponding to the first eigenvalue AW = λ1W


21

1 2

3 4

w1

w2

= λ 1

w1

w2

+ 2 = λ 1w1 w2 w1

+ = λ 13w1 4w2 w2

=2

λ 1 − 11W ,

We can normalize W by equating its coefficients total to unity. Dividing each coefficient the sum w1+w2, which equals to, does it.

λ 1 + 1

λ 1 − 1 The resultant normalized vector is

2

λ 1 + 1

λ 1 + 1

λ 1 − 1,

QUESTIONS 1. Is the analytical hierarchical process method a subjective or an objective tool? 2. What are the basic steps of the analytical hierarchical process method? 3. What is an eigenvalue? 4. What is the consistency index and the consistency ratio? 5. What is the meaning of weight wi in matrix A? 6. What is a normalized weight? PROBLEMS 1. In the process restructuring company AA, nine (1 through 9) major tasks of equal importance have been identified. To deal with these tasks, seven (a through g) areas of expertise are needed. Each of the nine tasks may call for all seven areas of expertise. For simplicity, Figure A1 shows the relationships between all expertise areas and the first and the last task only.


22

a b c d e f g

1 2 3 4 5 6 7 8 9

Figure A1. Partial relationship between tasks and expertise areas

For each area of expertise, assume not more than four different tasks cab be assigned. Perform the following:

(a) Setup your own task-expertise area matrices using the AHP notation (checking matrix consistency is not required)

(b) Determine eigenvectors (weight vectors) without calculating eigenvalues (c) Formulate a model for optimal selection of functional areas (d) Solve the model with a computer code, e.g., LINDO. (e) How would you model the case when area of expertise b would not be applicable to

tasks 3 and 6 and area of expertise f would not be applicable to tasks 4 and 8? 2. Company BB wants to implement an integrated product and process design methodology based on multidisciplinary teams. A group of analysts has created the data in Table A1. The new multidisciplinary teams will be formed from seven functional teams (departments). Experience indicates that the number of the functional team should be responsible for a limited number of projects to be handled by his/her interdisciplinary team. These numbers are closely related to the number of product engineering characteristics and are provided in Table A2. Table A1. Normalized importance measures of functional teams with respect to engineering characteristics


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1 ME MF DE QE FE EE RE

0.00716 0.00208 0.00117 0.00358 0.00070 0.00164 0.007500.00617 0.00193 0.00108 0.00334 0.00065 0.00188 0.007040.00675 0.00211 0.00119 0.00365 0.00071 0.00206 0.007700.00816 0.00485 0.00232 0.00312 0.00070 0.00366 0.006060.01592 0.00419 0.00316 0.00762 0.00220 0.01742 0.008510.01243 0.00220 0.00220 0.00622 0.00140 0.00622 0.006220.00183 0.00610 0.00951 0.00356 0.00356 0.00074 0.001140.00850 0.00281 0.00469 0.00312 0.00081 0.00412 0.007150.01748 0.00809 0.00612 0.00743 0.00299 0.00943 0.014870.01734 0.01109 0.01238 0.00561 0.00142 0.00754 0.001390.01263 0.00469 0.03822 0.00698 0.00137 0.00889 0.003160.03240 0.02249 0.01733 0.01007 0.00423 0.01249 0.001710.01273 0.00512 0.00255 0.00837 0.00479 0.02206 0.015410.00964 0.00730 0.02095 0.02307 0.01679 0.00876 0.029210.00491 0.02044 0.03658 0.01306 0.01875 0.00778 0.016390.01245 0.00924 0.01890 0.00935 0.01681 0.00433 0.007220.00155 0.00077 0.00693 0.00260 0.00363 0.00831 0.005190.00254 0.00146 0.00508 0.00418 0.00585 0.01194 0.00468

Brakes hydraulic systemVacuumSelf adjusting brakesMaster cylinderTorque converterPlanetary gears and controlsValve bodyReverse clutchEngine lubricating systemCylinder block and headCombustion chamberValves and portingInjection systemSafety characteristicsConvenience characteristicsMaterial choiceCircuit breakersSwitches

W 1 W 2 W 3 W 4 W 5 W 6 W 7

Table A2. Functional team – number of tasks matrix

Functional team type ME MF DE QE FE EE RE

Number of functional tasks

17 14 17 10 6 14 15

Form five and eight multidisciplinary teams and comment on the differences in their composition.

3. Company CC wants to form multidisciplinary teams to be involved in four design phases of electrical products (see Table A3). The multidisciplinary teams will draw from five functional departments as listed in Table A4.

Table A3. Design steps P1: Requirements formulation P2: Systems specifications P3: Conceptual design P4: Concept refinement

Table A4: Functional departments and the number of design phases

Functional department Allowed number of design phases Mechanical engineering (ME) 3


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Systems engineering (DE) 3 Quality engineering (QE) 2 Electrical engineering (EE) 4 Industrial engineering (IE) 3

(a) Assume all necessary data and illustrate all steps of the AHP methodology leading to the

establishments of the design step - functional department matrix of priorities (weights). (b) Determine the composition of three multidisciplinary teams by formulating and solving an

integer programming model.

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