Economic evaluation and analysis of flexible manufacturing systems

79

Engineering Costs and Production Economics, 12 (1987) 79-92 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

ECONOMIC EVALUATION AND ANALYSIS OF FLEXIBLE MANUFACTURING SYSTEMS* G.J. Miltenburg Faculty of Business, McMaster University, Hamilton, Ontario L8S 4M4 (Canada)

ABSTRACT

Many researchers have reported that traditional approaches to the financial justification of FMS's tend to discourage their adoption. This paper reviews a methodology for using traditional financial evaluation models to help evaluate FMS's and uses the methodology to

determine the general conditions under which they are profitable. We suggest that when FMS's are profitable, this methodology encourages the adoption of FMS's where other traditional approaches might discourage their adoption.

1. INTRODUCTION

erly applied, encourage the adoption of FMS's. The most important property o f a FMS is its flexibility. When evaluating FMS's, the components of flexibility must be accurately modelled. Most of the FMS evaluation methods do not do this. Flexibility has three components: (1) flexibility to produce a variety of products using the same machines as well as the flexibility to produce the same product on different machines; (2) flexibility to produce new products on existing machines; and (3) flexibility of the machines to accomodate changes in the design of products (see refs. [ 7 ] and [8] for a more complete discussion of flexibility. ) There are four FMS evaluation methods that are popular today. ( 1 ). Most firms contemplating the purchase of new manufacturing systems use the "payback method". That is they calculate a payback period for each potential manufacturing system and purchase the system with the best payback. The calculations are very simple, all

Many finns have either introduced or are considering flexible manufacturing technology [1]. These firms see FMS as a means for increasing productivity, profitability and quality as well as a means of maintaining a competitive edge in the market place. Unfortunately, many researchers have reported that traditional approaches to the financial justification of FMS's tend to discourage their adoption [ 2-5 ]. Michael and Millen [ 6 ] suggest that traditional financial evaluation models are more suited to meet short-term profitability goals rather than long-term strategic goals. This paper reviews a methodology for using traditional financial evaluation models to help evaluate FMS's and uses the methodology to determine the general conditions under which FMS's are profitable. We show that traditional financial models, prop*Presented at the Fourth International Working Seminar on Production Economics, Igls, Austria, Feb. 17-21, 1986.

0167-188X/87/$03.50

© 1987 Elsevier Science Publishers B.V.

80 variables are assumed to be deterministic, account is not taken of flexibility and future uncertainties are ignored. Needless to say this is incorrect and discourages the adoption of FMS. ( 2 ) . A n o t h e r evaluation m e t h o d is the "qualitative checklist method". This method lists all the advantages and benefits, both direct and indirect, of flexible manufacturing systems and usually concludes that these systems are better than traditional systems. Another conclusion is that the firm must invest in these systems if it is to remain competitive. The calculations (if there are any) are similar to those of the first method. For an excellent discussion of some of these issues see Kulatilaka [ 9 ]. ( 3 ). A third evaluation method is the "experience method". Estimates are made for a number of variables ( such as n u m b e r of products, required volumes, future changes, etc.) and are compared to predetermined critical values. On the basis of the comparison a particular manufacturing system is recommended. There are two problems with this method. First, the evaluation method may have been developed in one industry and may not be appropriate in other industries. Second, even if the method is very good, it does not give the manufacturing manager the numbers he needs to convince financial top management. (4). The best evaluation method is the "modelling method". In this method mathematical models are developed for each manufacturing system. The models consist of both stochastic and deterministic variables, and the models capture the important flexibility components for the particular problem. Since many of the inputs are stochastic, the outputs will also be stochastic - - typically Net Present Value cumulative density functions (cdf). In this paper we review this methodology (see also Miltenburg and Krinsky [ 10]) and show that the other three evaluation methods are special cases of this method. We will also show the general conditions under which each manufacturing system is preferred. Section 2 briefly describes the traditional

financial evaluation models that will be used. Section 3 discusses mathematical models for c o m m o n flexible manufacturing systems. The methodology for the modelling evaluation m e t h o d is given in Section 4. Section 5 develops the conditions under which each manufacturing system is preferred to the other systems. 2. TRADITIONAL FINANCIAL EVALUATION MODELS

Many financial models can be used to help evaluate projects. For the problem in this paper (the firm must choose the best FMS from among a number of mutually exclusive alternatives) the Net Present Value (NPV) is the appropriate criterion. See, for example, Schall et al. [11 ]. The NPV is the difference in the present value of the after-tax cash inflows and outflows. If the NPVis positive (that is, inflows exceed outflows), the project should be accepted. Since it would be incorrect to compare the NPV's of projects having different lives, each project's NPV should be converted to an Annuity Equivalent (AE), and the AE's of the projects should be compared. The larger the AE the more attractive the project. (The AE method assumes that each project is continually replaced at the end of its useful life by a project of like profitability. This essentially converts the fixed life investment to an equivalent infinite life investment.) Based on a survey of U.S. companies, Gitman and Forrester [ 12] report that many companies use other financial criteria; namely, the Internal Rate of Return (IRR) and the Payback (PB). The IRR of a project is that discount rate which equates the present value of the after-tax cash inflows with the present value of the after-tax cash outflows. The payback (PB) period of a project is found by counting the number of periods it takes before the cumulative forecasted cashflows equal the initial investment. For the problem we are considering the IRR and PB are incorrect criteria [11]. We will concentrate on NPV and AE although, for interest sake, we will also look at IRR and PB.

81 Although the problem is formulated as cashflow maximization problem, it can, in many cases, be formulated a cost minimization problem. This would be appropriate when, for example, the sale revenues are the same for projects (and only the costs vary from project to project). The details on the financial model that will be used are described in Miltenburg and Krinsky [ 10].

seconds) for the robot to assemble one part, PQ is the part quality (the fraction of defective parts to good parts), and TD is the average downtime at a station due to a defective part. The n u m b e r of shifts SH, to be worked is selected so that there is sufficient capacity to meet the production requirements. If PSi,, is the annual production requirements for assembly i in year t, HR is the number of production hours per shift per year and PE is the

3. M A T H E M A T I C A L MODELS FOR FLEXIBLE ASSEMBLY M A N U F A C T U R I N G SYSTEMS

plant

NP

Six assembly manufacturing systems will be considered - - namely, manual assembly (MA), manual assembly with mechanical assistance (MAM), rotary or in-line indexing machines with special purpose workheads and free transfer lines with special purpose workheads (SPW), free transfer lines with robot workheads (RW), and robot assembly cells (RAC). (Figure 1 shows these manufacturing systems. ) The details of the models for these systems are given in Miltenburg and Krinsky [ 10] and are based on models developed by Boothroyd [13]. The model for the robot assembly cell (RAC) and an illustrative example are given here. The models are kept simple so that the methodology can be illustrated. The extension to more complex models is left for future research.

Robot Assembly Cell (RAC) This robot assembly cell uses two robots. Each robot has six degrees of freedom. While one robot is assembling a part, the other robot can, for example, pick up the next part. I f the assembly cell is carefully designed, the average time to complete a good assembly i, is TP~ = NA~* ( TR/2 + PQ* TD); where NAi is the number of parts in assembly i, i = 1,2...,Net, N P t is the number of different assemblies to be manufactured in year t, TR is the average time (in

efficiency,

then

~ VSi*TPJ3600 i=1

<~HR*PE*SH. (If there is insufficient capacity over 3 shifts, a second assembly cell is added.) The required initial investment per cell NP

is

I~ = 2 * C R + X

(CC+NT~*(CM+CG))

i=1

where CR is the cost of a robot, CC is the cost of a carrier, CM is the cost of the part feeding device, CG is the cost of a robot gripper, and NTi is the number of parts is assembly i that are different from parts in assemblies 1,2 . . . . . i - 1. Ifa part is redesigned then the part feeder and robot gripper will have to be changed. One supervisor is assigned to monitor each cell. The annual labour cost is NP

WT= WS* • (VSi*TPi/3600)/(HR*PE), i=1

where WS is the annual cost of a supervisor.

Example Suppose that two assemblies are to be produced in a robot assembly cell for the next seven years. Assembly 1 has NA 1= 6 parts and assembly 2 has NA2 10 parts (of which NT2 = 8 parts are different from assembly 1 ). A new assembly will be introduced in year 4. This assembly will have NA3=8 parts and NT3=6. All assemblies will have one part redesigned each year. Suppose that TR = 6 seconds, TD= 30 seconds, P Q = 0 . 0 5 , HR = 2000 hours/shift/year and P E = 0 . 9 5 . Costs are as follows: cost of robot CR=$110,000, part feeding device C M = $ 5 0 0 0 , robot gripper =

82

a) MA •

Manual Assembly

/

/

Transfer Devices (CB)

--

Human Operators (WA)

b) M A M . Manual Assembly with Mechanical assistance

lechanical Feeding Devices (CF) c,d) SPW • indexing and buffered lines with Special Purpose Workheads

Special Purpose Workhead (CW)

~ ~

~

Mechanical Part Feeder (CF) Rotary Indexing Assembly Machine

~

t

/

In-Line Transfer LJna

s) RW - transfer machine with Robot Workheads /

~

/

Assembly Robot (CR) f) RAC - Robot Assembly Cell

Assembly Robot (CR) Robot Part Magazine (CM) Work Carrier (CC) Fig. 1. Six assembly manufacturing systems.

CG= $1700, carrier C C = $1500 and the annual cost of a supervisor WS = $ 55,000. The tax rate is T X = 0.40, the robot assembly cell is

depreciated over D = 10 years and all assemblies are sold for $0.65 each. The average assembly times are then calculated: TP~ = 27

83 plete manufacturing problem are given in Tables 3 and 4. Since the approprite criterion is the annuity equivalent (AE), a transfer line with robot workheads (RW) would be the best manufacturing system. The second best system is the robot assembly cell (RAC). Notice that if the wrong criterion is used, namely IRR or PB, then the manual assembly (MA) would be selected. This is because the initial outlay is very small for manual assembly (RW would be the second choice). While obtaining estimates for all the variables in a manufacturing problem, it becomes obvious that some variables are deterministic (the value of a deterministic variable is known with certainty) while other variables are stochastic (their values cannot be estimated exactly). The mix of deterministic and stochastic variables will vary for each manufacturing problem depending upon the nature of the company and its experience with different FMS's. Although there may be many stochastic variables, some are more important than others. The sensitivity of the output variable, AE, to each of the stochastic variables can be mesured and the important stochastic variables can be identified [ 10 ]. To encode uncertainty in all of the important stochastic variables, cumulative density functions (cdf's) are estimated for each of them (by asking appropriate questions of the experts within the firm). Each important stochastic variable's cdf is then approximated by a number of discrete

seconds, TP2=45 and TP3=36. The annual production requirements are shown in Table 1. (Recall that the capacity of a shift is HR*PE= 1900 hours. ) Notice that in years 6 and 7 there is insufficient capacity with one assembly cell, and so a second assembly cell is needed. The required initial investment is It =$267,800, with additional investments of $6400 in years 2, 3 and 4 because of part design changes in assemblies 1 and 2. In year 4 assembly 3 is introduced, necessitating an investment of NT3*( CM+ GG) + CC= $20,700. An additional investment of $9600 is required in year 5 because of part design changes in the three assemblies. In year 6 a new robot assembly cell is required at cost 3

I6=2"CR+ Y~ (CC+NTi

(CM+CG))

i=l

=$288,500. As well, part design changes require an investment of $9600 for the original cell. Finally in year 7 an additional investment of 2*$9600 is required because of part changes. The cash flows are shown in Table 2. At a discount rate of 20%; NPV=$181,455.89, AE=$251,701 IRR = 0.556, PB= 1.8 years. Clearly the robot assembly cell is an excellent investment. 4. EVALUATION M E T H O D O L O G Y

Similar models and examples for the other assembly systems can be found in Miltenburg and Krinsky [10]. The results for one cornTABLE 1 Annual production requirements Year, t

1

2

3

4

5

6

7

VSt,t VS2,, VS3,t

127500 153000

140250 168300

154275 185130

169702 203643 119000

186672 224007 130900

205340 246408 143990

225874 271049 158389

2869

3156

3471

5008

5509

6060

6666

2

2

2

3

3

2

2

1

1

1

1

1

2

2

3" VSi.,*TPJ3600 SH No. cells

84 TABLE2 Cashflows Year

Revenue

1 2 3 4 5 6 7

$182325 200557.5 220613.25 320024.58 352027.03 387229.74 425952.71

Labour cost

Investment

$60400 66442 73074 105432 115979 127579 140337

$267800 6400 6400 27100 9600 298100 19200 634600

Depreciation 53560 44128 36582.4 34685.92 29668.74 83354.99 70523.99 352504.04

After tax cash flow -$173221 91720.5 96756.5 115529.9 143896.3 - 108967.6 180379.0

TABLE 3 Results of deterministic p h a s e - r e s u l t s under most likely conditions

AE ($)

Assembly system 1. 2.

3. 4. 5.

' MA

-

MAM SPW RW RAC

-

Manual Assembly Manual Assembly with Mechanical Assistance Assembly Machines with Special Purpose Workheads Assembly Machines with Robot Workheads Robot Assembly Cell

TABLE 4 Ranking FMS's from Table 3 Ranking

1 Best 2 3 4 5 Worst

Criterion

AE

IRR

PB

RW RAC MAM MA SPW

MA RW MAM RAC SPW

MA RW MAM RAC SPW

values. As many values as possible should be used. By systematically substituting all possible combinations of variable values into the models, the p d f for A E for each of the five assembly systems can be calculated. This procedure is depicted in Fig. 2. Each path represents one particular setting of all the variables. (Notice that the tree grows very rapidly when there are many important stochastic variables. If possible one should treat all stochastic vari-

251670 285819 - 678363 845477 352684

IRR (%)

44 22 4 23 18

PB (years)

3.4 >5 >6 5.06 6.1~6

ables as important. Unfortunately limited time and computer resources usually force us to identify and focus our attention on the most important stochastic variables.) This was done for the example we have been discussing. Our computer program calculated the A E cdf's shown in Fig. 3 (for each of the five manufacturing systems). Looking, for example, at the cdf for the robot assembly machine RW, we see that there is a 50:50 chance that A E will be above or below $750,000, and there is a 20% chance that A E will exceed $1.25 million. To order the manufacturing systems from best to worst, the following two step procedure is used: first is the use of first-order, second-order and third-order stochastic dominance (SD) to order the systems (see ref. [14] for a review of stochastic dominance); second, if SD does not exist between some systems, estimate the risk preferences of the decision-maker and use this to order the remaining systems. From Fig. 3, we

85 I ASSEMBLY SYSTEM

MA

IMPORTANTSTOCHASTICVARIABLES Ms

I

• . . . . PROJECT NP I NAP i...owi LIvES l K

I

ASSEMBLY I TI.ES I PO I

N.

(((4_((((

MAM

Fig. 2. Decision tree structure ( 5 × 3 X 2 s = 3840 branches). 1.0

A

~-

1.0

~ <

0.8

>

0.a 0.6

LU

~"

0.6

--.w

~

0.4 =

U.

0.4

n,,

.

-

.

-

0.2

0.2

0.0

z////

-11s -1'.o -ols o'.o o'5 1'.o l'.s AE (Annuity Equivalent),$million

2'.o ''x

Fig. 3. Cumulative density functions of annuity equivalents for five assembly manufacturing systems.

see that the transfer line with special purpose workheads, SPW, is the worst manufacturing system (using first-order SD). It appears that RW, the transfer line with robot workheads, is the best system. Unfortunately, we cannot use

0.0 -2

I

I -1

I

I 0

I

I 1

I

I 2

I 3

AE (Annuity Equivalent), $ million

Fig. 4. A typical preference curve for - 2<~AE<~3 ($ million).

SD to prove this. Since SD does not exist for RW, MA, MAM and SPW we need to estimate the risk preferences of the decision-maker (for a review of risk preference see ref. [ 15 ] ). Suppose that the decision-maker has the preference curve shown in Fig. 4. Table 5 shows the certainty equivalents for the five assembly sys-

86 TABLE5 Expected p ~ n c e s

~ r five assembly systems Assembly system

MA MAM SPW RW RAC

Annuity equivalent Mean

Variance

$ 365093 363141 -659597 891049 407069

3.650E+ 10 8.357E+ 10 2.808E+ 11 3.696E+ 11 9.770E+ 10

tems. The best assembly system is the transfer line with robot workheads, followed by the robot assembly cell, manual assembly, manual assembly with mechanical assistance and the transfer line with special purpose workheads. Finally we ask, "Should more information be gathered before the final decision is made?". It is customary to calculate the value of perfect information. This provides an upper limit on the a m o u n t of resources that can be expended in further studies and analysis to reduce the uncertainty in a variable [ 16]. In the above example, the value of perfect information is zero for all the important stochastic variables (considered alone). Eliminating the uncertainty in any one stochastic variable does not change the decision. The best assembly system is still RW. However with perfect information about VSi, t and MGROWi, t (the total annual demands and the annual market growth rates) the best FMS might be RAC. The value of perfect information about VS and M G R O W is AE(perfect information about VS and MGROW) - AE(no information) = $ 9 0 8 , 4 5 0 - $891,049 = $17,401 where the first term is obtained by revising the original decision tree and the second term is the expected A E of the best decision from the original tree (Table 5). Decision If all uncertainty could be eliminated about future demands, at a cost of less than

Expected preference

Certainty equivalent

Rank

0.5716 0.5705 0.3454 0.6673 0.5790

361982 356459 -681874 862123 399259

3 4 5 1 2

$17,401.37 then it would be profitable to do the necessary studies. A study which would eliminate part of the uncertainty would be worth less. It is unlikely that such studies could be done for less than $17,401.37. If this is the case, the final decision should be made. In this example the "best" decision is to use a transfer line with robot workheads (RW) to manufacture all assemblies. 5. CONDITIONS UNDER W H I C H ONE TYPE OF FMS IS PREFERRED TO OTHERS To determine the conditions under which one manufacturing system is preferred to all other systems a 2 6-1- experiment was run. The experiment consists of 32 problems, each of which is characterized by six factors. They are: A (Volume) =Initial total annual d e m a n d for each assembly. B (NP) = Initial number of assemblies to be manufactured. C (NAP) = N u m b e r of additional new assemblies to be manufactured over the next five years. D(PQ) = P a r t quality, the ratio of faulty parts to good parts. E (ND) = N u m b e r of part design changes over the next five years. F ( M G R O W ) = A n n u a l growth in market size for each assembly. The output for each problem is the cumulative density function of the annuity equivalent AE,

87 for the manufacturing system under consideration. The six input factors ( A - F ) influence the output response. We wish to determine the individual effect of these factors, as well as whether the factors interact with each other. An economical way to do this is to select two levels ( + and - ) for each factor. The levels are selected to encompass the range of interest for each factor. The factor levels are given in Table 6. We then analyze the problems formed from combinations of the factor levels, to determine the effects of the factors on the output response variable. The main effect of a factor j, ej, is the average change in the response due to a change in j; that is the difference between the average response when j is at its ( + ) level and the average response when it is at its ( - ) level. It could be, however, that the effect of factor j l , depends on the level of some other factor j2. This interaction is called the two-factor interaction effect ej~jz and is defined to be half the difference between the average effect of factor j l , when j2 is at its ( + ) level (and all other factors other than j 1 and j2 are held constant), and the average effect o f j l when j2 is at its ( - ) level. Similarly, we an calculate three-factor interactions and four-factor interactions ( for a review of these concepts see ref. [ 17 ]). Rather than analyze all possible combinations of the factor levels (a complete 2 6 factorial design experiment) we will use a 2 6-p fractional factorial design experiment. This reduces the number of problems that need to be analyzed from 2 6 to 2 6-p. p is determined by making certain assumptions about higher order interactions. In a 2 6-p experiment some interactions will be "aliased" with other interactions. We might, for example, wish to calculate the AD interaction effect, but find that the interaction we calculate is actually AD + BCEF. If four-factor interactions are negligible then we have a good estimate for the AD interaction effect. After considering a n u m b e r of possible frac-

tional factorial designs in light of the above concepts, a 2 6-~ experimental design was selected. The subscript V indicates that this design is a resolution Vdesign. (No main effect or two-factor interaction is aliased with any other main effect or two-factor interaction.) As we shall see the higher-order interaction effects are negligible. Table 7 shows the actual experimental design and Table 8 shows the alias structure. As mentioned, the output response variable is the cdf of the annuity equivalent for each FMS. A cdf is described by a number of values including a mean, standard deviation, etc. Suppose we are only interested in the effects of the six factors on the mean annuity equivalent ~TE. The mean annuity equivalents for the 26-1 experiment are shown in Table 9, while Table 10 gives the main effects and interaction effects. The first row in Table 10 is read as follows. Increasing the initial total annual market d e m a n d for each assembly from the low level ( - ) to the high level ( + ) increases the annuity equivalent by $317,885 for the manual system, $594,715 for the manual system with mechanical assistance, by $1,201,646 for the assembly line with hard automation, $1,219,370 for the line with robotic automation, and by $567,500 for the robot assembly cell. The conclusion is that if the required production volumes are high, an assembly line with either hard or robotic automation should be considered. Similarly, factor B is interpreted as: if many different assemblies are to be produced (NP is high) then an assembly line with robotic automation will be profitable, while an assembly line with hard automation will be very unprofitable. Obviously, factor A, the initial total annual d e m a n d for each assembly, is the most important factor for all systems. It has a large effect on both the assembly line with hard and robotic automation, and a small effect for the robot assembly cell and the two manual assembly systems. Another interesting result is the effect of factor D, part qual-

88 TABLE 6 Factor levels for FMS experiment A Factor

Level

Value Assembly

A (Volumes) +

Total Annual Market Demand (units)

Probability

900,000

1,000,000 1,000,000 650,000 400 000 600 000 400 000 900 000 850 000 500 000 700 000 450 000 350 000 200 000 400 000 200 000 600 000 600 000

B (NP)

NP 5 3

Probability 1.0 1.0

C (NAP)

NAP 1,1,1,0,1 2,1,1,0,1 0,1,0,1,0

Probability 0.4 0.6 1.0

[32 0.005 0.05

Probability 1.0 1.0

ND 2,2,2,2,2 3,3,3,3,3 4,4,4,4,4 1,1,1,1,1 2,2,2,2,2

Probability 0.3 0.4 0.3 0.6 0.4

MGROW 0.15 0.07

Probability 1.0 1.0

D

(PQ)

E (ND)

F (MGROW)

+ -

ity. If part quality is high then the robotic assembly cell and the hard automation line become attractive manufacturing systems. Notice (from Table 10) that relative tO the main effects the two factor interaction effects

1.0

1.0

are small and the three factor interaction effects are negligible. Our assumption that three factor and higher order interactions are negligible seems to be reasonable. Other experiments were run using different

89 TABLE

TABLE8

7

2 6-~ E x p e r i m e n t a l

Problem

design

Aliasst~cture~r2~tdesi~

experiment

Factor

A l

for FMS

.

B .

C

.

.

2

+

.

D

.

E

F=ABCDE

.

. -

A

BCDEF

B

ACDEF ABDEF

+

D

ABCEF

+

E

ABCDF

F

ABCDE CDEF

3

-

+

-

4

+

+

.

5

-

-

+

-

-

+

AB

6

+

-

+

-

-

-

AC

BDEF

7

-

+

-I-

-

-

-

AD

BCEF BCDF

.

-

Alias

C

.

.

Effect

.

.

8

+

+

+

-

-

+

AE

9

-

-

-

+

-

+

AF

BCDE

10

+

-

-

+

-

-

BC

ADEF

11

-

+

-

+

-

-

BD

ACEF

12

+

+

-

+

-

+

BE

ACDF

13

-

-

+

+

-

-

BF

ACDE

14

+

-

+

+

-

+

CD

ABEF

15

-

+

+

+

-

+

CE

ABDF

16

+

+

+

+

-

-

CF

ABDE

17

.

+

+

DE

ABCF

18

+

-

-

-

+

-

DF

ABCE

19

-

+

-

-

+

-

EF

ABCD

20

+

+

-

-

+

+

ABC

DEF

21

-

-

+

-

+

-

ABD

CEF

22

+

-

+

-

+

+

ABE

CDF

23

-

+

+

-

+

+

ABF

CDE

24

+

+

+

-

+

-

ACD

BEF

25

-

-

-

+

+

-

ACE

BDF

26

+

-

-

+

+

+

ACF

BDE

27

-

+

-

+

+

+

ADE

BCF

28

+

+

-

+

+

-

ADF

BCE

29

-

-

+

+

+

+

BCD

AEF

30

+

-

+

+

+

-

BCE

ADF

31

-

+

+

+

+

-

32

+

+

+

+

+

+

.

.

.

output response variables (the variance o f the annuity equivalent, and the ratio o f the mean to the variance) and different factor values. The conclusions were as follows.

(Table7)

profitable, even when part quality is low and when the number of part design changes each year is high.

Manual assembly with mechanical assistance

Manual assembly system A manual assembly system is best when the number o f different assemblies to be manufactured is not high, the number o f new assemblies to be added in the future is not high, the production volumes are low, and the annual market growth is small. Manual assembly is

A manual assembly system with mechanical assistance is best when the number o f different assemblies to be manufactured is low, the number o f new assemblies to be added in the future is not high, the number o f part design changes each year is not high, the production volumes are low to medium, and the annual

90 TABLE9 Expefimentalresults, AE(meanannuityequivalent)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Manual

MMA

Hard

R Line

R Cell

260,010. 4 536,313.3 315,378.1 547,173.8 308,948.7 530,295.0 407,878.5 814,537.4 310,979.6 535,418.8 314,196.8 749.032.9 307,819.3 640,700.7 542,00~.2 854,747.6 257,650.4 458,382.6 254,646.1 620,195.7 253,620.4 602,634.6 448,693.2 722,275.1 248,742.2 637,454.5 383,313.5 663,176.5 328,117.1 625,379.7 478,911.6 968,814.3

128 033.8 765 148.9 242 366.6 652 237.3 251 401.6 593 296.4 209 640.1 1,090 083.8 287 653.3 628 308.6 146 480.3 971 810.2 163 142.5 952 913.2 441 992.9 949 567.7 129 688.7 450 972.6 - 7 9 307.4 691 141.5 - 4 1 629.4 685 397.5 150 837.1 629 454.5 49,556.5 729,236.5 128,168.3 556,987.1 151,495.5 566,086.0 44,998. i 1,006,425.5

-731,452.8 494,277.0 - 929,010.8 - 283,778.2 - 867,179.9 - 252,942.6 - 1,639,609.3 97,943.9 - 217,596.7 426,982.1 979,662.5 997,587.8 882,832.1 971,980.5 - 778,651.5 159,750.3 848,658.5 - 347,813.0 1,844,604.8 - 270,340.8 - 1,696,425.7 -224,774.3 - 1,945,425.6 1,217,455.5 - 913,055.9 609,860.5 1,139,985.8 - 350,001.5 1,018,058.4 -215,013.5 1,908,812.8 288,956.0

283,758.5 1,703,341.5 862,240.3 1,561,705.2 819,068.1 1,503,892.6 761,252.3 2,604,735.0 695,372.1 1,295,547.7 526,704.5 2,397,797.9 526,786.1 2,332,376.7 1,406,362.1 2,310,308.2 488,818.2 1,037,205.6 236,116.4 1,916,202.9 205,340.7 1,779,955.9 936,622.5 1,686,828.4 218,222.0 1,775,123.1 795,264.3 1,539,734.1 766,980.4 1,508,134.6 614,771.4 2,745,707.9

259 872.6 900 667.1 348 639.1 502 848.6 302 784.9 496 445.5 103 511.9 742 307.4 842 875.5 1,172,220.9 683,016.1 2,053,378.9 663,666.5 1,918,463.9 1,191,547.4 1,629,538.9 175 367.1 343 952.8 - 7 2 221.3 341 373.7 - 6 9 571.6 391 844.8 164 996.5 166 489.9 405 953.6 1,549,652.7 774,354.0 1,042,437.7 730,492.6 1,043,255.6 511,848.9 1,805,253.8

market growth is medium. This system is profitable even when part quality is low.

Hard automation assembly line A hard automation assembly line is best when the production volumes are high, the annual market growth is large, the n u m b e r of different assemblies to be manufactured is low, the number of new assemblies to be added in the future is low, the n u m b e r of part design changes each year is low, and the part quality is high.

Robot assembly line A robot assembly line is best when the production volumes are high, the annual growth is

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-

-

-

-

-

-

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large, the n u m b e r of different assemblies to be manufactured is high, the number of new assemblies to be added in the future is high, the n u m b e r of part design changes each year is low to medium, and the part quality is not low.

Robot assembly cell The robot assembly cell is best when the conditions are such that there will be very high utilization of the cell. If conditions are such that there is poor utilization of the cell then another manufacturing system will be better. If many cells are needed then a robot assembly line or hard automation assembly will be better. With this in mind, the robot assembly cell is

91 TABLE 10 Effects and interaction results for A E Effect

Manual

MMA

Hard

A B C D E F AB AC AD AE AF BC BD BE BF CD CE CF DE DF EF ABC ABD ABE ABF ACD ACE ACF ADE ADF AEF BCD BCE BCF BDE BDF BEF CDE CDF CEF DEF

317,885.4 140,190.2 108,923 78,102.0 - 1,497.8 62,596.9 31,549.0 17,539.0 27,195.2 12,691.9 16,439.9 64,852.6 24,757.4 815.3 12,205.5 4,098.9 4,187.6 - 3,407.0 11,374.4 3,905.7 5,120.5 3,749.3 2,707.7 - 9,902.0 75.5 - 4,421.1 4,324.0 - 2,132.4 6,162.6 - 3,622.5 - 5,814.0 Aliased with AEF Aliased with ADF Aliased with ADE Aliased with ACF Aliased with ACE Aliased with ACD Aliased with ABF Aliased with ABE Aliased with ABD Aliased with ABC

594,715.5 83,942.6 85,470.1 76,572.5 - 164,091.8 189,302.3 63,213.4 43,065.3 23,765.4 3,021.2 43,966.2 66,282.0 5,812.2 - 32,955.0 12,406.3 11,832.6 - 18,392.4 12,809.2 477.4 6,268.8 -2,393.2 6,246.7 -906.6 - 1,122.0 - 2,646.0 6,794.7 4,613.6 3.251.4 -372.9 321.9 - 3,700.0

1,201,646 - 376,906 - 300,087 472,424.8 - 539,219.7 493,597 121,919.3 91,546.1 139,448.4 -- 3,078.2 137,123.4 32,136.2 67,770.3 - 89,823.0 54,546.5 72,986.2 - 53,976.5 28,657.1 - 3,738.9 53,495.3 -514.9 - 14,663.4 12,837.4 2,034.4 16,141.2 15,866.1 10,019.5 5,564.5 9,588.0 27,451.1 3,290.9

-

best when the production volumes are low to medium, the number of different assemblies to be manufactured is low to medium, the number of new assemblies to be added in the future is low, the number of part design changes each year is low, and the part quality is high. The combination of required volumes and number of assemblies must result in good utilization of

R Line 1,219,370 369,839 326,310.5 - 205,951.2 510,291.3 108,590.7 79,913.6 74,913.6 - 9,150.3 91,194.3 77,542.2 32,424.2 - 39,030.9 43,147.8 44,647.2 -40,978.6 18,395.5 15,036.7 36,555.7 3,873.9 - 167.6 9,737.2 7,614.2 - 3,166.2 21,773.9 1,591.2 - 6,478.1 8,232.2 11,278.9 5,912.2

R Cell 567,500.1 12,400.8 - 12,156.0 848,850.8 - 323,079.1 334,606.8 4,367.3 6,416.9 233,806.0 - 59,994.5 120,234.7 9,491.6 158,198.4 - 74,823.0 22,562.7 133,428.2 - 47,749.4 3,579.7 36,646.9 129,653.2 - 14,086.1 13,890.1 36,787.4 - 18,477.9 6,090.4 17,016.4 2,600.3 5,358.7 13,176.3 25,329.3 15,486.7

the cell. The annual market growth should be medium to large and should help improve the utilization of the cell. 6. CONCLUSION It is difficult to evaluate FMS's for a particular manufacturing problem because there is

92 much uncertainty about the amount of flexibility required (demands, new products, and product changes), about the financial variables (discount rate, tax rate, etc.) and about the production variables (assembly times, quality, etc.). Only modelling can capture the components of flexibility and the future uncertainties. Modelling should be used to help evaluate FMS's. The models used in this paper were kept simple so that the methodology can be illustrated. The extension to more complex models (to include dependencies between variables, marketing effects, R and D, etc.) is left for future research.

ACKNOWLEDGEMENTS This research was supported, in part, by grant A5474 from the Natural Sciences and Engineering Research Council of Canada.

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