1987 Evaluating Flexible Manufacturing Systems

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Evaluating Flexible Manufacturing SystemsG. John Miltenburg a & Itzhak Krinsky ba Production and Management Science Faculty of Business, McMaster University Hamilton,Ontario, Canada, LSS 4M4b Finance and Business Economics Faculty of Business, McMaster University Hamilton,Ontario, Canada, L8S 4M4Version of record first published: 09 Jul 2007.

To cite this article: G. John Miltenburg & Itzhak Krinsky (1987): Evaluating Flexible Manufacturing Systems, IIETransactions, 19:2, 222-233

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Evaluating Flexible Manufacturing Systems

G. JOHN MILTENBURG Associate Professor of Production and Management Science

Faculty of Busin<ss, McMaster University Hamilton, Ontario, Canada, L8S 4M4

ITZHAK KRINSKY Associate Pmfersor of Finance and Business Economics

Faculty of Business, McMarter University Hamilton, Ontario, Canada, L8S 4M4

Abstract: Many firms are considering Flexible Manufacturing Systems (FMS) as a means for increasing productivity, quality and profitability. In this paper a methodology for properly comparing and evaluating FMS's is presented. The appropriate financial criteria are presented. Mathematical models of different FMS's are presented. The important stochastic variables are determined. The principles of stochastic dominance, risk preference and the value of information; and a decision analysis cycle are used to evaluate the FMS's.

A Flexible Manufacturing System (FMS) can be described as a set of transformation stations on which a variety of parts are automatically processed and between which parts are automatically transported. FMS's are considerably more complex than this definition suggests. An overview of the technology, and descriptions of FMS's can be found in several articles. (A summary of some of the theoretical work that is currently being done on FMS's can be found in [17], and in recent articles in the Journal of Manufacturing System 11982 on].)

Many firms have either introduced or are considering flexible manufacturing technology (Suri and Whitney 1211). These firms see FMS as a means for increasing productivity, profitability and quality as well as a means of maintaining a com- petitive 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. (See, for example, Kaplan 1121, Burstein and Talbi [5], Gold [lo], and Suresh and Meredith [20].) Michael and Milen 1151 suggest that traditional financial evaluation models are more suited to meet short-term profitability goals rather than long-term strategic goals. This paper presents a methodology for using traditional financial evaluation models to help evaluate FMS's. It is argued that when these models are properly used, they do indeed encourage the adoption of FMS's.

The most important property of a FMS is its flexibility. Flexibility has three components. (1) There is the flexibility to produce a variety of products using the same machines as

Received February 1985: revised August 1985, F e b w 1986, and June 19.36. Handled by the Manufacturing and Automated Production Department.

well as the flexibility to produce the same product on different machines. (This allows firms to easily increase or decrease production capacity.) (2) There is the flexibility to produce new products on existing machines, and (3) there is the flexibility of the machines to accomodate changes in the design of products. (See Buzacott [6] and Browne et al. [4] for a more complete discussion of flexibility.) When evaluating FMS's, these components of flexibility must be accurately modelled.

In this paper we propose a methodology for selecting from among a number of flexible manufacturing systems. Com- ponents of the methodology include:

1) using deterministic variables, stochastic variables, and models to capture the nature of each manufacturing system;

2) using the correct financial criterion-discounted cash flows;

3) a mechanism for screening the more important stochastic variables from the less important (so that attention can be directed to the important variables);

4) a framework for doing sensitivity analysis and determining the value of attempting to reduce the amount of uncertainty in the problem (value of information);

5) a mechanism for taking account of the risk attitudes of the decision makers.

Although other researchers use some of these components (Knott and Getto 1131, Suri and Hildebrant 1221); most researchers assume that the problem is deterministic (Booth-

222 0470-817X~85M600-01821$2200i0 O 1987 " I I E Volume 19, Number 2, IIE Transactions, June 1987

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royd [3]), use the wrong financial criterion (Dorf [$I), or consider primarily the qualitative aspects of the problem (Ar- be1 and Seidmann [I], Kulatilaka [14]).

Failure to accurately model and capture the nature of a FMS, and using the wrong financial criterion, are, in our opinion, the primary reasons why FMS's seem to be difficult to justify.

There are two kinds of manufacturing systems that can be considered-assembly systems and forming systems. Assem- bly systems assemble components into final products while forming systems actually form components or final products. This paper evaluates only assembly manufacturing systems because assembly activities are similar in most manufacturing firms. The methodology suggested below captures the nature of each manufacturing system better than any other methodology we are aware of. It integrates all the key demand conditions (volumes, number of products, growth), engineering variables (cycle time, capacity, quality, etc.) and financial variables (taxes, interest rate, depreciation, etc.).

The next section briefly describes and justifies the financial evaluation model that will be used. Then mathematical models for six flexible manufacturing systems are presented. (The systems differ in the "amount" of flexibility that they have.) This is followed by a review of the methodology, and an illustration of the complete methodology with a worked example. The final section summarizes the results in this paper and describes possible extensions.

Traditional Financial Evaluation Models

Many financial models can be used to help evaluate projects. For the problem in this paper (the Iinn must choose the best FMS from among a number of mutually exclusive alter- natives) the Net Present Value (NPV) is the appropriate criterion. See, for example, Schall et al. [19]. The Net Present Value (NPV) is the difference in the present value of the after-tax cash inflows and outflows. If the NPV is positive (that is, inflows exceed outflows), the project should be ac- cepted. Since it would be incorrect to compare the NPVs 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 A E the more attractive the project. By so doing, we assume a like-for-like replacement of projects system because of the difficulty of determining the costs of acquiring and operating future gen- erations of manufacturing systems. The alternative to AE is the NPV common life multiple technique which uses an evaluation internal equal to the lowest common multiple of the lives of the projects under consideration. (In the example, which follows, the lowest common multiple is 840 years.) Hence, A E simplifies the computations. Based on a survey of U.S. companies, Gitman and Forrester [9] reveal that some firms use other criteria. Namely, 53.6 percent of the companies use the Internal Rate of Return (ZRR) and 8.9 percent use the Payback (PB) as their primary technique for evaluating projects. 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. On the sur- face ZRR and NPV look the same. However, as pointed out by Copeland and Weston 17, p. 551, only "the NPVmle avoids all the problems which the IRR is heir to. It obeys the value additivity principal, it correctly discounts at the opportunity cost of funds, and, most importantly, it is precisely the same thing as maximizing the shareholders' wealth." 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. (Some companies discount the cashflows before they compute PB.) In any case, the PB and the discounted P B rules depend on an arbitrary cutoff date, beyond which the project will be rejected, and ignore all cashflows after that date. We will concentrate on NPV and A E although, for interest sake, we will also look at IRR and PB.

The details of the specific financial model that is used are described in Appendix 1.

Mathematical Models for Flexible Assembly Manufacturing Systems

Six assembly manufacturing systems will be cons ide re6 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.) Consider the production of a family of assemblies where each assembly consists of a number of parts. The assembly is produced on one of the above assembly systems. Assume that a number of different assemblies are to be produced in year 1. The number of assemblies (NP,), the number of parts (NAj) in each assembly i ( i = 1, 2, . . . , NP,), and the production requirements for each assembly (VS,,,), may or may not all be known. The manufacturing system consists of a number of stations and at each station NS parts are assembled. Each station has a "workhead"-either a human operator (WA), a special purpose workhead (CW), or a rohot (CR). The work-in-process is mounted on a work carrier or pallet (CC), and is transferred from one station to the next by a transfer device (CB or CT). The production schedule is as follows. Set up and produce the entire year's requirements for assembly 1. Then change over for assembly 2 and produce the entire year's requirements for assembly 2. Continue for the entire family of assemblies. The more flexible assembly systems can be changed over to manufacture all assemblies. (The transfer devices, the robots and the assembly operators can be reused. However, the work carriers (CC), the mechanical feeding devices (CF), the robot part magazines (CM) and the robot grippers (CG) must he changed.) If non-programmable automation (SPW) is used, then a different assembly system is required for each assembly. Up to three s h i s (SH = 3) can he used to produce the total requirements for all assemblies. During the life of an assembly, a number of parts may he redesigned (for marketing considerations). If this happens

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a) MA - Manual Assembly model for the Robot Assembly Cell and an illustrative ex- Work Carriers (CC, ample are given here. (In what follows the subscript 1 (year)

will be suppressed for clarity.)

b) MAM - Manual Assembly with Mechanical assistance Robot Assembly Cell, RAC (Figure 1-f)

The robot assembly cell uses two robots. Each of these sophisticated robots has six degrees of freedom. While one robot is assembling a part, the other robot can change grippers

Mechanical Feeding Oevicer (CF) rn and pick up the next part. If the assembly cell is car?fully designed, the average time to complete a good assembiy i, is

c,d) SPW . indexing and buflered lines wiln Special Purpose Workheads TPi = NAi * (TRE + P Q * TD); where TR is the average

e) RW . iransfer machine with Robot Workheadr

Assembly Robot lCRl

f l RAC - Rabol Assembly Cell

Asasmbly Rob3 (CRI

Roo04 Pad Magszine lCMl

Work Carrier iCCl

Figure 1. 6 Assembly Manufacturing Systems

some of the assembly equipment must be changed--specif,- cally the carriers (CC), partfeeders (CF), robot grippers (CG), robot part magazines (CM), and the special purpose workheads (CW). In addition, if some of the assemblies have common parts (NT), the automatic feeding devices (CF) , robot grippers (CG) and robot part magazines (CM) can be reused.

For the sake of analytical tractability we will use these simple models. (The extension to more complex models is left for future research.) For example, producing the entire year's requirements in a single run, overlooks inventoq lot sizing considerations, production scheduling, etc. Concep- tually, it is a straightfonvard task to add more variables and make other assumptions so that the models are more appropriate for a particular firm. This is suggested in the final section.

The details of the models for all the assembly systems (except the Robot Assembly Cell) are given in Appendix 2. The

time (in seconds) for the robot to assemble one part, PQ is the part quality (the fraction of defective pans to good parts), and TD is the average downtime at a station due to a defective part. S H is selected so that the required production capacity does not exceed the available capacity. That is s VSi * TP;I i" i = l

3600) s HR * PE * SH; where HR is the number of pro-

duction hours per shift, and PE is the plant efficiency. (Of course if there is insufficient capacity over 3 shifts, a second assembly cell would be added.) The required initial invest-

NP ment per cell is I1 = 2 * CR + 1 (CC + NTj * (CM +

i = l

CG)) where CR is the cost of a robot. If a part is redesigned then the pan feeder (CM) and robot gripper (CG) will have to be changed. If one supervisor is assigned to monitor each

NP cell, the annual labour cost is WT = WS * (VS, * TPjI

i = l

3600)l(HR * PE), 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, = 6 parts and assembly 2 has NA2 = 10 parts (of which NT2 = 8 pans 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, PQ = 0.05, HR = 2000 hourdshiftlyear and P E = 0.95. Costs are as follows-cost of robot CR = $110000, robot pan magazine CM = $5000, robot gripper CG = $1700, carrier CC = $1500 and the annual wst of a supervisor WS = $55000. The tax rate is TX = 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 TP, = 27 seconds, TP2 = 45 and TP3 = 36. The annual production requirements are:

22A 1IE Transactions, June 1987

Year, t VSI,~ J's29

vs3,t X VS;,, * TPi13600 No. shifts, S H No, cells

1 2 3 4 5 6 7 127500 140250 154275 169702 186672 205340 225874 153000 168300 185130 203643 224007 246408 271049

119000 130900 143990 158389 2869 3156 3471 5008 5509 6060 6666 2 2 2 3 3 2 2 1 1 1 1 1 2 2

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(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 II = $267800, 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 + CG) + CC = $20700. An additional investment of $9600 is required in year 5 because of pan design changes in the three assemblies. In year 6 a new robot assembly cell is required

3 at cost Z6 = 2'CR + (CC + NTi(CM + CG)) = $288500.

i = l

As well, pan 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. Using equations A1 to A7 (from Appendix l ) with this model gives:

then determined. The next (informational) phase uses the results of the first two phases to determine the economicvalue of eliminating uncertainty in each of the important variables. If there are profitable sources of information, then the decision should be to gather the new information. Hence the design and execution of the information-gathering program follow. Often the new information requires revisions to the original analysis and so the first three phases are repeated. (Usually the modifications are slight.) This iterative procedure is repeated until there are no longer any profitable sources of new information. At this point the principles of stochastic dominance and risk preference are used to determine the "best" decision from the probability distributions of the outcome variable for each alternative. (For additional information see, for example, Howard and Matbeson [ l l ] or Raiffa [IS].)

Year Revenue REV,

$182325 200557.5 220613.25 320024.58 352027.03 387229.74 425952.71

Labour Cost LAB,

$60400 66442 73074

105432 115979 127579 140337

Investment Depreciation 1, DEP,

$267800 53560 6400 44128 6400 36582.4

27100 34685.92 9600 29668.74

298100 83354.99 19200 70523.99

634600 352504.04

After Tax Cash Flow, A TCF, - $173221

91720.5 96756.5

115529.9 143896.3

- 108967.6 180379.0

At a discount rate of 20%; Selecting the Assembly Manufacturing System NPV = $181455.89, A E = $251701 IRR = 0.556, PB = 1.8 years. We will now use the methodology and the models of the

previous sections, to select the "best" assembly manufactur- Clearly the robot assembly cell is an excellent investment. ing system.

Methodology

The methodology takes the form of an iterative procedure called the Decision Analysis Cycle (see Figure 2). The procedure is divided into three phases. In the first (deterministic) phase, the variables affecting the decision are defined and a model showing the relationships between the variables is developed. The impoltance of each variable is also determined. In the next (probabilistic) phase uncertainties (that is, prob- abilities) are encoded on the more important variables. The associated probability distribution of the outcome variable is

i) Deterministic Phase For the financial model and the assembly system models

discussed previously, the decision maker's specialists are asked to provide estimates for the most likely values of all the variables. For the sake of illustration, suppose they gave the most likely values listed in Appendix 3 (Deterministic Variables). Substituting these estimates into the models of the previous sections, gives the results shown in Tables 1 and 2. Since the appropriate criterion is the Annuity Equivalent (AE), a Free Transfer Line with Robot Workheads (RW) would be the best manufacturing system. The second best

- Figure 2. The Decision Analysis Cycle p. 9, Howard and Matheson [I9831

June 1987, IIE Transactions

PRIOR INFORMATION I)

A

INFORMATION GATHERING

DETERMINISTIC PHASE

PROBABILISTIC INFORMATIONAL PHASE PHASE

. DECISION I) ACT

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Table 1. Results of Deterministic Phase--Resuits Under Most Likely Conditions Assembly System AE IRR PB 1. MA-Manual Assembly $251 670 44% 3.4 years 2. MAM-Manual Assembly with Mechanical Assistance 285819 22 >5 3. SPW-Assembly Machines with Special Purpose Workheads -678363 4 >6 4. RW-Assembly Machines with Robot Workheads 845477 23 5.06 5. RACRobot Assembly Cell 352684 18 6,16

system is the Robot Assembly Cell (RAC). Notice that if the wrong criterion is used-namely IRR or PB-then the Man- ual Assembly (MA) would he selected. This is so because the initial outlay is smallest for Manual Assembly. (The second choice would be RW.) For the rest of this paper we will limit our attention to the Annuity Equivalent (AE), since it is the appropriate criterion.

While estimating the most likely values it becomes evident 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). To illustrate; suppose the decision-maker's experts gave the most likely values and ranges shown in Appendix 3 (Sto- chastic Variables). That is, eighteen of the variables are deterministic while sixteen are stochastic. (Of course, the mix of deterministic and stochastic variables will vary from firm to lirm depending upon the nature of the firm and its expe- rience with different FMS's.)

Although there are many stochastic variables, some are more important than others. The sensitivity of the output variable A E to each of the stochastic variables is then mea- sured so that the important stochastic variables can be identified. (If the output variable is sensitive to changes in a stochastic variable, then the stochastic variable is called an important stochastic variable.) Table 3 shows the sensitivities, for the estimates in Appendix 3. These sensitivities were calculated as follows. A stochastic variable was set to its low value and all other variables were set to their most likely values. Using the models of the previous sections, AE's were calculated for all five assembly systems. The average AE, E; the mean absolute deviation of AE, MAD; and the ratio MAD/= were then calculated. (This ratio is a measure of risk per unit of return.) The stochastic variable was then set to its high value and the procedure was repeated. Then the average ( M A D I E ) , based on all the high, low and most likely values, is calculated. Those stochastic variables which produce a large average (MAD/=) are called important stochastic variables because they have an important effect on the variabilities of the AE's for the five assembly systems. The stochastic variables which produced a small average ( M A D I E ) do not have an important effect on the variability

of the AE's and so can be treated as deterministic variables. An alternative procedure would be to treat each FMS sep- arately and pick the important stochastic variables for each FMS, rather than for all FMS's. There are other more sophisticated procedures for determining the relative importance of the stochastic variables. The above procedure has the advantage that it is accurate, it takes both risk and return into account and it is easy for a decision-maker to understand.

Table 3 shows that the most important stochastic variable is the annual demand for the assemblies, MS. Other stochastic variables such as market share, MSHARE, and market growth, MGROW, which affect the annual demand, are also very important. (These three variables emphasize the great importance of demand.) Next in importance are the project lives and the risk-free interest rate, IR; followed by the number of new assemblies introduced each year, NAP, and the number of annual part design changes, ND. Finally there are the other production variables such as assembly times, part quality, etc. Notice that the important stochastic variables are either variables which measure the "required flexibility" of the assembly system, or are financial variables. (Recall that flexibility has three components-flexibility to meet changing demands (MS, MSHARE, MGROW): flexibility to accom- modate new products (NAP); and flexibility to modify products (ND).)

To summarize; in the deterministic phase a model was developed, a most likely case was analyzed, and the important stochastic variables were identified.

ii) The Probabilistic Phase Since some of the variables are stochastic, the output var-

iable, AE, for each assembly system will also be stochastic.

Table 2. Ranking FMS's From Table 1

Table 3. Deterministic Phase Results-Sensltivities of AE's to Stochastic Variables

Variable Average (MADIE) '100 Rank ,

NP 11.78 10 NAP 25.10 4 MS 69.15 1 MGROW 6.27 It MSHARE 18.27 6 Project Life 32.22 2 TX 12.76 9 k 31.25 3 TA 30.66 TM 29.22 7 TW 2.98 TR 17.45 TD 4.11 PE 6.27 12 PO 13.59 8 ND 23.88 5

Ranklng I-Best 2 3 4 s w o r s t

226 IIE Transactions, June 1987

Criterion AE IRR PB RW MA MA RAC RW RW MAM MAM MAM MA RAC RA C

SPW SPW SPW

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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. By systematically substituting all possible combinations of variable values into the models, the cdf for AE for each of the five asembly systems can be calculated. This procedure is depicted in Figure 3. 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 variables as important stochastic variables. Unfortunately Limited time and computer resources usually force us to iden- tify and focus our attention on the important stochastic variables.) Each important stochastic variable's cdf is then approximated by a number of discrete values. As many values as possible can be used. For illustrative purposes, three branches are nsed for the annual demand MS, and two branches are used for NP, NAP, MGROW, Project Lives, k, TA, TM, TW, TR, PQ and ND. (The number of branches depends upon the importance of the stochastic variable, the nature of its distribution, and the available computer re-

sources.) The variables PE, TD and TX will be treated as deterministic variables. Although they are stochastic variables, they are not important stochastic variables (Table 3) and the ranges of possible values for these variables are rel- atively small (Appendix 3).

Using the cdf s from Appendix 3, our computer program calculated an A E cdf for each of the five manufacturing systems. (See Figure 4.) Looking, for example, at the cdf for the robot assembly machine we see that there is a 50:50 chance that A E will be above or below $750000, and there is a 20-percent chance that AE will exceed $1.25 million. To order the manufactnhg systems from best to worst, the following two step procedure is used. First; use first-order, second-order and thid-order stochastic dominance (SD) to order the systems. (See, for example, Bawa [2] for a review of stochastic dominance..) Second; if SD doesn't exist between some systems, estimate the risk preferences of the decision- maker and use this to order the remaining systems. From Figure 4, we see that the assembly machine with special purpose workheads, SPW, is the worst manufacturing system (using the principle of first-order SD). It appears that RW,

Figure 3. Decision Tree Structure (5 x 3 x = 3840 branches)

ASSEMBLY SYSTEM

June 1987, IIE Transactions 227

IMPORTANT STOCHASTIC VARIABLES

MS NP PROJECT I NAP MGROWl I ASSEMBLY pQ I TIMES I ND

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AE (Annulty Equlvalenl), Smillion Figure 4. Cumulative Density Functions of Annuity Equivalents for Five Assembly Manufacturing Systems

the assembly machine with robot workbeads, is the best system. Unfortunately, we cannot use 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, for example, Howard and Matheson [Ill.) Suppose, for the sake of illustration, that the decision-maker has the preference curve shown in Figure 5. Table 4 shows the certainty equivalents for the five assembly systems. The best assembly system is the assembly machine with robot workheads, followed by the robot assembly cell, manual assembly, manual assembly with mechanical assistance and the assembly machine with special purpose workheads.

iii) Informational Phase In this phase the uppermost question is; "Should more

information be gathered before the final decision is made?". A special case is the case of perfect information-that is, the value of an important stochastic variable will be known exactly after perfect information is gathered. The value of perfect information provides an upper limit on the amount of resources that can be expended, in further studies and analysis, to reduce the uncertainty in a variable. The value of information is the difference in the output variable between the best decision without information and the best decision with new information. The information has no value if it results in the same decision as in the without information case. (See Raiffa [IS].)

In the illustrative 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

AE(Annu1ty Equivalent), Ernlllion Figure 5. A Typical Preference Curve for -2 s AE s 3 ($million)

is still RW. However with perfect information about MS and MGROW (that is-the total demand) the best FMS might be RAC. The value of perfect information about MS and MGROW is

A E (perfect information about MS and MGROW) -AE (no information) = $908450 - $891049 = $17401

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 4).

iv) Decision If all uncertainty could be eliminated about future de-

mands, at a cost of less than $17401 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 $17401. If this is the case, the final decision should be made. In this example the "best" decision is to use a robot assembly machine (RW) to manufacture all assemblies.

Summary and Extensions

This paper set out to show the proper methodology for using traditional financial evaluation models to evaluate flexible manufacturing systems. Specifically, we set out to select the "best" flexible manufacturing system for a particular sit- uation. There was considerable uncertainty about the amount of flexibility that was required (demands, new products, and


Table 4. Expected Preferences For Five Assembly Systems Assembly System

MA MAM SPW RW RAC

Annuity Equivalent Expected Certainty Mean Variance Preference Equivalent

$365093 3.650E + 10 0.5716 361,982 363141 8.357E + 10 0.5705 356,459

- 659597 2.808E + 11 0.3454 -681,874 891 049 3.696E + 11 0.6673 862,123 407069 9.770E + 10 0.5790 399,259

Rank 3 4 5 1 2

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product changes), about the financial variables (discount rate, tax rate, etc.) and about the production variables (assembly times, quality, etc.). Simple mathematical models of five potential FMS's were developed. The important stochastic variables were identified, and estimates for all variables were obtained from experts. Cumulative density functions of the annuity equivalent for each potential FMS were evaluated and the "best" FMS was selected. An example was worked and it showed that the best FMS was a robotic assembly line, while the next best FMS was a robotic assembly cell.

This methodology also gives valuable insight into the amount of flexibility that is required, the important decision variables, and the value of doing studies and gathering additional information. In another project we are investigating the general conditions under which certain types of FMS's are "best". We believe that this paper and our other work show that traditional financial evaluation models, if properly used, do encourage the adoption of robotic FMSs.

Possible extensions to this work would be:

i) Add lot-sizing and scheduling considerations to the mathematical models for the five FMS's. (It should be noted that these considerations would make the robotic assembly line, and the robotic assembly cell even more attractive. Setup times are very small for robotic assembly lines and cells and so small-lot production is profitable.)

ii) Take account of the dependencies (correlation) between the stochastic variables; especially between the demands for various assemblies, and between the demands and the finan- cia1 variables.

iii) Consider mixed manufacturing systems. For example, use a robotic assembly cell for assemblies 1, 2 and manual assembly for assembly 3, etc.

iv) This paper has considered only the financial aspects. There are other factors which will also influence the firm's choice of flexible manufacturing system. These factors include strategic considerations (such as the direction in which the firm's industry is going, domestic and foreign competition and markets, and the nature of the firm's labour relations); quality considerations; the desire to develop high-tech expertise within the firm; and so on. Some of these factors can also be modelled and included in the analysis.

ACKNOWLEDGEMENTS

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

REFERENCES

[l] Arbel, A. and A. Seidman, "Performance E~aluation of Flexible Man- ufacturing Systems". IEEE Trruuacrionr (SMCJ, 14. 606617 (1984).

[2] Bawa, V. S., "Stochastic Dominance: A Research Bibliography", Man- agement Seienee, 698-719 (1982).

131 Bwthroyd, G., "Emnomia of Assembly Systems", l o u r ~ l of Monu- fanuring System, 1, 111-127 (1982).

[4] Browne, J . , Dubois. D., Rathmill, K., Sethi, S., and K. E. Stecke, "Classification of Flexible Manufacturine Systems", T k FMS Moxarino, - . 114-117 (1984).

[S] Burstein, M. C, and M. Talbi, "Emnamic lustlflcation for the Intro- duction o f Flexible Manufarmring Technology: Traditional Procedures Venus a DynamicrBased Approach", Proceedings of tkr First ORSAI TIMS Conference on FMS, 1W-106 (1984).

161 Buzaeott, I. A,, "The Fundamental Principles of Flexibility in Manu- fa:l~rtng Sys~ernr", Proceed.ngr of rhr t 8 r r 6 fncemononal Conicrenrr on F.V.+Orrohrr 1082 honh Holland Yuol,rhlng Co., Kru York

[7] Copeland, T. E. and 1. F. Weston, Fimncwl Theory and Corpomle Policy, Addison-Wesley Publishing Co.. Reading, Masachusens, (1984).

[8] Dod, R. C., Robots and Automared Mnnufmturvlg, Restan Pubbrhing Co., Reston, Virginia (1983).

[9] Gitman, L. 1, and 1. R. Forrester, "A Survey of Capital Budgeting Techniques Used by Major U.S. Arms", Fimnciol Mamgcmenr, 66-71 (1977).

[lo] Gold, B., "CAM Sets New Rules for Production", Howard Business Review, 88-94 (1982).

[ l l ] Howard, R. A, and J. E. Matheson. Rcodings on the Principles and Applications of Deckion Annfysis. Strategic Dceisionr Group, Menlo Park, California (1983).

[I21 Kaplan, R., "Measuring Manufacturing Performance: A new Challenge for Managerial Accounting Rerearch", The Accounting Review, 686-705 (1983).

1 Knott. K. and R. D. Getto, "A Model For Evaluating Robot Syrtems Under Uncertainty", Internotional lourno1 of Production Ruearch, 20, 155-165 (1982).

[14] Kulatilaka, N., "Financial, Economic and Strategic Issues Concerning The Decision To Invest In Advanced Automation", Inrcrmt iod louwl of Produetion Research, 22, 949-968 (1984).

[IS] Michael, 0. I. and R. A. Millen, "Economic Justi6cation of Modem Computer-Based Factory Automation Equipment: A Status Repon", Proceedings of the Fin1 ORSAITIMS Conference on FMS, 30.35 (1984).

1161 Operations Research Saciety o f America, and The Institute of Manage- ment Sciences, Proceedings of the First ORSAITIMS Confernnee on FMS-Operdonr Resenreh Models and Applicotionr-August 1984.

[I71 Proceedings of the Firstlntermtionol Confererne on FMS-October IW. Nonh Holland Publishing Co., New York.

[IS] Raiffa, H., Deckion A d y s k , Addison-Wesley, Reading: Mass. (1968). [I91 Schall, L. D., G. L. Sundemand W. R. Geusbeek, "Survey and Analysis

of Capital Budgeting Methods", The lourml of F i m n , 33, 281-287 (1978).

[20] Surerh, N. C. and 1. R. Meredith. "A Generic Approach to Jurtifying Flexible Manufacturing Systems", Proceedings of the First ORSITIMS Conference on FMS, 36-42 (1984).

[21] Suri, R. and C. K. Whitney, "Decision Suppon Requirements in Flexible Manufacturing", Iournal of Mvwfocruring Systems, 3.61-69 (1984).

[22] Suri, R. and R. R. Hildebrant, "Modelling Flexible Manufacturing Syr temr Using Mean-Value Analysis", lournnl of Monufacruring System, 3, 27-38 (1984).

Appendix 1-Financial Model

The inputs to the financial model are the demand variables, engineering variables and financial variables, while the out- puts are the NPV and AE, IRR, and PB for each FMS.

Exogenous Variables NP,-number of different assemblies to be manufactured

in year r MSj,l--total market size for assembly i in year 1 (in units

demanded per year), i = 1, 2, 3, . . . , NPI

MSHAREtsha re of the assembly i market for the fmn


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MGR0W;-annual market growth rate for assembly i

1,-investment in year t, t = 1, 2, 3, . . . N--useful life of the project (for NPV calculations)

D-life of the project for depreciation purposes

WT,-total wage costs in year t

SPj,--selling price for assembly i in year t

TX-tax rate

k-risk free interest rate

Endogeneous Variables MSi,,-total market size for assembly i in year t

VSi,,-annual sales of assembly i in year t by the firm

REV;-total revenues in year t

DEP,-total depreciation in year t

BVt-book value of the project in year t

ATCF,--after tax cash Row in year t

Relationships Between Variables MS;,, = MS;,r-l (1 + MGROW;)

VSr,, = MS,,, * MSHARE, NPt

REV, = 2 VS,, SP,,, , = I

('41)

' I-' ,-I DEP, = - 2 I, - DEP,) D i = o j ; o

('4-2)

BVo = 0, BV, = BV,-1 - DEP, + I,

ATCF, = (REV, - WT,)(1 - TX) + DEP,TX - 1, (A3)

ATCF, BVN (A41

AE = NPV

1 (A5) I-- (1 + k)N

IRR is calculated £tom

PB satisfies PB 2 [(REV, - WT,)(l - TX) - It] = 0 (A7)

1= I

For simplicity it is assumed that the risk free rate k (used to discount the cash Rows) is constant over the life of the project. The total cost per year is made up of labour costs and in-

vestment costs. (That is overhead costs are ignored.) Depre- ciation is calculated using the double declining balance method (equation A2). Finally, notice that the last term in the NPV and IRR equations is the discounted book value (BV) of the project at the end of its useful life. This simple model can be reduced or enriched (in terms of the number of variables and relationships) to meet the needs of a particular firm.

Appendix 2-Mathematical Models for FMS's

Define the following variables.

Exogenous Variables (i) TIMES (seconds)

TA -time to assemble one part manually

TM - time to assemble one part manually with mechanical assistance

TW - time to assemble one part with special purpose workhead (nonprogrammable automation)

TR - time to assemble one pan with robot workhead (programmable automation)

TD - downtime at a station due to a defective part

(ii) EQUIPMENT COSTS (dollars) CB - cost per station of transfer device on manual assem-

bly system

CT - cost per station of transfer device on automated assembly system

CC - cost of carrier (pallet)

CF- cost of mechanical feeding device for manual and non-programmable assembly systems

CM - cost of part magazine (feeding device) for robot systems

CW - cost of special purpose workhead

C1 -basic cost of robot

C2 - additional cost of robot per degree of freedom

CG - cost of robot gripper

(iii) PLANT VARIABLES PE - plant efficiency (fraction of available time worked)

PQ - part quality (fraction of defective parts to acceptable parts)

NR - number of assembly workers per station on automated assembly systems

NOS - number of supervisors on an assembly system

HR - number of production hours per shift

WA - annual cost of one assembly worker

WS - annual cost of one supervisor


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(iv) PRODUCTION VARIABLES NS; - the number of parts assembled at each station for

assembly i

NAj - number of parts in assembly i, i = 1, 2, . . . , NP.

NT; - number of parts in assembly i that are different from assemblies 1, 2, . . . , i - 1

ND;, - number of part design changes for assembly i in year t

Endogenous Variables TPi - the average production time for a non-defective as-

sembly i

NSR - number of stations required in the assembly system

SH - number of production shifts for assembly system

Mathematical models for the first five assembly systems of Figure 1 will now be described. They are based on models developed by Boothroyd 131. In what follows the subscript r (year) will be suppressed for clarity.

MA - MODEL FOR MANUAL ASSEMBLY (Figure 1-a) Select the required number of shifts SH, and the number

of parts to be assembled in each station NS, for each assembly i (i = 1, 2, . . . , NP), so that there is sufficient capacity to

NP meet the production requirements. That is: 1 VS; * TP, s

; = I

HR * PE * SH where TP; = NSj*TA(l + PQ). (Every TP seconds. on average, a good assemblv will be ~roduced bv - . - the assembly machine.) The number of stations required (NSR) in this manual assembly system is: NSR = max [NA,I NS,] (i = 1, 1, . . . , NP). Assume that there is one operator at each station and that each operator has access to two work carriers (CC) on the conveyor (to allow for minor delays) and that each station has a transfer device (CB). Finally, notice that only the work carriers have to be changed when the assembly system changes over to a different assembly. The initial investment for a manual assembly system is, therefore:

I, = NSR(NPS2*CC + CB). The total annual labour costs are:

NP WA 1 NR VS, TP;

MAM-MODEL FOR MANUAL ASSEMBLY WITH ME- CHANICAL ASSISTANCE (Figure 1-b)

The difference between this model and the previous model is that mechanical feeding devices are available at each station to speed up the assembly process. (A different feeding device is required for each different part. When a part is redesigned, a new feeding device is required.) The equations are as above, except that TPj = NSjbTM*(l + PQ), and

NP I1 = NSR*(NP*Z*CC + CB) + CF' 1 NE.

,=I

SPW-MODEL FOR ROTARY AND IN-LINE INDEX- ING ASSEMBLY MACHINES (Figure 1-c)

These assembly machines are non-programmable. There- fore each assembly requires a dedicated machine with di- ferent special purpose workbeads, different work carriers and different part feeders. Each station in the assembly machine assembles one part only. (Obviously, for such "hard automation" to be profitable, the volumes must be very large.)

For each assembly i, (i = 1, 2, . . . , NP) select SHi, so that there is sufficient capacity to meet the demand requirements. That is VS;'TP;I3600 s HRSPE*SH where TPj = TW i NAj*PQ*TD. Each station in the assembly machime consists of work carriers (CC), a feeding device (CF), and a special purpose workhead (CW) (all of which must be changed if a part is redesigned) and a transfer device (CT). The initial investment required for assembly machine i is Ii = NAja(CC + CF + CW + CT). The labour wsts consist of operator and supervisor costs. One operator runs 1INR stations on the assembly machine and one supenisor monitors llNOS assembly machines. The annual labour wst for machine i, is:

WT; = (NR*NAiYWA t NOS* WS) *(VSja TPjI%OO)/(HR'PE).

The initial investment in all NP indexing assembly ma- NP

chines is I = x I; while the total annual labour cost is NP ;=I

WT = x WT;. i = l

SPW-MODEL FOR IN-LINE FREE TRANSFER (BUFF- ERED) ASSEMBLY MACHINES WITH SPECIAL PUR- POSE WORKHEADS (Figure 1-d)

If the number of parts in assembly i (NA;) is large, downtime due to defective parts, can be excessive when rotary and in-line indexing assembly machines are used. In this case an in-line assembly machine with buffer inventories between the stations will be used. Boothroyd [3] recommends the in-line free transfer assembly machine be used whenever NAi 3 10 and that the size of the buffer inventories (BI) be approxi- mately [O.S*TDITW] where [XI is the smallest integer greater than or equal to X. He estimates that, on average, a good assembly is produced every TW + PQ'TD seconds. For each assembly i, where NAi 3 10 (i = 1, 2, . . . , NP), select the required number of shifts SH; such that VSj*TPjB600 s HR*PE*SH;, where TPi = TW + PQ'TD. The initial investment for assembly machine i is I; = NA;*(CC + CF + CW + CT t BFCC), and the annual labour wst is WT; = (NRXNA;*WA + NOS*WS)*(VS;*TPjB600)/(HR*PE). (If a part is redesigned then a feeding device (CF) and a special purpose workhead (CW) will have to he changed.)

RW-MODEL FOR IN-LINE FREE TRANSFER (BUFF- ERED) ASSEMBLY MACHINE WITH ROBOT WORK- HEADS (Figure I-e)

This assembly machine is the same as the in-line free transfer machine with special purpose workheads except that the


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workheads are now programmable. That is, the robot workheads can be reprogrammed for different tasks. (In that sense this assembly system is similar to manual assembly with mechanical assistance-model 2, because the human operators can also do different tasks.) The cost of each robot is CR where CR = C1 + D F C 2 . C1 is the basic cost of a robot and C2 is the additional cost per degree of freedom of the robot. It is reasonable to assume that four degrees of freedom are required for assembly Line robots.

Select the required number of shifts SH, and the number of parts to be assembled at each station NS,, for each assembly i, i = 1, 2, . . . , NP such that there is sufficient capacity

NP to meet the production requirements. That is, C VSi*TP;I

i - 1

3600 S HR*PEaSHwhere TPi = NSiX(TR + PQ*TD). The number of stations required in the assembly machine is, NSR = max[NA;lNS;], i = 1, 2, . . . , NP. Again we have buffers of size BI = [0.50*TDITR] located between all stations. The required initial investment is

NP I, = NSR*(CR + CT) + CM*Z NT;

i = l ,VP + (CG + CC(1 + 81))' 2 (NA,INS;). i = l

If design changes are made then the robot part feeders (CM) and the robot grippers (CG) need to be changed. Labour costs consist of operator and supervisor costs. (Notice that if assembly i has NA; parts and NS, parts are assembled at each station, then NAjINSi stations are required to complete the assembly.) Therefore the annual labour costs are;

Appendix 3 Most Likely Values and Ranges for Variables Defined in Traditional Financial Valuation Models

Deterministic Variables (Most Likely Values)

CB = $7000 CT = 16000 CC = 1500 C F = 7000

CM = 5000 CW = 10000 C1 = 50000 C2 = 10000

CG = 1700 WA = 40000 WS = 55000 HR = 2000 NR = 0.333

NOS = 0.25 D = 10

6 parts 6 parts

6 7 8 9

SP,, = $0.65 i = 1 ,2 , . . . , 9 r = 1,2 , . . . (For simplicity, the selling price for all assemblies is the same.)

IIE Transactions, June 1987

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Stochastic Variables Variable Most Likelv Value Range

NPI = number of different assemblies to be manufactured in year 1

NAP, = number of new assemblies to be manufactured in year t

MS<,I = total annual demand for item i in year 1

MGROWi MSHARE;

Project Life

T X = Tax Rate k = Risk free interest rate

TA TM 7w TR TD

PE PQ NDi, = Annual Part Design Changes

t = 2 . . . I t = 3 . . . 0 1 = 4 . . . I t = s . . . 0

i = 1 750000 i = 2 900000 i = 3 700000 i = 4 550000 i = 5 300000 i = 6 500000 i = 7 300000 i = 8 800000 i = 9 750000

0.10 i = l , 2 , . . . , 9 0.17 i = l , 2 , . . . , 9

M A 4 years MAM 5 SPW 6 RW 7 RAC 8

0.40 0.10

10 seconds 8 5 6

30

0.95 0.05

1' i = 1 , 2 , . . . , 9

*Each assembly will have 1 pan design change every year, for 5 years, beginning in the next year after it is introduced.

Probability Distributions Variables

Variable (Value; Probability), (Value; Probability), . . . NPt (5; 0.6) ( 4 ; 0.4) NAP, (1, 0, 1, 0; 0.6) (2, 1, 1, 0; 0.4) MS,,I (Most Likely Value from above; 0.5)

(Low Value; 0.3) (High Value; 0.2)

MGROWi (0.10; 0.50) (0.07; 0.50) Project Life (4, 5 ,6, 7 , 8; 0.5) (7, 8, 9, 10, 12; 0.5) k (0.10; 0.60) (0.12; 0.40) TA, TM, 7W, TR (10, 8, 5,6; 0.6) (9, 7, 4,5; 0.4) PQ (0.05; 0.60) (0.035; 0.4) ND (1, 1 , . . . ; 0 . a ) (2, 2, . . . ; 0.40)

i For Important Stochastic Ontario, Canada. Prior to this, he worked in Manufacluring Engineering at General Motors. John holds a Ph.D. horn the University of Waterlw. His research interests indude the development of optimal and heuristic approaches for analyzing mmplex inventory and production problems; including c w r - dinated control of inventories, transfer lines, flexible manufacturing systems and just-in-time production systems. Dr. Milfenburg has published anider in the In te r~~ iono l Journal of Production Research, INFOR, Engineering Costs and Production Economies, IIE T r a m l i o n s and Novol Rcswrck Lopistier Quanerly.

Dr. Itrhak Krinsky is an A~nociate Professor of Finance and Business b nomia, in the Faeully of Business, McMaster University, Hamilton, Ontario, Canada. Dr. Krinsky has conducted research in insurance, portfolio analysis, financial markets, and econometrics. His current research interens include the development of prediction models for mergers and acquisition, calculating the mst of equity capital for insurers and the Statistical pmpenies of elasticities. Dr. Krinsky has published articles in the J o u m l o f Fimneiolond Quonrilotive

Dr. G. John Miltenburg is Associate Profernor of Production and Manage- Analysis, Review of Economic$ and S!mislics, Journal of Risk and Insurmce, men1 Science, in the Faculty of Business, at McMa~ter University, Hamilton, Applied Economics, Journol of Inrrr~lional Money and FiMnce and athern.


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Documents

1987 Evaluating Flexible Manufacturing Systems