Manufacturing ﬂexibility: Measures and relationships

Theory and Methodology

Manufacturing ¯exibility: Measures and relationships

Rodney P. Parker a,*, Andrew Wirth b

a School of Business Administration, The University of Michigan, 701 Tappan Street, Ann Arbor, MI 48109-1234, USAb Department of Mechanical and Manufacturing Engineering, The University of Melbourne, Parkville, Victoria 3052, Australia

Received 1 August 1994; accepted 1 June 1998

Abstract

The study and formulation of manufacturing ¯exibility measures has been inhibited by the lack of a conceptual

structure to encourage model development. In this paper, we introduce a framework to facilitate the development of

¯exibility measures. It also proves to be useful in validating measures of ¯exibility types. Measures of various ¯exibility

types are drawn from the literature and compared with the purposes and criteria for the ¯exibility types and the `best'

measures are presented. For volume and expansion ¯exibility, the framework is used to develop new measures. This is

followed by a discussion of the relationships among ¯exibility types and some sample relationships are highlight-

ed. Ó 1999 Elsevier Science B.V. All rights reserved.

Keywords: Flexible manufacturing systems; Flexibility measures; Manufacturing

1. Introduction

Flexible manufacturing systems (FMSs) aretechnologies combining the bene®ts of both com-puters and numerical control machine tools. Theyhave been hailed as the solution to challengesfacing manufacturing industries world-wide.However, soon after the rapid growth in FMSinstallations, operations managers realized that thesimple investment in ¯exible manufacturing sys-tems would not readily answer the market's desirefor more rapid delivery, more product variety,more customized product designs, and higher

product design turnover as evidenced by reducedproduct life cycle lengths. Several companies haveillustrated how successful use of FMS has resultedin the above mentioned bene®ts to customers (e.g.Motorola, Toyota). These companies have realizedthat a successful technical implementation alone isnot enough and that FMS investment must cor-relate with the corporate and manufacturingstrategy the ®rm is following. When both businessand technical success is achieved, the celebrated¯exibility bene®ts may ensue, as recognized byVoss (1988). However, there is ample evidence (seeJaikumar, 1986) to suggest that the managementof these technical systems is no easy task.

Bolwijn and Kumpe (1990) and De Meyer et al.(1989) have identi®ed `¯exibility' as the focus ofthe next competitive battle. De Meyer et al. state

European Journal of Operational Research 118 (1999) 429±449www.elsevier.com/locate/orms

* Corresponding author. Tel.: 1 734 647 9596; fax: 1 734 647

8133; e-mail: [email protected]

0377-2217/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved.

PII: S 0 3 7 7 - 2 2 1 7 ( 9 8 ) 0 0 3 1 4 - 2

that this battle ``will be waged over manufacturers'competence to overcome the age old trade-o� be-tween e�ciency and ¯exibility''. However, confu-sion over what constitutes ¯exibility still occurs.Gerwin (1993) suggests that the lack of full un-derstanding of manufacturing ¯exibility is inhibi-ting progress towards the utilization of ¯exibilityconcepts in industry and impeding manufacturingmanagers from evaluating and changing the ¯exi-bility of their operations. Gunasekaran et al.(1993) and Gerwin (1993) identify the measure-ment of ¯exibility and performance as an impor-tant hurdle to achieving a full comprehension ofFMS behavior, and a stepping stone to establish-ing full economic-based measures. Gunasekaran etal. (1993) also state that the complex inter-rela-tionships among various aspects of ¯exibility willbe further advanced by the development of ¯exi-bility measures and that understanding these ¯ex-ibility trade-o�s ``can help the management tosupport the manufacturing strategy of the ®rm''.Empirically measuring ¯exibility in manufacturinghas begun recently (see Dixon, 1992; Upton,1994, 1997) in speci®c industries. Such studiespromise much but sound measures of ¯exibilityneed to be developed ®rst. In this paper we intro-duce a framework to facilitate ¯exibility measuredevelopment, introduce two new measures, andanalyse the relations among some ¯exibility types.

2. Manufacturing ¯exibility

2.1. Flexibility taxonomies

The taxonomy of ¯exibility types established byBrowne et al. (1984) has formed the foundation ofmost subsequent research into measuring manu-facturing ¯exibility. In an excellent review, Sethiand Sethi (1990) identify over 50 terms for various¯exibility types, although generally the basis of allwork has been that of Browne et al. For com-pleteness we restate the ¯exibility type de®nitionsbelow.

Machine ¯exibility ``refers to the various typesof operations that the machine can perform with-out requiring prohibitive e�ort in switching fromone operation to another'' (Sethi and Sethi, 1990).

Process ¯exibility is the ability to change be-tween the production of di�erent products withminimal delay.

Product ¯exibility is the ability to change themix of products in current production, also knownas mix-change ¯exibility (see Carter, 1986).

Routing ¯exibility is the ability to vary the patha part may take through the manufacturing sys-tem.

Volume ¯exibility is the ability to operatepro®tably at di�erent production volumes.

Expansion ¯exibility is the ability to expand thecapacity of the system as needed, easily andmodularly.

Operation ¯exibility is the ability to interchangethe sequence of manufacturing operations for agiven part.

Production ¯exibility is the universe of parttypes that the manufacturing system is able tomake. This ¯exibility type requires the attainmentof the previous seven ¯exibility types.

Measures for most of these ¯exibility types havebeen attempted. However, there has not been aconsistent structured approach to the measuredevelopment and, therefore, the success of thesemeasures has been sporadic. Gupta and Goyal(1989) presented a classi®cation of ¯exibilitymeasures ``based on the ways researchers havede®ned ¯exibility and the approaches used inmeasuring it''. The categories de®ned are: (1)measures based on economic consequences; (2)measures based on performance criteria; (3) themulti-dimensional approach; (4) the Petri-netsapproach; (5) the information theoretic approach;and (6) the decision theoretic approach. Themeasures created and evaluated in this paper arebased on performance criteria and economic con-sequences, although the multi-dimensional ap-proach is also examined. Gupta and Goyal (1989)intend the multi-dimensional approach to encom-pass the variety of distinct dimensions. There are avariety of dimensions along which the measurescan be developed and compared. A listing of thesedimensions follows.

The following taxonomy is a compilation ofmutually exclusive ``dimensions of comparison''from the literature. These dimensions are charac-teristic coordinates which help describe the nature

430 R.P. Parker, A. Wirth / European Journal of Operational Research 118 (1999) 429±449

of the ¯exibility types. The de®nitions of the di-mensions and their respective authors are:

System vs machine: Buzacott (1982) regardsmachine level ¯exibility as a ¯exibility type whichis contained or determined by the machine whereasa system level ¯exibility is one which comes fromthe capabilities of the entire system.

Action vs state: Mandelbaum (1978) considershow ¯exibility accepts change. If the ability toperform well in the new state is already there whenthe change takes place, state ¯exibility is present. Ifthis ability is acquired by taking appropriate ac-tion after the change takes place, action ¯exibilityis present.

Static vs dynamic: Carlsson (1992) states ``Static¯exibility refers to the ability to deal with fore-seeable changes (i.e. risk), such as ¯uctuations indemand, shortfall in deliveries of inputs, orbreakdowns in the production process'' and ``Dy-namic ¯exibility refers to the ability to deal withuncertainty in the form of unpredictable events,such as new ideas, new products, new types ofcompetitors, etc.''.

Range vs response: Slack (1987) suggestedmanagers thoughts about ¯exibility were assistedby considering range and response dimensions.Range ¯exibility is typically regarded as the extentto which a system may adapt, whereas response¯exibility captures the rate at which the system canadapt.

Potential vs actual: Browne et al. (1984) dis-cusses the dimensions of potential and actual¯exibility, particularly with respect to routing¯exibility. Potential ¯exibility occurs when the¯exibility is present but is utilized only whenneeded, such as a part being re-routed when a

machine breakdown occurs. Actual ¯exibility re-fers to the ¯exibility which is utilized regardless ofthe environmental status.

Short term vs long term: Carter (1986) andothers suggest the categories for which a ¯exibilitytype in¯uences the system or the system's envi-ronment in particular time frames, and thereforethe ¯exibility type is considered to be either ashort, medium or long term ¯exibility.

Table 1 contains the dimensions of comparisonthat are clearly dominant. Where both are clearlypresent, we enter ``both''. This table is only a guideand several of the entries are included with heavyquali®cations.

An interesting observation from Table 1 is thatthere seems to be a consistent positive correlationbetween the system vs. machine focus and theshort vs. long-term time frame. With only acouple of exceptions, machine focused ¯exibilitytypes tend to be ones that impact in the shortterm (minutes to days) and system focused ¯exi-bility types tend to in¯uence performance in thelonger term (years). We suggest this con®rms in-tuition as we would consider the investment of acomplete system as one, which is driven primarilyby the strategic manufacturing mission of thecompany which traverses the long-term timeframe.

2.2. Developmental framework model

The basis of the framework (illustrated inFig. 1) is straightforward: we believe the lack ofconsistency across existing ¯exibility measures isdue directly to the lack of discussion of the pur-

Table 1

Taxonomy of dimensions of comparison

Dimensions Flexibility types

Machine Process Product Routing Volume Expansion Operation

System vs. machine Machine Machine Mixed System System System N/A

Action vs. state State State Action State Action Action State

Static vs. dynamic Static Static Dynamic Static Static Static Static

Range vs. response Both Both Both Both Both Both Both

Potential vs. actual Actual Actual Actual Usage Actual Actual Both

Short, medium, long term Short Short Medium Short-medium All Long Very short

R.P. Parker, A. Wirth / European Journal of Operational Research 118 (1999) 429±449 431

poses of such measures. Most of the literaturepurely lists proposed measures but rarely men-tions the purposes and criteria against which themeasure can be judged, qualitatively or quantita-tively. This paper seeks to establish a clearly de-®ned list of the uses for the measure of a ¯exibilitytype and a list of criteria against which a pro-posed measure may be judged. In some cases themeasure itself is de®ned, keeping in mind thepurpose of the ¯exibility type and how the mea-sure may be used. The purposes of the ¯exibilitymeasure will be largely determined by the ¯exi-bility measure category, de®ned in Gupta andGoyal (1989).

Clearly, great creativity and e�ort will still berequired in developing ¯exibility measures butexplicitly tabulating the purposes and criteria willassist in achieving a successful measure. In Sec-tion 2.3 the development tool is used to validateexisting measures for ¯exibility types, drawn fromthe literature. Flexibility measures for various¯exibility types are assessed relative to a list ofcriteria generated after the purposes of the ¯exi-bility type and ¯exibility measure are examined.Accordingly, a ``winner'' is found for each ¯exi-bility type; the winners are judged to be thosemeasures which comply with the greatest numberof criteria, or potentially a weighted sum if cer-tain criteria are deemed more important thanothers.

2.3. Evaluations of existing measures

Using the framework described above we ex-amined the literature with the intention of ana-lyzing the existing measures, comparing themeasures with purposes and criteria establishedseparately. We found acceptable measures for ®veof the eight Browne et al. ¯exibility types and de-cided that further development of measures forthese types would not be constructive.

Machine ¯exibility is the ability to perform avariety of operations on a single machine. Thepurposes of the measures are generally to capturecharacteristics of machine ¯exibility not portrayedby other equipment descriptors such as price, size,speeds, tolerances, weight and part limits. Somecriteria for machine ¯exibility performance mea-sures include: they must describe the main fea-tures, that is, the ability to change betweenoperations with minimal setups and delays; theymust be amenable to calculation (this would meanthat they can be computed on a PC spreadsheet atmost, and preferably on a calculator); they wouldmore naturally be given in performance measureterms rather than monetary terms; they should``increase (decrease) in value if the machine can domore (fewer) tasks with positive e�ciency'' (Brilland Mandelbaum, 1990); they should ``increase(decrease) in value if the e�ciency for doing anyone task increases (decreases)'' (Brill and Man-

Fig. 1. Flexibility measure development model.


delbaum, 1990); they should `ìncrease (decrease)in value if the importance weight of any doabletask increases (decreases)'' (Brill and Man-delbaum, 1990); and they should ``be applicable tocontinuous as well as discrete and multi-dimen-sional background sets of possible tasks'' (Brilland Mandelbaum, 1990). Brill and Mandelbaum(1989, 1990) de®ned a measure for machine ¯exi-bility which tends to satisfy the purposes and cri-teria. The measure is a weighted normalized sumof task e�ciencies. Task e�ciency (some papersrefer to it as e�ectiveness) is a measure of how wellthe machine can perform the relevant task. Thesee�ciencies are weighted by how important the taskis to the production of the part or product,whether the importance could be determined bytime or economic factors. There is a large degree oflatitude that may be exercised in applying thismeasure. If a task cannot be completed, it is allo-cated an e�ciency rating of zero, or equivalently,is excluded from the machine-task capability set.The e�ciency rating is judged according to somestandard established by the user. An example of astandard could be the time of execution of the taskon the fastest known machine, and hence, the ef-®ciency measure could be the measure of howclosely a particular machine's time for a speci®ctask compares with the best known time, increas-ing as it gets closer to the best time.

It can be seen in Table 2 that there is a directcorrespondence between the purposes and criterialisted. Table 2 also illustrates that the Brill andMandelbaum measure satis®es all the given crite-ria. A simple count of the satis®ed criteria can

serve as arbiter of whether the measure is satis-factory or not. Alternatively, a continuous metriccould be applied to the judgment of how well eachcriterion is met and a normalized sum or weightednormalized sum could be used to judge merit.

Process ¯exibility is the ability to change be-tween the production of di�erent products withminimal delay. Browne et al. (1984) say it is ``theability to produce a given set of given part types,each possibly using di�erent materials in severalways''. Sethi and Sethi (1990) set out the purposesof process ¯exibility, namely to reduce batch sizesand reduce inventory costs. Other contributorssuggest it can minimize the need for duplicate orredundant machines (Carter, 1986), and protectagainst market variability (Carter, 1986) by ac-commodating shifts in the product mix demand bythe market. The criteria of a measure include:describe the main features of process ¯exibility,namely the ability to change between the manu-facture of di�erent products without prohibitivechangeover time or cost; be amenable to calcula-tion; increase (decrease) with increasing (decreas-ing) product portfolio size; increase (decrease) withan increasingly (decreasingly) versatile materialhandling system and increasingly (decreasingly)adaptive jigs; and increase (decrease) with de-creasing (increasing) changeover cost and de-creasing (increasing) changeover time. De Groote(1992) developed a pair of measures (the reciprocalof the setup cost and the maximum number ofsetups per unit time) which satisfy the criteria quitewell but concludes that the nature of the ¯exibilitytype prohibits the creation of a single measure.

Table 2

Analysis of the Brill and Mandelbaum (1989, 1990) machine ¯exibility measure

Purpose Criteria Compatibility

The main features of machine ¯exibility should be

described, namely to ``perform several operations on

one part to save several setups'' Sethi and Sethi (1990)

Should `ìncrease (decrease) if the machine can

perform more (fewer) tasks with positive e�ciency''

(Brill and Mandelbaum, 1990)

Yes

Should `ìncrease (decrease) if the e�ciency for

doing any one task increases (decreases)'' (Brill

and Mandelbaum, 1990)

Yes

To be computed on a PC Should be a single equation, or at most a small

set of equations

Yes

To be used within a larger study to represent machine

¯exibility

Should be able to represent discrete and

continuous operations

Yes


This results in ambiguities under certain circum-stances which would suggest further developmentis required.

Product ¯exibility is the `àbility to change overto produce a new (set of) products(s) very eco-nomically and quickly'' (Browne et al., 1984). Es-sentially this means the ability to change the mix ofproducts in current production, and indeed Carter(1986) refers to this as mix-change ¯exibility. Sethiand Sethi (1990) rightly state that product ¯exi-bility is distinguished from process ¯exibility onthe basis that addition of new parts will `ìnvari-ably involve some setup''. The purpose of a mea-sure of product ¯exibility would be to act as adescriptor of this aspect of manufacturing ¯exi-bility. Possible usages of a product ¯exibilitymeasure could occur in a manufacturer's strategicplan in positioning himself with respect to hisproducts. The criteria of a measure include: cap-ture the dominant dimensions of comparison; beapplicable to various manufacturing technologies;increase (decrease) with the increasing (decreasing)number of parts introduced per time period; in-crease (decrease) with an increasing (decreasing)size of the universe of parts able to be producedwithout major setup; increase (decrease) with in-creasing (decreasing) scope of the boundaries ofCAD, CAM and CAPP systems; increase (de-crease) with the increasing (decreasing) level ofsystem integration of the developmental tools; in-crease (decrease) with decreasing (increasing) timeof design implementation through the system; in-crease (decrease) with decreasing (increasing) setuptime when introducing a new product to the cur-rent production portfolio; and increase (decrease)with decreasing (increasing) setup cost when in-troducing a new product to the current productionportfolio. Kochikar and Narendran (1992) pro-pose an introducibility measure which relates tohow well a particular product can be made by thesystem and, therefore, how the system can make anew set of products. Only some of the above cri-teria were met by Kochikar and Narendran'smeasure so further development is required. Spe-ci®cally, their measure focuses on the processingtime of operations so consideration of costs is ex-cluded. Also, their de®nitions of òperation' wouldneed to be expanded to include the initial design

processes in order to satisfy the criteria concernedwith designing the product.

Routing ¯exibility is the phenomenon wherebya part may take a variety of alternative pathsthrough the system, visiting various machinesduring its manufacture, and thus accommodatingchanges in machine availability. Machine avail-ability changes if a machine breaks down or if amachine is already engaged in production. Thepurpose of a routing ¯exibility measure is to cap-ture the ability of the system to absorb an eventsuch as machine breakdown and continue to op-erate with minimal strain. The most likely usagewould be by operations managers when allocatingcapacity for particular orders. In addition it islikely to be used during the system investmentevaluation phase for comparison among manu-facturing equipment alternatives and thus shouldnot be technology speci®c. A routing ¯exibilitymeasure should: increase (decrease) with increas-ing (decreasing) number of routes in the system;increase (decrease) with increasing (decreasing)operation capability of the machines; increase(decrease) with increasing (decreasing) machineavailability; increase (decrease) with increasing(decreasing) material handling system versatility;and be comparable among systems of di�eringsizes. Measures for routing ¯exibility are plentifulin the literature. Kochikar and Narendran (1992)present a measure which adheres to the criterialisted above. It focuses essentially on a speci®cpart-system example and evaluates the technicalpossibility of manufacturing at each stage of pro-cessing.

Operation ¯exibility is the `àbility to inter-change the ordering of several operations for eachpart type'' (Browne et al., 1984). The purpose ofoperation ¯exibility is to raise the level of machineutilization by interchanging the sequence of oper-ations or substituting an operation when theoriginally designated operation is unavailable. Thepurpose of an operation ¯exibility measure is topermit managers freedom in deciding how to al-locate production capacity in real time. For ex-ample, if a speci®c machine performing aparticular task breaks down, a production man-ager could redirect all the parts waiting for thattask to machines performing alternative tasks


while that machine is repaired. This could onlyoccur if the operation ¯exibility had been built intothe system and part-type design. Of course, thisredirection could occur when the system wascongested also, thus providing another mechanismfor smoothing production. Another purpose of themeasure could be as a comparison among alter-native designs for a prospective product. An oper-ation ¯exibility measure should: increase (decrease)with increasing (decreasing) number of inter-changeable operations within the part's processplan as a proportion of the total number of op-erations; and increase (decrease) with increasing(decreasing) number of machines available toperform the interchanged operations. Kumar(1987) proposes an entropic style operation ¯exi-bility measure which meets the criteria well. Thereare some small problems with respect to interpr-etation of de®nitions in Kumar (1987) but other-wise the measure is acceptable.

3. Using the developmental framework model

The framework has been used as a validationtool above. We now propose using it as a devel-opment tool to create measures for two of the re-maining Browne et al. (1984) ¯exibility types. Asno satisfactory measures were found in the litera-ture for volume and expansion ¯exibility we at-tempt these below. Development of a measure forproduction ¯exibility will not be tried due to theambiguity of this ¯exibility type. A discussion ofthe role of production ¯exibility will follow. Themeasures developed here are consistent with theabove criteria, but are not uniquely de®ned bythem. We believe they will prove useful in appli-cations.

3.1. Volume ¯exibility

Volume ¯exibility is considered to be the abilityto operate e�ciently, e�ectively and pro®tablyover a range of volumes. Greater volume ¯exibil-ity, ceteris paribus, is attained by having loweroperating ®xed costs, lower variable costs, higher

unit prices, or greater capacity. Primarily thismeans lowering costs, variable or ®xed, since oftenprices are market driven and capacity amountdecisions are often chosen in reaction to demandexpectations. Characteristically, higher levels ofautomation result in higher ®xed costs and re-duced variable costs, whereas the opposite is morecommon for conventional technologies.

Purpose: The purpose of volume ¯exibility is toguard against uncertainty in demand levels. Ger-win (1993) suggests the uncertainty is the aggre-gate product demand and the strategic objective ismarket share. If an enterprise has higher ®xedcosts or high variable costs (labor, material) it ismore di�cult to widely vary pro®table productionvolume compared with an enterprise for whichvariable or ®xed costs are lower. Therefore, thelatter ®rm will be able to weather demand declinesand is less likely to dismiss its existing workforceduring downturns, whereas the former enterprisewill be more susceptible to market vagaries. In thelonger term, the company with the more volume¯exible production system is the one more likely toendure economic troughs.

The objective of a measure of volume ¯exibilityis to gauge the range of pro®table volumes and thelimits of this range. The measure is likely to beused in strategic planning when looking at mediumto long term product marketing and analysis ofpotential tendering for contracts which encroachupon these time frames. For example, a companymay wish to tender for a mixture of contractswhich re¯ect di�ering volumes and time horizonsthus minimizing the risk of falling below somelower volume pro®tability limit.

Criteria: A volume ¯exibility measure should:not be technology speci®c, that is, it should beapplicable to any technology; be comparableamong systems of di�ering volumes; and increase(decrease) with increasing (decreasing) range ofpro®table production volumes.

Measures: An obvious ®rst measure is the rangeover which the system remains pro®table. Browneet al. (1984) state that volume ¯exibility may bemeasured ``by how small the volumes can be for allpart types with the system still being run pro®t-ably''. We suggest the range over which the systemis pro®table be de®ned by a lower limit where the


volume is the break-even point and an upper limitwhich is the maximum capacity of the productionsystem. The break-even point for the productionof a single product is de®ned as the quantity forwhich the Average Total Cost is equal to theMarginal Revenue, that is when the pro®t is zero.We suggest the following as an initial measure forvolume ¯exibility:

VF � VR

Cmax

� Cmax ÿ aNB

Cmax

;

where VR is the pro®tability range, Cmax is themaximum capacity of the system, a is the numberof capacity units required per part produced, andNB is the lower limit of the pro®table productionrange, that is the break-even point. The produc-tion capacity limit, Cmax, is the total productionavailability. For example, it may be that theavailable capacity is 8 hours per day Cmax� 8. Agiven product may require production of 2 hoursper part (a� 2), so a maximum of four parts couldbe made each day. The implied constraint is thatax 6 Cmax for feasible production x. This measurehas a theoretical range from 0 to 1, where zeromeans there is absolutely no scope for demand¯uctuation and 1 means that there is scope fordemand changes across the entire capacity range.This de®nition is obviously useful for one productmanufacturing scenarios only. To extrapolate thisto the multi-product manufacturing setting, wemust substitute the break-even analysis for manyproducts.

Break-even occurs when operating income iszero, that is, there is no operating loss or operatingpro®t. Consider the following equation: Sales ÿVariable costs ÿ Fixed costs � Operating income,that is PuN ÿ CuN ÿ F�Operating Income,where Pu is the unit price, Cu is the unit variablecost, N is the number of units, and F is the ®xedoperating cost. So for N�NB,

PuNB ÿ CuNBF � 0:

The break-even point for a single product,therefore, is

NB � FPu ÿ Cu

� Fb;

where b�Pu ÿ Cu is the contribution margin forthe product. Consequently, volume ¯exibility for asingle product scenario is

VF � 1ÿ aFbCmax

:

An implied assumption is that production isfeasible somewhere within the available capacity.Speci®cally, the number of units required to break-even (F/b) is less than the available production forthe part (Cmax/a), so F/b6Cmax/a. The one productcase is overly restrictive, however, since mostmanufacturers have a multi-product portfolio.Consider the situation for two products and asingle capacity constraint. Here the break-evenpositions form a line rather than a single point andthe positions of maximum capacity also form aline (see Fig. 2). The maximum capacity is speci-®ed as a line below which are all the feasiblecombinations for product mix volumes of x1 andx2. Likewise, the break-even is de®ned as a line onwhich every combination of x1 and x2 creates zeropro®t. The production volumes are the combina-tions of x1 and x2 values below the maximum ca-pacity line, that is the pro®table and unpro®tableareas. The feasible production mixes are de®ned asa1x1 � a2x26Cmax and the break-even line is de-®ned as b1x1 � b2x2 � F where bi is the contribu-tion margin of one unit of product i and ai is thenumber of capacity units required to make oneunit of product i. Therefore, pro®table productionlies below the maximum capacity line and abovethe break-even line, as shown in Fig. 2.

As for the single part-type case, it is assumedthat F =bi6Cmax=ai for all part-types i. In the twoproduct case, this has the diagrammatic e�ect (seeFig. 2) of requiring the entire break-even line tofall on or below the capacity constraint. Relaxingthis assumption would result in a reduction of thepro®table production region. For the followingvolume ¯exibility measure to remain valid underthis relaxation, the unpro®table regions wouldneed to be excluded from consideration and theparameters reevaluated accordingly. We do notconsider this relaxation here.

Consequently, unpro®table production lies be-low the break-even line and the volume ¯exibilitymeasure may be de®ned as


VF � 1ÿ Area of smaller triangle

Area of larger triangle

� �1=2

� 1ÿ �F =b1��F =b2��1=2��Cmax=a1��Cmax=a2��1=2�

� �1=2

� 1ÿ FCmax

a1a2

b1b2

� �1=2

:

More generally, for n products the break-evenis a (n ÿ 1) dimensional hyperplane, and themeasure is

VF � 1ÿ FCmax

Yn

i�1

ai

bi

!1=n

:

The nth root is necessary for the measure toremain valid for comparisons among systems thathave di�erent numbers of products. If we partitionone product into n separate but identical products,then we would not expect volume ¯exibility to bea�ected by this process. Yet

F n

Cnmax

Yn

i�1

ai

bi

!! 0 as n!1;

which follows from the earlier assumption, ifF/bi < Cmax/ai holds for the additional identical

products. Therefore, without the nth root the VFmeasure would increase merely by adding to thecomplexity of the product mix. We see that the VFmeasure is a reasonable de®nition.In fact, the VFmeasure:· increases (decreases) as F, the ®xed operating

cost, decreases (increases). This has the e�ectof lowering (raising) the threshold volume wherethe product mix becomes pro®table and hence,expanding (contracting) the pro®table range.

· increases (decreases) as Cmax, the maximum ca-pacity, increases (decreases). This increases (de-creases) the upper limit of the range, henceexpanding (contracting) the pro®table range.

· increases (decreases) as the contribution mar-gins, bis, increase (decrease). This relates to in-creasing (decreasing) the pro®tability of one ormore product(s) in the mix and hence enablinga more (less) pro®table range of production.

· increases (decreases) as the ais decrease (in-crease). This e�ectively allows production ofmore (fewer) of the same products than beforeby merely using less (more) production capacity.Table 3 shows the correspondence between the

purposes and criteria, and also how well thismeasure satis®es the criteria. The developmen-tal framework model was particularly helpful in

Fig. 2. Volume ¯exibility diagram for two products.


distilling the objectives of such a measure andappropriate criteria for judging it.

3.2. Expansion ¯exibility

Expansion ¯exibility is considered to be theability to easily add capacity or capabilities to theexisting system. Sethi and Sethi (1990) describe itas ``the ease with which its capacity and capabilitycan be increased when needed''. Sethi and Sethi(1990) quote several means of attaining expansion¯exibility including building small productionunits, having modular ¯exible manufacturing cells,having multi-purpose machinery that does notrequire special foundations and a material han-dling system that can be more easily routed, hav-ing a high level of automation that can facilitatemounting additional shifts, providing infrastruc-ture to support growth, and planning for change.

Consider the investment alternatives open to acompany: (1) invest heavily in conventionalequipment to cover capacity needs in the foresee-able future, (2) invest in a minimum e�cientquantity of conventional capacity and delay ad-ditional investment until further market informa-tion is gained, (3) invest in a minimum e�cientquantity of expansion ¯exible capacity and delayadditional investment until further market infor-mation is gained. There are arguments for andagainst each alternative. For example, the advan-tage of (1) is that the equipment cost of a completesystem is likely to be less than incremental in-vestments that sum to the same capacity. Thedisadvantages of (1) include the large ®nancial

commitment at a single point in time, and the lackof information regarding level and type of demandwhich may result in inappropriate and over- orunder-investment in equipment. A strategic ad-vantage that expansion ¯exibility endows upon a®rm is that a company may not need to purchaseall its equipment at the one time but can incre-mentally invest in the additional capital. This al-lows the ®rm to apportion funds in a way overtime to minimize ®nancial vulnerability by mini-mizing large up-front debt or substantially de-pleting cash reserves. This can somewhat insureagainst hostile takeover or similar threats. Also theadditional incremental investment is likely to bemore attuned to the company's real needs than asingle forecast at the initial investment stage.Hayes and Jaikumar (1988) argue against whatthey call ``irrational incrementalism'' with regardto CIM systems. They state that the bene®ts aCIM system can deliver can only result if the entiresystem is in place and operating. We argue that theminimum e�cient quantity in expansion ¯exiblesystems includes all the infrastructure which con-stitutes a CIM system. The additional investmentswe speak of are ones of additional capacity orproduction capabilities only.

Expansion ¯exibility is intended to permit acompany to expand production progressively,rather than purchase all equipment upfront whichmay place a prohibitive burden on the company. A®rm could purchase capacity as required. Initially,the company could purchase enough capacity toprovide minimum e�cient production, and asmarkets expand and market share increases, thecompany could then purchase any additional ca-

Table 3

Analysis of the volume ¯exibility measure

Purpose Criteria Compatibility

To guard against aggregate demand ¯uctuations Should increase (decrease) with an increasing

(decreasing) range of pro®table volumes

Yes

To be applicable to a variety of production technologies Should not include aspects particular to speci®c

manufacturing systems or technologies

Yes

To gauge the range of pro®table volumes for a

multi-product ®rm

Should permit a direct comparison between

single product and multi-product ®rms

Yes

Should be able to compare systems of di�ering

volumes and capacities

Yes

To be used as a quick reference for operational managers. Should be easily calculable Yes


pacity to meet new demands. These new capacityacquisitions could be undertaken in the knowledgethat the implementation and integration process islikely to be less disruptive than it might otherwisebe if expansion ¯exibility were not present. Also,the additional capacity may be purchased withbetter information than we may have at the initialinvestment stage.

Purpose: A measure of expansion ¯exibilitywould permit senior management to decide be-tween investments in a non-expansion ¯exible(conventional) system and an expansion ¯exiblesystem in a capacity-planning context. As such,having a numerical monetary amount could proveuseful in direct comparisons of the di�erent man-ufacturing technologies. The bene®t of a conven-tional system is that the upfront costs, per capacityunit, are likely to be less than an expansion ¯exiblesystem of the same size. The drawback of a con-ventional system is that the integration time andcost of additional capacity investments are higherthan for an `equivalent' ¯exible capacity.

Criteria: An expansion ¯exibility measureshould: capture the dominant dimensions ofcomparison; not be technology speci®c; allowcomparisons between large upfront investments ofconventional systems and smaller incremental in-vestments of expansion ¯exible capacity; and notlimit the number of stages of investment in theexpansion ¯exible scenario.

Measures: There is little in the literature re-garding measures of expansion ¯exibility. Steckeand Raman (1986) suggest a measure of expansion¯exibility would be a function of ``the magnitude ofthe incremental capital outlay required for pro-viding additional capacity: the smaller the marginalinvestment, the greater the expansion ¯exibility''.However, no explicit function is proposed. Sethiand Sethi (1990) cite a measure of Jacob whichdepends on a ratio of di�erences between long-termpro®ts of various systems. Wirth et al. (1990) pro-pose that the value of ¯exibility in decision analysiscan be measured by the di�erence between theExpected Monetary Values (EMVs) of a decisionwith information and a decision without informa-tion. It is assumed this information is gained bydelaying a decision. This approach was also thebasis of Mandelbaum (1978) work into ¯exibility in

decision making. We extend this line of thinking toexpansion ¯exibility. The di�erence between theEMV of the ¯exible option (EMVF) and the EMVof the conventional option (EMVC) results in theexpansion ¯exibility measure (EF), i.e.

EF � EMVF ÿ EMVC:

This model is, of course, highly dependent onthe comparison between the two systems. It doesnot provide a `stand-alone' measure of expansion¯exibility whereby a system can be evaluated on itsown merits. It does, however, capture the primaryattribute of expansion ¯exibility, that is, its ad-vantage over conventional systems. If the expan-sion ¯exible system o�ers lower costs than theconventional system, EF will exceed 0. An ad-vantage of this measure is that it is measured indollar, or currency, terms. This can assist in a ®-nancial evaluation and in a presentation to aboard of directors who are used to dealing pri-marily with monetary ®gures. By the same token,however, the transferability of the measure toother industries and circumstances is lost since theproportions of the investment are obvious. Themodel we formulate is deliberately limited for il-lustrative purposes. It could be easily extended toaccommodate several investment periods ratherthan just two. It could also accommodate addi-tional investments in the conventional equipment,although it is trivial to show that if the marginalcost of additional conventional capacity is greaterthan that of ¯exible capacity, the ¯exible capacityalternative will always have a superior EMV. Themarginal cost of additional conventional capacityis greater than that of the ¯exible capacity since thelatter technology is designed for integration intoexisting systems, using modular equipment de-signs. The conventional capacity is not designed todo this and therefore, the cost of additional ca-pacity includes the implementation and integrationcosts, which boost the cost above that of the¯exible equivalent.

Our model assumes: contribution margin, andhence operating costs, are equal for each of thetechnologies; only a single product is manufac-tured; the manufacturer can produce as manyunits as demand dictates or capacity allows, which-ever is the smaller; capacity may be purchased in


continuous amounts; in period 1, demand is un-known but an estimate is evaluated by a weightedsum of demand estimates; the weightings areprobabilities of various `world states' of demandfor the product; demand is perfectly known atperiod 2, and managers can purchase an additionalamount of capacity to exactly meet the knowndemand; and the manufacturer is risk neutral, andhence uses the expected monetary value criterionas a basis for ®nancial evaluation. This, in e�ect,means the ¯exible option will always manufactureto demand, whereas the conventional option willmanufacture as much as demand or maximumcapacity will allow.

Assume a demand set D1;D2; . . . ;Dm whereD16D26 � � � 6Dm with associated probabilitiesp1; p2; . . . ; pm; for some odd integer, m > 0. If theconventional capacity purchased is CC, then

EMVC �Xm

i�1

pip min�Di;CC� ÿ kCCC;

EMVF �Xm

i�1

pipDi ÿXm

i�1

pikFDi;

where p is the contribution of the product, kC isthe unit acquisition cost of the conventional ca-pacity, and kF is the same for the ¯exible capacity.Note, appropriate discount factors can be builtinto the acquisition costs, without loss of gener-ality.

By plotting EMVC against CC, as in Fig. 3, wecan see that the maximum EMVC does not nec-essarily occur at the weighted sum of the demandsbut could be at one of the demand levels. Theprobability distribution used to create the curve inFig. 3 was discrete, symmetrical and increasing to

Fig. 3. EMVC vs CC.


a maximum at the mean (for an odd integer, m).This distribution was used to resemble a normaldistribution. The shape of the curve depends onthe shape of the probability distribution of thedemands. Whereas the mean of the demandprobability distribution was 750 in this simplenumerical example, the largest EMVC was ob-served at CC� 810.

Fig. 4 shows the demand values with their as-sociated probabilities and where CC lies in thecontinuum. Suppose CC assumes a value betweenDk and Dk�1. This is valid because the choice of CC

will be determined by maximizing EMVC as fol-lows. From the above de®nition, we have

EMVC � pXk

i�1

piDi � pCC

Xm

i�k�1

pi ÿ kCCC:

Now,

oEMVC

oCC

� pXm

i�k�1

pi ÿ kC:

Hence, if pPm

i�k�1 pi ÿ kC > 0 then CC P Dk�1; andif p

Pmi�k�1 pi ÿ kC < 0 then CC6Dk; where

16 k6mÿ 1. Thus,

C�C � Dj� where pXm

i�j��1

pi6 kC < pXm

i�j�pi;

where CC is the optimal level of conventional ca-pacity. (We assume, without loss of generality,that kC < p and hence 16 j�6m. If kC > p nocapacity should be purchased. If j� �m the leftterm in the in equality for kC above is read as 0.)

Now, assume further that the discrete demanddistributions are constructed as in Fig. 5. Sopj �

Pji�1 ai. By inspection we can see that (with-

out loss of generality) demand can assume 2n + 1values (m� 2n + 1), and we can scale the distri-bution so that Di � l� iÿ nÿ 1 for i 2 f1;2; . . . ; 2n� 1g.

So

a1 � �a1 � a2� � � � � �Xn�1

i�1

ai � � � � � �a1 � a2�

� a1 � 1

i.e.

Xn�1

i�1

ai�2nÿ 2i� 3� � 1: �1�

Also,

r2

2� a1

Xn

j�1

j2 � a2

Xnÿ1

j�1

j2 � � � � � an

X1

j�1

j2

� a1

n�n� 1��2n� 1�6

� a2

�nÿ 1�n�2nÿ 1�6

� � � � � an1 � 2 � 3

6

and so,

r2 �Xn

i�1

ai�nÿ i� 1��nÿ i� 2��2nÿ 2i� 3�

3;

�2�where r2 is the variance of the demand distribu-tion. Let us denote the value of EMVC where CC �C�C by EMVC� . Now EF � EMVF ÿ EMVC� . As-sume, for simplicity, that p/kC� 2 so thatC�C � l � Dn�1.

Fig. 4. Demand line showing CC between Dk and Dk�1.


Proposition 1. r2 is maximized for the discreteuniform distribution. That is,

a1 � 1

2n� 1; aj � 0 for j � 2 to n� 1:

Proof. Consider the following linear program:

max a1

n�n� 1��2n� 1�3

� � � � � an1 � 2 � 3

3

s:t:

a1�2n� 1� � a2�2nÿ 1� � � � � � 3an � an�1 � 1

and ai P 0 for all i:

By the theory of linear programming, there is atmost one variable greater than zero in the solutionto this linear program with one constraint. Clearly,a1 has the highest ratio of objective function co-e�cient to constraint coe�cient of all the vari-ables:

�nÿ i� 1��nÿ i� 2��2nÿ 2i� 3�3�2nÿ 2i� 3�

so, a1 � 1=�2n� 1�; a2 � � � � � an�1 � 0: �

Now,

EMVC�

p� a1�lÿ n� � �a1 � a2��lÿ n� 1� � � � �� a1 � � � � � an��lÿ 1�

� l1

2� 1

2�a1 � � � � � an�1�

� �ÿ 1

2l

� nla1 � �nÿ 1�la2 � � � � � 1 � lan

� 1

2�a1 � � � � � an�1�l

ÿ a1

Xn

i�1

iÿ a2

Xnÿ1

i�1

iÿ � � � ÿ an

X1

i�1

i

� ��2n� 1�a1 � �2nÿ 1�a2 � � � � � an� l2

ÿ a1

n�n� 1�2

ÿ a2

�nÿ 1�n2

ÿ � � � ÿ an1 � 2

2

� l2ÿ a1

n�n� 1�2

ÿ a2

n�nÿ 1�n2

ÿ � � � ÿ an1 � 2

2;

where the last equality follows from Eq. (1). Now,

EMVF � �pÿ kF�X2n�1

i�1

piDi � �pÿ kF�l;

which is a constant, independent of all ai. So,

EF

p� a1

n�n� 1�2

� a2

�nÿ 1�2� � � � � an

1 � 22

ÿ constant:

Given r2, we seek to maximize EF. Suppose

EF� � maxai;r2�k

EF:

Proposition 2. EF� is a monotonically increasingfunction of r2.

Proof. We have

max a1

n�n� 1�2

� a2

�nÿ 1�n2

� � � � � an1 � 2

2� f ;

s:t:

a1�2n� 1� � a2�2nÿ 1� � � � � � 3an � an�1 � 1;

a1

n�n� 1��2n� 1�3

� � � � � an1 � 2 � 3�

3� r2

and ai P 0 for all i:

So we must show for this linear program thatthe marginal price for the second constraint isgreater than or equal to zero. Since there are twoconstraints, there are at most two variables greaterthan zero in the optimum solution. Let us considerthree cases.

Case 1: an�1 > 0 at optimum, for some r2.Suppose the other positive variable is as. Soas(2n ÿ 2s + 3) + an�1� 1 and

Fig. 5. Demand distribution constructed by components.


as�nÿ s� 1��nÿ s� 2��2nÿ 2s� 3�

3� r2:

Therefore

fmax � as�nÿ s� 1��nÿ s� 2�

2

� 3r2

2�2nÿ 2s� 3� ;

an increasing function of r2. So, provided e issu�ciently small, increasing r2 to r2 + e increasesfmax.

Case 2: an�1� 0 for some r2. Suppose as, at ¹ 0,16 s < t6 n.

Ksas � Ktat � 1; msas � mtat � r2;

f � psas � ptat;

where K, m, and p are constants from Eqs. (1) and(2), and the mathematical program under exami-nation. Now increase r2 to r2 + e, where e is smallenough so that as, at remain greater than zero.Now de®ning Das� as(r2 + e) ÿ as(r2) and simi-larly for Dat,

Ks Kt

ms mt

� �Das

Dat

� �� 0

e

� �:

By Cramer's rule,

Das � ÿeKt

Ks Kt

ms mt

�� Dat � eKs

Ks Kt

ms mt

�� ;Ks

ms� 3

�nÿ s� 1��nÿ s� 2� <Kt

mtsince s < t:

Therefore

Ks Kt

ms mt

�� < 0; so Das > 0;Dat < 0;

Dasps � Datpt � ÿeKtps � eKspt

Ks Kt

ms mt

�� ; �4�

ps

Ks� �nÿ s� 1��nÿ s� 2�

2�2nÿ 2s� 3� :

Let 1 + n ÿ s� x and so

ps

Ks� x�x� 1�

2�2x� 1� ;

d

dxx�x� 1�

2�2x� 1� ��2x� 1�2 ÿ 2�x2 � x�

�2x� 1�2

� 2x2 � 2x� 1

�2x� 1�2 > 0:

So (ps/Ks) is a decreasing function of s, which leadsto

ps

Ks>

pt

Ktand so psKt ÿ ptKs > 0: �5�

It follows from Eqs. (4) and (5) that Dasps �Datpt > 0 and hence fmax increases with r2 for thiscase as well.

Case 3: at � 1=�2nÿ 2t � 3� and all otherai � 0. The argument for Case 2 can be slightlymodi®ed to show that when r2 is increased tor2 + e, for su�ciently small e, Dat < 0 andDas < 0 for some s < t and fmax increases withr2. h

Propositions 1 and 2 suggest that the expansion¯exibility measure is greater in situations ofgreater risk, or variance. Fig. 6 shows the rela-tionship of EF� vs. r2 for a sample discrete de-mand distribution numerically. For example, weapproximate a normal demand distribution by adiscrete one, setting m� 11 and letting the prob-ability distribution for demand be symmetric withmean 750 and pi increasing from demand values400±750 and decreasing from demand values 750±1100. During this exercise, a constant mean de-mand of 750 was maintained. If we now vary r2 weobtain the behavior of EF� shown in Fig. 6.

The results, summarized in Fig. 6, were ob-tained by calculating EF for various values of thevariance of the probability distribution. The set ofEF values against variance (Fig. 6) was built by®xing the variance of the distribution for any onecase and using an optimizing algorithm within aspreadsheet application to maximize EF. Sincemany probability distributions can exist for agiven value of variance, some intervention wasrequired by setting initial `starting' positions of thedistribution in order to achieve the maximal valuesof EF for each variance value. Therefore, both the


propositions and the numerical experiments sug-gest EF increases monotonically with variance.This implies that EF is increasingly important asthe certainty regarding the demand levels dimin-ishes. In fact, EF is maximized for a uniform de-mand probability distribution, which representsthe highest uncertainty under the `normality'constraints mentioned earlier. (Removing these`normality' constraints results in EF being maxi-mized when all the probability is allocated to theextreme low and high demand values and none inbetween. This scenario, however, is unrealistic; itwould be very unusual for the knowledge aboutthe demand to be so polarized.)

In conclusion, the model captures the dominantcharacteristic of expansion ¯exibility, hedgingagainst unknown demand. The expansion ¯exiblecapacity returns a higher EMV than the conven-tional capacity as the variance, or uncertainty, ofthe probability demand distribution increases.This means it would be worthwhile delaying aninvestment decision, or investing only part of thenecessary capacity, when there is higher demanduncertainty, until a time when demand levels are

more certain. This certainty may take the form ofsuccess in contract tendering, a change in govern-ment investment or protection policy, or marketsuccess of an associated (that is, positively demandcorrelated) product.

3.3. Production ¯exibility

Production ¯exibility was included in the orig-inal ¯exibility taxonomy by Browne et al. (1984).There has been little debate over its role in the¯exibility arena. Browne et al. and others imply itrepresents the culmination of the extents or e�ectsof the other seven ¯exibility types. An immediateand obvious measure is simply the sum of previousseven ¯exibility measures. This, however, does notaccount for the varying importance of di�erent¯exibility types in di�erent production systems,under di�erent business circumstances. An im-provement could be a weighted sum to account forthese di�ering circumstances and situations.However, this still requires that all ¯exibilitymeasures be in the same units and leaves other

Fig. 6. Expansion ¯exibility as a function of variance of the demand probability distribution.


questions unanswered: Are these seven ¯exibilitytypes the only ones that are needed to fully des-cribe ¯exibility in an organization? Who decidesthe relative importance (weightings) of the ¯exi-bility types? What is the role of production ¯exi-bility? How are these ¯exibility types related?

It appears that production ¯exibility is an at-tempt to capture the holistic aspects of ¯exibility.Previous authors (see Chung and Chen, 1989) havepursued a similar line of thought although signi-®cant gaps still exist in our understanding. Twoitems which may extend our understanding ofproduction ¯exibility are (1) an examination of therelationships among ¯exibility types and (2) alisting of the ``dimensions of comparison''. Theformer is pursued in the next section and the latterwas discussed in Section 2.1.

4. Relationships among ¯exibility types

The real challenge for managers and research-ers are not only to appreciate the existence of avariety of ¯exibility types but also the existence ofrelationships and trade-o�s among them. It is allvery well to refer to a required level of a particular¯exibility but the non-monetary costs of attainingthis ¯exibility should be comprehended too. Thesenon-monetary costs could include a decrease inother ¯exibility types which in turn could a�ectproduction objectives (e.g. machine utilization),service objectives (e.g. delivery timeliness) ormarket objectives (e.g. product availability). Un-derstanding the relationships among ¯exibilitytypes is paramount for understanding the mana-gerial task required to manage enterprise ¯exibili-ty. Given this, it is perhaps surprising there hasbeen so little research into these relationships ortradeo�s. Of course, one reason for this may bethat the relationships are complex. Some rela-tionships seem apparent, and we will discuss someof these, but others are not obvious and changewith manufacturing systems and usage.

Browne et al. (1984) presented a diagram whichindicated the hierarchical relationship among¯exibility types (see Fig. 7). The arrow indicates``necessary for''. Therefore, machine ¯exibility isnecessary for product, process and operation

¯exibilities and so on. This implies that there is, forexample, a positively correlated and supportiverelationship of machine ¯exibility to product ¯ex-ibility. As Browne et al. state, ideally all FMSswould possess the greatest amount possible of allthese ¯exibility types but, of course, the cost wouldbe prohibitive. Therefore, decisions regardingamounts desired and required by the companyneed to be made and information regarding thetradeo�s and relationships among the ¯exibilitytypes will aid these decisions. Gupta and Goyal(1992) are the only authors who have carried out astudy using simulation into the relationshipsamong ¯exibility types. Other authors have men-tioned relationships they have recognized, but todate, the Gupta and Goyal study is the only onethat attempts to examine all the relationships in acomprehensive manner. These authors use com-puter simulation to examine the e�ect of di�erentsystem con®gurations and di�erent loading/scheduling strategies on various performance pa-rameters. However, the performance parameterschosen are machine idle time (MIT) and jobwaiting time (JWT) which, we believe, places anoveremphasis on the time or response aspects ofmanufacturing ¯exibility. Also we believe that byconcentrating the analysis on these two parametersalone, some tenuous conclusions are drawn. Guptaand Goyal draw conclusions based purely onchanging con®gurations and the subsequent e�ecton these performance parameters. For example,they state (p. 532): ``let us increase the job types toten. A statistically signi®cant di�erence will indi-cate a change in machine idle time. If the machines

Fig. 7. Hierarchical relationship between ¯exibility types

(source: Browne et al., 1984).


incur a higher idle time while processing ten jobtypes then it can be inferred that an increase inproduct variety has adversely a�ected volume¯exibility. It may be noted that increasing productvariety implies an inherent increase in the product¯exibility of the manufacturing system. The systemwould not be able to process more job types oth-erwise. This demonstrates an inverse relationshipbetween product ¯exibility and volume ¯exibility''.Following such logic, Gupta and Goyal (1992)suggest several relationships. They also examinethe e�ects of several loading strategies and dis-patching strategies. They conclude by stating: ``wewould like to state that this study is based onsimulation and therefore it is assuming in nature.The results are system speci®c and may not begeneralized to other systems''. This indicates somereservations these authors had. The primary out-comes of the Gupta and Goyal (1992) study is thee�ect of di�erent loading/scheduling schemes onmachine idle time and job waiting time and sec-ondly, upon some ¯exibility types.

Below, we examine some relationships among¯exibility types. This work is preliminary ratherthan de®nitive and we believe much further workwill be required before we gain a thoroughknowledge of these relationships. We will discussonly a limited number of these relationships, withan objective of initiating further work in the area.Also, our work is qualitative and indicative of thegeneral trend of the relationship rather than anabsolute statement. A comprehensive, empiricalstudy into the tradeo�s and relationships is beyondthe scope of this paper but hopefully it will, incombination with model building and simulationwork, lead to a fuller understanding. Flexibilityrelationships, we imagine, will be closely inter-twined with managerial issues and substantialmanagerial insights will be developed. After ourdiscussion, we will present a table which willsummarize this qualitative discussion of relation-ships among the ¯exibility types.

Machine vs process: Buzacott (1982) suggeststhere should be a positive relationship betweenthese two ¯exibility types, that is, as machine¯exibility increases so does ``job'' ¯exibility. Hestates that ``in systems that are inadequately con-trolled so that it is not possible to exploit diversity

in job routing it is possible for machine ¯exibilityto decline with job ¯exibility''. He proposes thatthe capabilities that endow a machine with ma-chine capability also complicate it to the degreewhere machine reliability is a problem. Also thesecapabilities will contribute to a lowering of ma-chine e�ciency and hence, machine ¯exibility. Hesuggests for a single machine, machine ¯exibility ismostly independent of process ¯exibility.

Generally, we agree that a positive relationshipexists here since the capabilities which underpinboth ¯exibility types are common, namely, CNCcapabilities, tool magazines and automatic toolloaders. The ability to change between operations(machine ¯exibility) directly assists in the ability tochange between di�erent products (process ¯exi-bility). Intuitively, an increase in the range of op-erations able to be performed by a machine willexpand the range of products that can be producedon that machine. There are other factors whichdrive process ¯exibility and therefore there is not adirectly proportional relationship, especially sincemachine ¯exibility relies heavily on the mode ofusage. Several authors (Browne et al., 1984; Sethiand Sethi, 1990) have suggested that machine¯exibility is a foundation and prerequisite forprocess ¯exibility.

Machine vs product: Again, machine ¯exibilityis acknowledged as a prerequisite for product¯exibility, as it provides the foundation capabili-ties, that is performing several operations on theone machine. Just as this permits changing be-tween products (process ¯exibility) because di�er-ent products typically have di�erent operations intheir process plans, machine ¯exibility permits theintroduction of additional products to the currentproduct mix. This means that as machine ¯exibil-ity increases, that is more operations are able to beconducted on the machine, there is a greater like-lihood that the machine will be able to undertakethe production of newly introduced parts, thusre¯ecting a higher product ¯exibility. Gupta andGoyal (1992) suggest that increasing the number ofmachines enhances the ability of the system tomake ``changes required to produce a given set ofpart types'', which is machine ¯exibility, and alsolowers the waiting times for jobs, which thereforesupplements ``the system's capability to change-


over to produce a new part, thus improvingproduct ¯exibility''. As mentioned previously,some of Gupta and Goyal's (1992) deductionscould be called into question, although their con-clusions regarding the ¯exibility relationships aregenerally sound.

Machine vs operation: We believe machine¯exibility underpins operation ¯exibility. By hav-ing machine ¯exibility, the potential for the usageof operation ¯exibility is ampli®ed, although themajority of operation ¯exibility is drawn from thedesign of the part and the subsequent inter-changeability of tasks. Given that any given parthas the innate capabilities of operation ¯exibility,an increased machine ¯exibility will permit agreater usage of the potential. However, the con-verse is not true; an enhanced potential operation¯exibility of a part will not increase the ability of amachine to perform additional operations. This, infact, re¯ects the directional hierarchy of Fig. 7whereby machine ¯exibility is ``necessary for''operation ¯exibility, but the direction of the arrowis not reversible.

Routing vs operation: Several authors havecommented that these two ¯exibility types areclosely related but few have discussed this at length.The relationship again is unidirectional. Increasingthe ability to route and reroute a part through asystem, that is routing ¯exibility, will permit anincreased ability to use the operation ¯exibility of apart by allowing the part to visit various machineswhen the sequence of tasks is changed. Providingmore routes in the system allows greater versatilityin task resequencing. However, endowing a partwith greater operation ¯exibility does not, inturn, permit greater ability to reroute a part. Thisre¯ects the Browne et al. (1984) hierarchy.

Routing vs volume: Gupta and Goyal (1992)state that they interpret an increase in the MIT asa reduction in the volume ¯exibility of the system,since volume ¯exibility is the ability to operatepro®tably at di�erent production volumes and ifthere is a higher MIT, then the system is not op-erating as pro®tably as it might be. This is, webelieve, a misinterpretation of the de®nition ofvolume ¯exibility. Volume ¯exibility is the extentof the production range over which the system canoperate pro®tably and a particular usage showing

a lower machine utilization does not re¯ect achange in the volume ¯exibility. We believe thisrelationship could be related in that an increase inrouting ¯exibility increases the maximum potentialsystem capacity and hence increases volume ¯exi-bility. This is because machines that were notpreviously connected are now joined thus in-creasing the maximum potential system capacity.Another possibility is that the additional infra-structure (for example: AGVs, de®ned routes) thatis associated with an increase of routing ¯exibilitycould in fact increase the ®xed cost component ofthe cost structure and therefore, subsequently de-crease volume ¯exibility, depending on how ®xedcosts are calculated. Therefore, it would seem thatthis relationship could certainly be nonlinear. Al-though Gupta and Goyal (1992) do not explicitlystate this ®nding of non-linearity, they ®nd thatsmaller system con®gurations produce a positiverelationship between routing and volume ¯exibilityand larger system con®gurations produce a nega-tive relationship. A possible cause for this may bethat for larger con®gurations, the ®xed cost of therouting infrastructure could overwhelm the utili-zation bene®ts and the relationship switches froma positive to a negative orientation. Gupta andGoyal (1992) do not provide an explanation formost of the results they observed.

In summary, there has been little thorough in-vestigation into the relationships among ¯exibilitytypes, even though there is great potential formanagerial insights into ¯exibility competitive-ness. We have collected some of the ``accepted''relationships and provided them in Table 4. This isnot a complete listing and the blank spaces suggestan opportunity for further work. Further, theserelationships will vary greatly according to a va-riety of environmental and usage factors.

5. Concluding remarks

This paper has presented a framework to fa-cilitate the development of ¯exibility measures bydirecting the focus onto the purposes and criteriaof the measure. This development framework en-ables existing measures to be evaluated, as shown


for machine, process, product, routing, and oper-ation ¯exibility. It also permits development ofnew measures as shown for volume and expansion¯exibility. There are several pairs of `dimensions ofcomparison' which can also aid this developmentby furthering the understanding of these ¯exibilitytypes. We also raise the issue of relationshipsamong ¯exibility types. Little work has been donein this area so far but we believe it will be ofsubstantial importance in the future to the study ofmanufacturing ¯exibility.

References

Bolwijn, P., Kumpe, T., 1990. Manufacturing in the 1990s:

Productivity, ¯exibility and innovation. Long Range Plan-

ning 23 (4), 44±57.

Brill, P.H., Mandelbaum, M., 1989. On measures of ¯exibility

in manufacturing systems. International Journal of Produc-

tion Research 27 (5), 747±756.

Brill, P.H., Mandelbaum, M., 1990. Measurement of adaptivity

and ¯exibility in production systems. European Journal of

Operational Research 49, 325±332.

Browne, J., Dubois, D., Rathmill, K., Sethi, S.P., Stecke, K.E.,

1984. Classi®cation of ¯exible manufacturing systems. The

FMS Magazine, April, pp. 114±117.

Buzacott, J.A., 1982. The fundamental principles of ¯exibility

in manufacturing systems. Proceedings of the First Inter-

national Congress on FMS, pp. 13±22.

Carlsson, B., 1992. Management of ¯exible manufacturing: An

international comparison. OMEGA 20 (1), 11±22.

Carter, M.F., 1986. Designing ¯exibility into automated man-

ufacturing systems. Proceedings of the Second ORSA/TIMS

Conference on FMS, Ann Arbor, Michigan, pp. 107±118.

Chung, C.H., Chen, I.J., 1989. A systematic assessment of the

value of ¯exibility from FMS. Proceedings of the Third

ORSA/TIMS Conference on FMS, Cambridge, Massachu-

setts, pp. 27±34.

De Groote, X., 1992. Flexibility and product diversity in lot-

sizing models. Working paper no. 92/05/TM, INSEAD,

Fontaineblean, France, pp. 1±17.

De Meyer, A., Nakane, J., Ferdows, K., 1989. Flexibility: The

next competitive battle ± the manufacturing futures survey.

Strategic Management Journal 10, 135±144.

Dixon, J.R., 1992. Measuring manufacturing ¯exibility: An

empirical investigation. European Journal of Operational

Research 60, 131±143.

Gerwin, D., 1993. Manufacturing ¯exibility: A strategic

perspective. Management Science 39 (4), 395±410.

Gunasekaran, A., Martikainen, T., Yli-Olli, P., 1993. Flexible

manufacturing systems: An investigation for research and

applications. European Journal of Operational Research 66,

1±26.

Gupta, Y.P., Goyal, S., 1989. Flexibility of manufacturing

systems: Concepts and measurements. European Journal of

Operational Research 43, 119±135.

Gupta, Y.P., Goyal, S., 1992. Flexibility trade-o�s in a random

¯exible manufacturing system: A simulation study. Interna-

tional Journal of Production Research 30 (3), 527±557.

Hayes, R.H., Jaikumar, R., 1988. Manufacturing's crisis: New

technologies, obsolete organizations. Harvard Business

Review, Sep±Oct, pp. 77±85.

Table 4

Descriptive relationships between ¯exibility types


Jaikumar, R., 1986. Postindustrial manufacturing. Harvard

Business Review, Nov±Dec, pp. 69±76.

Kochikar, V., Narendran, T., 1992. A framework for assessing

the ¯exibility of manufacturing systems. International

Journal of Production Research 30 (12), 2873±2895.

Kumar, V., 1987. Entropic measures of manufacturing ¯exibil-

ity. International Journal of Production Research 25 (7),

957±966.

Mandelbaum, M., 1978. Flexibility in decision making:

An exploration and uni®cation. Ph.D. Thesis, Department

of Industrial Engineering, University of Toronto, Canada.

Sethi, A.K., Sethi, S.P., 1990. Flexibility in manufacturing: A

survey. International Journal of Flexible Manufacturing

Systems 2, 289±328.

Slack, N., 1987. The ¯exibility of manufacturing systems.

International Journal of Operations and Production Man-

agement 7 (4), 35±45.

Stecke, K.E., Raman, N., 1986. Production ¯exibilities and

their impact on Manufacturing Strategy. Working paper no.

484, School of Business Administration, The University of

Michigan, Ann Arbor, MI, pp. 1±36.

Upton, D.M., 1994. The management of manufacturing ¯ex-

ibility. California Management Review 36 (2), 72±89.

Upton, D.M., 1997. Process range in manufacturing: An

empirical study of ¯exibility. Management Science 43 (8),

1079±1092.

Voss, C.A., 1988. Success and failure in advanced manufactur-

ing technology. International Journal of Technology Man-

agement 3 (3), 285±297.

Wirth, A., Samson, D.A., Rickard, J., 1990. The value of

¯exibility and control in decision analysis. International

Journal of Information and Management Science 1 (2), 107±

113.


Manufacturing ﬂexibility: Measures and relationships

Documents

Transcript of Manufacturing ﬂexibility: Measures and relationships