*Corresponding author. Tel.:#39-02-23992800; fax:# 39-02-23992720.
E-mail address:[email protected] (G. Toletti)
Selecting quality-based programmes in small
"
rms:
A comparison between the fuzzy linguistic approach
and the analytic hierarchy process
Giuliano Noci, Giovanni Toletti*
Department of Economics and Production, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milan, Italy
Received 11 March 1998; accepted 27 October 1999
Abstract
Over the last few years, a large number of"rms have implemented TQM programmes in order to introduce e!ective quality systems and to achieve high-quality products. However, many empirical studies demonstrate that most of the adopted quality-based programmes did not improve the small"rms'competitiveness and pro"tability. The reasons for such failures are manifold. Among them, the lack of an operating tool able to support managers in the identi"cation of quality-based priorities particularly a%icts small "rms. In this paper the authors attempt to suggest an integrated decisional tool. In particular, according to main characteristics of quality-based programmes, they analyse how MADM techniques should be used to identify quality-based priorities. ( 2000 Published by Elsevier Science B.V. All rights reserved.
Keywords: Total quality management; Fuzzy linguistic approach; Analytic hierarchy process; Small "rms; Quality investments' evaluation
1. Introduction
Over the last few years, a large number of"rms have implemented TQM programmes in order to introduce e!ective quality systems and to achieve high-quality products [1,2]. However, many empiri-cal studies demonstrate that most of the adopted quality-based programmes did not improve the small"rms'competitiveness and pro"tability [3}7]. In our opinion such a failure depends on two sets of reasons:
1. distinctive features characterising small"rms; 2. general problems a!ecting all"rms in the
assess-ment of quality-based programmes.
1.1. Distinctive features characterising smallxrms
1. In order to implement TQM initiatives, par-ticipation of all the supply value chain actors is fundamental. In this perspective small and medium
"rms can have some disadvantages because of their low propensity to collaborate with suppliers and/or customers. Furthermore, the low bargaining power characterising small and medium companies does not allow them to transfer to suppliers and/or customers the costs related to the adoption of quality-based investments.
Fig. 1. Decisional process for the selection of the priorities in quality management.
2. Small"rms are characterised by some distinc-tive features. On one hand, they can facilitate the implementation of quality-based programmes and on the other, can make it more di$cult. Indeed, small "rms take advantage, with respect to large companies, of their higher production #exibility, but, at the same time, they are subjected to some peculiar constraints such as limited competencies, resources, time and data [8,9], reducing their capa-bility in implementing total quality management programmes.
1.2. Problems awecting allxrms
1. It is not only di$cult to distinguish between `what is qualitya and `what is nota, but also to understand the meaning of`goodaand`bada qual-ity [6,10,11]. Such ambiguities make the identi" ca-tion of the quality targets and the measurement of the achieved performance very complex proced-ures. Hence, according to the goal setting theory [12,13], we would say that, in order to achieve the planned objectives, managers need to identify tar-get indicators that are easy measurable and that are closely related to results.
2. At the state of the art, there is a lack in operating tools able to support managers through-out the decisional process (see Fig. 1) [14}16].
Whereas, speci"c and e!ective models aimed only at evaluating and selecting the most promising
quality-based investment [16}23] do exist, it is a fact that the pre-selection of the feasible quality-based alternatives is rather neglected. The problem is all the more important since the existing models require a lot of data and a time consuming analysis. Hence, they are useful only to compare a few qual-ity-related investments, thus requiring a pre-selec-tion of the most interesting alternatives. This a!ects all the companies, but particularly concerns small
"rms, these being a!ected by the above enlightened problems. Such"rms are unable to deal with the wide number of quality investment alternatives to be considered and, for this reason, they tend to imitate the quality initiatives of large com-panies, without properly considering their own peculiarities.
In the light of these issues, the aim of this paper is to provide small"rms'managers with an operating tool able to support the identi"cation of the qual-ity-based alternatives that must be evaluated in detail with speci"c tools. Hence a "rm, with its limited resources, would have to consistently analyse only few options.
Hence, the remainder of the paper consists of four major sections: (i) Section 2 analyses the prob-lem of the evaluation of TQM investments in SMEs, identifying a process that has to be followed for their evaluation; (ii) Section 3 proposes a taxon-omy of the data that have to be considered or collected; (iii) Section 4 describes how it is possible to rank di!erent quality investments typologies im-plementing two multi-attribute decision-making techniques (i.e. fuzzy linguistic approach (FLA) and analytic hierarchy process (AHP); (iv) and"nally, Section 5 applies to the real situation in which the two MADM techniques proposed in order to evaluate their performance.
2. The evaluation of TQM investments in SMES
Fig. 2. The selection of the best quality investments.
a complete evaluation of each of these. Hence, it would be particularly important to allow SMEs managers a quick screening of the most promising alternatives. In this respect we suggest a method for ranking a set of feasible quality investments typolo-gies in order to enlighten those that would have to be analysed more carefully (see Fig. 2). Hence, the
"rst step of the managers'decisional process (i.e. the selection of the possible investment alternatives) is greatly simpli"ed because their only need is to identify the speci"c investments to evaluate among the categories the one with the best rank.
The suggested method consists of three steps providing managers with an operating tool which ranks di!erent quality investments:
1. Dexnitionof a taxonomy of quality-based
invest-ments aimed at properly identifying a set of alternatives to be evaluated.
2. Identixcationof the "rm's exogenous and
endo-genous quality priorities. The former are those
priorities exogenous to the"rm's quality system, depending for instance on the environmental context, whereas the latter are those priorities closely related to a"rm's quality de"ciencies. It is a matter of fact indeed that a "rm can be in#uenced in its capital budgeting process both by the competitive context in which it operates and by the failures of its quality system. Thus, it is "rst necessary to identify some typical com-petitive contexts that would allow us to de"ne
the di!erent exogenous quality priorities of a"rm and, then, to model a"rm's quality system in order to show the possible reasons for the endogenous ones.
3. Ranking of the di!erent typologies of
invest-ments according to the taxonomy of quality-based investments just introduced and to the corporate quality priorities that have been iden-ti"ed.
According to this framework, a software tool aimed at supporting SMEs managers in identifying their company's quality priorities, has been de-veloped. Such a tool has three main characteristics:
f it has embedded in itself a taxonomy of quality-based investments, thus limiting the alternatives to be analysed;
f it has a framework guiding SMEs managers in the self-evaluation of their "rms exogenous and endogenous quality priorities;
f it gives managers the possibility of using both a software (developed by ourselves) allowing the ranking of TQM investments according to the FLA, and a software (chosen among the many available [24]) allowing the same ranking through the utilisation of the AHP.
evaluated, thus providing SMEs managers with a pre-selection of alternatives to evaluate and in the process simplify the managers' selection process.
3. The relevant data
Once the three-step method that has to be fol-lowed for the evaluation of TQM investments is introduced, it is necessary to identify the relevant data needed to implement it. According to the steps just described, three main categories of data have to be considered. The"rst concerns the feasible qual-ity-based investments, whereas the others are related to the identi"cation of exogenous and endogenous quality priorities. In order to achieve this information we have to de"ne:
(1) the set of feasible quality investments;
(2) the competitive context in which the"rm oper-ates;
(3) the"rm's quality system.
3.1. The set of feasible quality investments
Many approaches for classifying quality-based investments have been suggested. Among them, we consider one based on two critical variables [16]: (i) the type of problem under evaluation and (ii) the
"nancial cash outlay needed for the implementa-tion of each investment.
The type of problem under evaluation re#ects the area of the corporate quality system a!ected by the investment, making easier the identi"cation of the speci"c performance in#uenced by each alternative. It is possible to distinguish between local and
systemic investments: the former aimed at improving
the performance of a speci"c activity or organisa-tional unit of the quality system, while the latter a!ects the whole corporate quality system. Among the local investments we have
f engineering or marketing; f quality of supplies;
f inspection (both inbound and on line/"nal); f technology;
f training.
In the area of systemic investments instead there are
f investments in product certi"cation; f investments in quality system certi"cation.
The"nancial cash outlay points out the "nancial risk of each investment allowing SMEs managers to choose carefully the approaches more correct for their evaluation.
It must be noted that, for the objective of this paper, it is not important to distinguish between product and process certi"cation, but it is necessary to separate inbound inspection from on line/"nal inspection. Hence, we will consider seven invest-ments including the merger of the certi"cation ones o!set by the separation of inbound and on line/
"nal inspection.
3.2. The competitive context
In order to identify a "rm's exogenous quality priorities, we have to de"ne the competitive context in which it operates. To this aim we have to charac-terise a"rm through both its environmental con-text and its con"guration.
3.2.1. The environmental context
The environmental context in which a"rm oper-ates can be described by means of three classes of variables [16]: customer's bargaining power, bind-ing force of regulations and "rm's bargaining power vs. suppliers.
According to the "rst two variables, we de"ne two di!erent environments:
(i) compulsory environments(customers'high
bar-gaining power and/or presence of binding force of regulations): the"rm is compelled to under-take the requested investments just to remain in the market;
(ii) free environments (customers' low bargaining
power and no binding force of regulations): the
"rm is free to undertake any investment or not, depending on other motivations.
which allow the "rm to save costs (for instance those related to stock maintenance) and (ii) execute design and engineering jointly with suppliers.
In the light of these issues and of main results of state of the art literature [16] it is possible to identify under which conditions some quality-based initiatives appear preferable.
f In compulsory environments all the investments
required by the market must be implemented. This is, for instance, the case where product and/or quality system certi"cation is required to com-pete in some speci"c markets (an example being the English one). In small"rms, the achievement of the certi"cation of the quality system could imply some disadvantages since it decreases the
#exibility of operating procedures which is one of the most important points of strength of small companies. Nevertheless, the losses caused by the impossibility to enter a speci"c market could overcome those due to lower#exibility.
f In free environments, engineering and/or marketing
investments are a priority. These interventions
have three aims: (i) the proper identi"cation of the needs of both real and potential customers, (ii) the correct translation of these needs into project speci"cations, and, "nally, (iii) product engineer-ing accordengineer-ing to the de"ned speci"cations.
f In contexts characterised by axrm's high
bargain-ing power vs. suppliers, investments in quality of
supplies can be successfully implementedand, at
the same time, engineering investments will be
undertaken. The former can enable the "rm to
reduce (or completely avoid) costs and loss of time concerned with the purchase of defective raw materials and/or semimanufactured prod-ucts. The latter allows the"rm to improve and to speed up the production process, for instance through codesign and guarantee of inputs quality.
f In contexts characterised by axrm's low
bargain-ing power vs. suppliers, testing and inspection
investments arevery important. Such investments
limit the absorption of"nancial resources due to working defective raw materials and components and, at the same time, improve the company's economic performance by reducing both (i) the cost for work in progress/products to be rejected and reworked and (ii) the cost of lost sales or
costs related to customers'complaints due to the delivery of defective products.
3.2.2. Thexrm+s conxguration
The "rm's con"guration has been described in terms of [16]: managers'competence, level of prod-uct quality performed by the"rm with respect to the competitors' standard, and turbulence of the market.
Considerations about these variables allow us to identify under which conditions each quality-based investment is more suitable.
f Inxrms characterised by a low management
com-petence, the adoption of training investments is
a priority. Indeed, successful implementation of quality-based investments requires a consider-able managerial e!ort. For this reason, the intro-duction of further initiatives is not wise until managers have gained appropriate skills.
f Firms that achieve a product quality consistent
with competitors should introduce engineering
and/or marketing investments in order to better
satisfy customers'needs and make an increase of market's share possible.
f Firms which realise low-quality products should
introduce engineering and/or marketing inv
est-ments, aimed at precisely identifying customers'
expectations.
f In xrms characterised by a high rate of defective
products the adoption of investments in training
(for improving employees' skills), in inspection (for preventing the use of defective raw materials and the sale of defective products),and in techno-logy(for obtaining more simply, faster and with less defects the desired outputs)is dominant.
f In turbulent contexts, investments requiring a small
cash outlay represent a suitable option. In such markets, the frequent changes in customers' ex-pectations remarkably reduce the life cycle of both products and equipment. Therefore, these changes require a continuous innovation of a"rm's processes and outputs. For these reasons the reduction of such expenditures could repres-ent a suitable solution.
f In turbulent markets engineering investments can
Table 1
The identi"ed contexts
Firm's bargaining power vs. suppliers
High Low
Market turbulence Market turbulence
High Low High Low
Product quality vs the competitors'one High 2 1 6 5
Low 4 3 8 7
#exible as well; thus, they allow the"rm to react quickly to changes in customer's needs.
3.2.3. The typical contexts
By referring to the six variables describing a"rm's environmental context and its internal
con-"guration we can identify some typical contexts. In this perspective, our analysis can be articulated at two di!erent levels.
At a"rst level, we underline that: (i)"rms work-ing in compulsory environments have to introduce all the investments requested by the market and (ii) non-quality-oriented "rms (i.e. companies which have not been paying attention to quality systems and, hence, are not likely to have high-quality com-petence) have to "rst adopt training investments before they can implement TQM programmes.
At a second level, in free environments (i.e. mar-kets where binding force of regulations does not exist), we introduce eight di!erent contexts (see Table 1) by combining the"rm's bargaining power vs. suppliers, relative level of product quality with respect to the competitors'one and market turbu-lence, in order to identify main investment priori-ties in each of them. Naturally, the identi"cation of these priorities is connected to the choice of a
speci-"c evaluation technique and, for this reason, we will delay the related analysis in Section 4.
3.3. The quality system
The modelling of the corporate quality system is requested in order to identify the endogenous qual-ity priorities of the"rm. In this respect we refer to a state-of-the-art model [14] which de"nes few subsystems sequentially linked and characterised
by speci"c parameters describing the contribution of each subsystem to the company's overall quality performance.
Subsystem 1: Design and engineering. The
activ-ities associated with this subsystem can be grouped into two main categories: (i) determining cus-tomers' expectations and (ii) translating such expectations in to product speci"cations.
Subsystem 2:Testing of raw materials and inbound
inspection. This subsystem is characterised by a"rst
phase, of testing raw materials and semimanufac-tured products purchased by the"rm, and by a sec-ond one, of continuous, or periodic inspection of the work in process.
Subsystem 3: Process and xnal inspection/testing.
This subsystem is concerned not only with the company's operations (in particular, it includes also on-line inspection), but also with the"nal inspec-tion of the"nished products and the testing needed before introducing them on the market.
Each subsystem is described in terms of physical variables expressing the quality performance. They are related to theinput, the`statea(i.e. main activ-ities carried out to improve the company's quality performance) and the output of the subsystem. Among these variables we are interested in the following"ve that are independent:
d
$: representing the quality of the design;
d
& : representing the defectiveness of raw materials;
e
1: representing the etion of incoming defective components;!ectiveness in the identi"
ca-d
e
2: representing, at the same time, the ein the on-line identi"cation of defective items!ectiveness and the e!ectiveness in identifying defective
"nal products.
The analysis of the performance achieved by the
"rm in each of these parameters could allow us to identify its endogenous priorities of investment through:
f a benchmark (when possible) with the perfor-mances achieved by the main competitors on the same variables aimed at establishing the weak-ness of the"rm;
f a comparison among the"ve independent vari-ables aimed at ranking the urgency of speci"c quality investments.
4. Multi-attribute decision-making techniques
The models describing the set of investment al-ternatives, the competitive context in which a"rm operates and its quality system represent the basis of a tool using multi-attribute decision-making (MADM) techniques in order to achieve a rank of di!erent investments alternatives.
The choice to utilise such methods is due to the consideration that conventional"nancial tech-niques (i.e. discounted cash #ows, or DCF tech-niques), being incapable of considering those bene"ts that are di$cult to measure in monetary terms (i.e. intangible bene"ts), often fail to assess the e!ectiveness of quality investments and hence do not correctly support the manager's decision making [25]. Therefore, various ` non-conven-tionalatechniques for the appraisal and selection of investments have been suggested and can be grouped into two major categories: modi"ed DCF and MADM techniques [26]. This article focuses on the second, because it is our wish to make the use of linguistic assessments in the investments evaluation possible.
Among the MADM methods proposed in the literature, we have considered both the FLA and the AHP in order to compare the di!erent results that can be achieved with such techniques [25,27}40,42,43].
In this section we will describe how it is possible to rank the quality investments utilising these two methods.
4.1. TQM investments evaluation with the fuzzy
linguistic approach
At this level we aim at implementing the FLA (see Appendix A for a brief general description of the FLA) according to the model suggested in Section 3.
4.1.1. The competitive context
As we have seen the evaluation of the competi-tive context allows managers to determine the exogenous priorities of a"rm. In operating terms it requires the decision maker to assess the import-ance of the seven investments previously described in each of the eight free contexts.
Hence, we propose an assessment scale of "ve levels that, even if originally suggested by Liang and Wang [37] for robot selection, appears suitable for a wide range of decisional problems (for instance Rangone and Azzone used it for measur-ing manufacturmeasur-ing competence). It discriminates among
f very low priority; f low priority; f medium priority; f high priority; f very high priority.
Such a scale allows us to de"ne the priority of each investment according to the considerations previously enlightened (as seen in Table 2).
Now, as prescribed by the FLA, we introduce the fuzzy numbers corresponding to the assessment scale mentioned above [37]:
Table 2
The priority of each investment within di!erent contexts
Context Suggested investments PRIORITY
Context 1
Firm's HIGH bargaining power vs. suppliers; HIGH level of product quality in regard to the competitors'one; LOW turbulence of the market.
In engineering and/or marketing HIGH
In quality of supplies HIGH
In certi"cation HIGH
In inbound inspection LOW
In on line/"nal inspection MEDIUM
In technology VERY LOW
In training VERY LOW
Context 2
Firm's HIGH bargaining power vs. suppliers; HIGH level of product quality in regard to the competitors'one; HIGH turbulence of the market.
In engineering and/or marketing VERY HIGH
In quality of supplies VERY HIGH
In certi"cation LOW
In inbound inspection LOW
In on line/"nal inspection MEDIUM
In technology HIGH
In training HIGH
Context 3
Firm's HIGH bargaining power vs. suppliers; LOW level of product quality in regard to the competitors'one; LOW turbulence of the market.
In engineering and/or marketing LOW
In quality of supplies HIGH
In certi"cation LOW
In inbound inspection MEDIUM
In on line/"nal inspection MEDIUM
In technology VERY HIGH
In training HIGH
Context 4
Firm's HIGH bargaining power vs. suppliers; LOW level of product quality in regard to the competitors'one; HIGH turbulence of the market.
In engineering and/or marketing VERY HIGH
In quality of supplies VERY HIGH
In certi"cation MEDIUM
In inbound inspection MEDIUM
In on line/"nal inspection MEDIUM
In technology HIGH
In training VERY HIGH
Context 5
Firm's LOW bargaining power vs. suppliers; HIGH level of product quality in regard to the competitors'one; LOW turbulence of the market.
In engineering and/or marketing MEDIUM
In quality of supplies HIGH
In certi"cation VERY LOW
In inbound inspection VERY HIGH
In on line/"nal inspection HIGH
In technology VERY LOW
In training VERY LOW
Context 6
Firm's LOW bargaining power vs. suppliers; HIGH level of product quality in regard to the competitors'one; HIGH turbulence of the market.
In engineering and/or marketing VERY HIGH
In quality of supplies VERY LOW
In certi"cation HIGH
In inbound inspection VERY HIGH
In on line/"nal inspection HIGH
In technology HIGH
Table 2 (contined)
Context Suggested investments PRIORITY
Context 7
Firm's LOW bargaining power vs. suppliers; LOW level of product quality in regard to the competitors'one; LOW turbulence of the market.
In engineering and/or marketing LOW
In quality of supplies VERY LOW
In certi"cation VERY LOW
In inbound inspection HIGH
In on line/"nal inspection MEDIUM
In technology VERY HIGH
In training HIGH
Context 8
Firm's LOW bargaining power vs. suppliers; LOW level of product quality in regard to the competitors'one; HIGH turbulence of the market.
In engineering and/or marketing VERY HIGH
In quality of supplies VERY LOW
In certi"cation VERY LOW
In inbound inspection VERY HIGH
In on line/"nal inspection HIGH
In technology HIGH
4.1.2. The quality system
Once the exogenous priorities of a"rm is de"ned, it is necessary to establish the endogenous ones, in order to evaluate correctly the di!erent quality investments alternatives.To this aim we need to undertake four steps:
(i) we need to evaluate the quality-based perfor-mances achieved by the"rm with respect to the
"ve variables describing its quality system; (ii) we have to identify the degree of priority
at-tributed by managers to such variables for shareholders value creation;
(iii) we have to establish the expected impact of di!erent typologies of quality-based invest-ments on the identi"ed quality-related perfor-mances;
(iv) we have to determine the endogenous priority of each investment through a judgement ex-pressed in the same way as that utilised to describe the exogenous priorities.
In this perspective, we identify:
f "ve types of assessments measuring how di!erent quality investments can in#uence the perfor-mance achieved by the"rm on speci"c variables: very low in#uence, low in#uence, medium in# u-ence, high in#uence and very high in#uence; f "ve categories of weights indicating the
import-ance of each variable referring to the achieve-ment of a"rm's planned results: not important, little important, moderately important, impor-tant and very imporimpor-tant.
It is necessary to underline that, whereas the judge-ments concerning the relations between invest-ments and variables can be established once and for all, the importance of each variable with respect to the goals to achieve has to be always rede"ned depending on the speci"c quality situation of the
Table 3
Relations between variable characterising"rm's quality system and investments
Variable Related investments Relative in#uence
d
& In quality of supplies Very High In#uence
In certi"cation Very Low In#uence
e
1 In training Very Low In#uence
In technology Very Low In#uence In inbound inspection Very High In#uence
d
1 In engineering/marketing Low In#uence
In training High In#uence In technology High In#uence In certi"cation Low In#uence
e
2 In trainingIn technology Very Low InVery Low In##uenceuence In on line/"nal inspection Very High In#uence
d
$ In engineering/marketingIn technology Very High InVery Low In##uenceuence In particular, we think that the investments able to modify some of the "ve variables describing a"rm quality system, together with their relative in#uence are those described in Table 3.
The scale utilised to translate the in#uence of each investment is the same as previously sugges-ted, whereas we propose a di!erent scale in order to evaluate the weights describing the consistency of each quality performance in relation to the a"rm's overall objective [37]:
The fuzzy numbers describing the investments evaluation, deriving from this phase of the selection process, are determined by the sum of the fuzzy numbers obtained multiplying the relative in# u-ence of each investment in improving a speci"c variable by the corresponding weight of that vari-able in achieving a"rm's quality goals.
For instance, let us consider the evaluation of the investment in technology in a hypothetical"rmX. We suppose that, for the management of X, the weights describing the importance of the"ve qual-ity variables previously introduced are these: d
&, little important;e
1, little important;d1, important;
e
2, important;d$, moderately important. In such a situation the fuzzy number describing the import-ance of the technology investment can be achieved in this way (see also Table 4):
(0; 0; 0.2)?(0; 0.3; 0.5)=(0.6; 0.8; 1)?(0.5; 0.7; 1)=
(0; 0; 0.2)?(0.5; 0.7; 1)=(0; 0; 0.2)?(0.2; 0.5; 0.8)
"(0; 0; 0.1)=(0.3; 0.56; 1)=(0; 0; 0.2)=(0; 0; 0.16)
"1/4(0.3; 0.56; 1.46)
"(0.08; 0.14; 0.37)
The above fuzzy number can be translated, accord-ing to the scale utilised to describe both exogenous and endogenous priorities, to the judgement`low prioritya.
4.1.3. Thexnal result
Finally, we need to summarise the results achieved evaluating the competitive context and the quality system in order to identify investment priorities. This requires us to convert all the fuzzy numbers expressing the priorities of each pro-gramme into synthetic indicators capable of rating the di!erent investments:
Table 4
Evaluation of the technology investment
Variable Relative in#uence of the technology investment (corresponding fuzzy number)
Importance of each variable referring to the achievement of a"rm's planned results (corresponding fuzzy number)
e
$ Very Low In#uence (0; 0; 0.2) Moderately Important (0.2; 0.5; 0.8)
exogenous priority (0.6; 0.8; 1) and a low endo-genous one (0; 0.2; 0.4), thus achieving a total result of (0.3; 0.5; 0.7) corresponding to a medium priority);
f then, in order to rate real quality-based priori-ties, managers have to reverse the just obtained fuzzy numbers into linguistic assessments. In this perspective, they have, to for each fuzzy number, (i) calculate the centre of gravity X
G (X
G":SxdS/:SdSwhereSis the area included
between the membership function of the fuzzy number and the x-axis) and (ii) determine the fuzzy number representing the linguistic value whose centre of gravity is the nearest toX
G[31].
4.2. TQM investments evaluation with the AHP
Logically, utilising the AHP (see Appendix A for a brief description), we have to carry out the same actions characterising the implementation of the FLA. In this case, however, we will evaluate the di!erent quality-related investments on the basis of pairwise comparison judgements, referring this analysis both to the competitive context in which a"rm operates and to its quality system.
4.2.1. The competitive context
In order to evaluate the e!ectiveness of the seven quality investments that we consider in the eight contexts de"ned in the Section 3.1 it is necessary to make pairwise comparisons for each di!erent couple of investments in every context (obtaining in such a way the weights of the branches of the`Ea category of Fig. 3).
For instance, if we consider context 1, i.e. a con-text characterised by a "rm's high bargaining
power vs. suppliers, a high level of product quality vs. the competitor's one and a low turbulence of the market, we see that, in such a context, the import-ance of each quality investment can be evaluated as summarised in Table 5.
We have to rate in every context the seven qual-ity investments considered by referring to their higher or lower propensity to support the "rm's quality goals in that context.
4.2.2. The quality system
Referring to the evaluation of a "rm's quality performance, we can see that it consists of three steps.
Step 1 concerns the identi"cation of the contri-bution that a performance achieved on a particular variable (d
&,e1,d1,e2ord$) can o!er to the corpo-rate quality targets (in other words we have to assign the right weights to the branches of the`Da category). This step is characteristic of the speci"c quality situation of a"rm and, for this reason, it is not possible to provide general considerations. It is a management task to evaluate the exact contribu-tion of each variable in a"rm's-speci"c context.
Step 2 is related to the identi"cation of the in# u-ence that the seven quality investments considered have on the performance of a speci"c variable (weights of the`Facategory). The relationship be-tween investments and variables are not dependent on the context and, hence, they can be analysed once and for all. The results of the pairwise com-parisons between the di!erent investments for each variable are given in Table 6.
Fig. 3. Analytic Hierarchy Process: the structure.
Table 5
Pairwise comparison judgements and corresponding importance weightings
Eng./mkt. Supplies Training Technol. Certi"c. Inb. insp. Fin. insp. Rating
Eng./mkt. 1 1 7 7 1 5 3 0.255
Supplies 1 1 7 7 1 5 3 0.255
Training 1/7 1/7 1 1 1/7 1/3 1/5 0.029
Technol. 1/7 1/7 1 1 1/7 1/3 1/5 0.029
Certi"c. 1 1 7 7 1 5 3 0.254
Inb. insp. 1/5 1/5 3 3 1/5 1 1/3 0.060
Fin. insp. 1/3 1/3 5 5 1/3 3 1 0.118
that"rm's planned quality results (i.e. it assigns the weights of the branches`Aaand`Ba) in order to achieve the overall suitability rating of the seven quality investments considered. It is not possible to establish ex ante the relative importance of the two branches, because it is strictly dependent on the external/internal context. For such a reason this relation too, will be evaluated by SMEs managers. Once all the weights of the branches are known, the"nal ranking of the quality investments is im-mediately clear, according to the rules of the AHP technique.
5. Application
In this section we aim to compare the results achieved with the models based on the fuzzy lin-guistic approach and on the analytic hierarchy process with respect to a real application. To this end we considered a small"rm of the Lecco's engineering district in Italy (called in the paper PaperMach).
Table 6
(a) Importance of di!erent investments in order to improve the performance related tod &
Supplies Certi"cation Rating
Supplies 1 9 0.9
Certi"cation 1/9 1 0.1
(b) Importance of di!erent investments in order to improve the performance related toe 1
Training Technology Inbound inspect. Rating
Training 1 1 1/9 0.091
Technology 1 1 1/9 0.091
Inbound inspect. 9 9 1 0.818
(c) Importance of di!erent investments in order to improve the performance related tod 1
Engin./mkt. Training Technology Certi"cation Rating
Engin./mkt. 1 1/5 1/5 1 0.083
Training 5 1 1 5 0.147
Technology 5 1 1 5 0.147
Certi"cation 1 1/5 1/5 1 0.083
(d) Importance of di!erent investments in order to improve the performance related toe 2
Training Technology On line/"n. insp. Rating
Training 1 1 1/9 0.091
Technology 1 1 1/9 0.091
On line/"n. insp. 9 9 1 0.818
(e) Importance of di!erent investments in order to improve the performance related tod $
Engin./mkt. Technology Rating
Engin./mkt. 1 9 0.9
Technology 1/9 1 0.1
business toward machines aimed at the production of paper tablecloths and napkins.
PaperMach exploited the huge network of very small suppliers characterising the Lecco's district having in this way a high bargaining power vs. suppliers. It was also operating in a low turbu-lence context in which the technology as well as the customers' needs were consolidated, but it had a rather important problem of quality a! ect-ing its new typologies of machines (i.e. those aimed at the production of paper tablecloths and napkins).
For this reason its management decided to undertake a TQM investment.
It is a matter of fact that such a situation pro-vided us with the possibility of testing our model in a real environment managing a real investment decision. It was also a great opportunity to verify the user friendliness of the software tool we developed having in mind SMEs managers.
Table 7
Pairwise comparison judgements and corresponding importance weightings in Context 3
Eng./mkt. Supplies Training Technol. Certi"c. Inb. insp. Fin. insp. Rating
Eng./mkt. 1 1/5 1/5 1/7 1 1/3 1/3 0.036
Supplies 5 1 1 1/3 5 3 3 0.187
Training 5 1 1 1/3 5 3 3 0.187
Technol. 7 3 3 1 7 5 5 0.393
Certi"c. 1 1/5 1/5 1/7 1 1/3 1/3 0.036
Inb. insp. 3 1/3 1/3 1/5 3 1 1 0.081
Fin. insp. 3 1/3 1/3 1/5 3 1 1 0.081
5.1. Results achieved with the fuzzy linguistic
approach
In Section 4.1 we identi"ed the main investments priorities of context 3. In order to evaluate TQM priorities our aim is assigning the judgements refer-ring to the importance of the "ve quality-related variables in determining PaperMach's quality in-vestment priorities. An interview "rst with the entrepreneur and then with the operations manager of the"rm allows us to consider:
f d
&: moderately important; f e
1: moderately important; f d
1: very important; f e
2: little important; f d
$: not important.
Starting from these data and remembering the con-siderations done in Section 4.1, we calculate the overall fuzzy numbers which summarise, for each investment, all the assessments and the weights assigned (all the calculations are reported in Ap-pendix B). In this way, once the fuzzy numbers in linguistic judgements are translated, we are able to rank the seven investment alternatives:
1. investment in quality of supplies: medium/high priority;
2. investment in technology: medium priority; 3. investment in training: medium priority; 4. investment in inbound inspection: medium
priority;
5. investment in on line/"nal inspection: low/ medium priority;
6. investment in engineering and/or marketing: low priority;
7. investment in certi"cation: low priority.
With respect to this scale we can note that in the end PaperMach decided to buy a new machine characterised by a higher product quality, thus accomplishing the investment ranking second according to the FLA.
5.2. Results achieved with the analytic hierarchy
process
According to Section 4.2 we can enlighten the main investments priorities in context 3 (see Table 7). Then the pairwise comparison judgements about the importance of the "ve quality variables considered with respect to the achievement of a"rm's quality targets are reported in Table 8.
Finally, we have to compare the importance of the competitive context in which a "rm operates with that of its quality system. In the case of Paper-Mach, managers assigned the same importance to these two elements achieving in this way the weight of 0.5 for each branch.
In the light of these considerations and, referring also to the judgements given in Tables 6}9, we can determine the "nal judgements for every invest-ment and, hence, we can rank the di!erent invest-ment's alternatives:
1. investment in technology: overall judgement 0.3267;
Table 8
Pairwise comparison judgements and corresponding import-ance weightings of the"ve variables describing a"rm's quality system
3. investment in quality of supplies: overall judge-ment 0.1673;
4. investment in inbound inspection: overall judge-ment 0.1076;
5. investment in on line/"nal inspection: overall judgement 0.0720;
6. investment in engineering/marketing: overall judgement 0.0545;
7. investment in certi"cation: overall judgement 0.0496.
We can immediately note that the investment in technology chosen by PaperMach is coherent with the result of the AHP.
5.3. Implications for practice
In order to compare the e!ectiveness for man-agement of the FLA and the AHP, the two methods should be analysed in terms of four parameters:
f completeness of the analysis: i.e. the amount of
data considered in the evaluation;
f reliability of the output: how carefully the di!erent
investment alternatives are evaluated;
f ease of use of the technique: the di$culties that
users may incur utilising such methods;
f intuitiveness of the technique: the level of trust
that managers have in such methods because they are able to understand how they work.
Completeness. Both these techniques refer to the same data describing, on the one hand, the com-petitive context in which a "rm operates and, on the other, its quality system. Hence, they are char-acterised by the same level of completeness.
Reliability. The analysis of the reliability of these two methods requires us to understand how the two methods utilise the data in order to achieve the
"nal result and, then, verifying whether the two methods are able to achieve the same ranking among investments.
It is a matter of fact that both the techniques are able to rank di!erent quality investments in order to help managers throughout the decisional process of investments evaluation. However, it is also true that the results achieved are not always the same. This is, for instance, the case of the situation we have just analysed.
Really, the di!erences between the rankings are not overwhelming, i.e. all the investments are in the same order except the one in quality of supplies. However, this is a signi"cant exception indeed.
Using the FLA the investment in quality of sup-plies is ranked"rst, whereas the AHP put it in the third place.
In our opinion it can be explained analysing how the two methodologies evaluate the di!erent alter-natives. Indeed, even if in order to identify a weighted mean of the judgements associated with each investment the adopted techniques would seem equivalent, their modus operandi is di!erent. The FLA indeed identi"es the fuzzy number which de"nes the investment importance by nor-malising the sum of all the fuzzy numbers express-ing the relative priority of that investment. In this perspective it is clear that, if an investment achieves excellent results with regard to only one parameter, whereas it does not perform well referring to the other quality-related variables, the overall judge-ment will not be a very good one. This happens because, the use of an arithmetic mean does not allow for compensation among criteria.
In the case of PaperMach, for the technology investment, the low relative importance related to the variablese
1,e2andd$ is not su$ciently o!set by the good results achieved both referring to the variable d
Table 9
The determination of the technology investment's priority with the FLA
Competitive context Investment's priority Corresponding
fuzzy number
3 Very High (0.8; 1; 1) (0.8; 1; 1)
Quality variables: System's relative in#uence: System's importance:
e
1 Very Low (0; 0; 0.2) Mod. Imp. (0.2; 0.5; 0.8) (0; 0; 0.16)
d
1 High (0.6; 0.8; 1) Very Imp. (0.7; 1; 1) (0.42; 0.8; 1)
e
2 Very Low (0; 0; 0.2) Little Imp. (0; 0.3; 0.5) (0; 0; 0.1)
d
$ Very Low (0; 0; 0.2) Not Imp. (0; 0; 0.3) (0; 0; 0.06)
(0.11; 0.2; 0.33)
Final result (0.46; 0.6; 0.67)
Table 10
The determination of the technology investment's priority with the AHP
Relative priority
Total priority Competitive Context (weight"0.5)
0.3930 0.1965
Quality system (weight"0.5)
e
1! 0.091*0.164 0.0149
d
1" 0.417*0.565 0.2356 e
2# 0.091*0.077 0.0070
d
$$ 0.100*0.029 0.00290.2604 0.1302
0.3267
!Values derived from Table 6(b) and 8.
"Values derived from Table 6(c) and 8.
#Values derived from Table 6(d) and 8.
$Values derived from Table 6(e) and 8.
Fig. 4. The determination of the technology investment's prior-ity with the AHP.
result and, hence, it is able to correctly emphasise the importance of one characteristic in spite of the poor performance the investment can achieve on other variables (i.e. if an investment achieves an excellent performance referring to one parameter, it will also have a good"nal evaluation if it does not perform well according to the other variables).
In the light of these issues, the major di!erence between the proposed techniques is that:
f the AHP favours the investments that achieve at least a good performance in one of the evalu-ation criteria;
f the FLA prefers those investments that achieve equilibrate performance in all the parameters evaluated, not being able to isolate the e!ect of only one point of excellence.
Table 11
Performance of FLA and AHP
Parameters FLA AHP
Completeness " "
Reliability !! ##
Ease of use # !
Intuitiveness " "
will achieve poor performance in, at least, one of them. In contrast, the AHP does not overemphasise the performances of marginal importance, giving instead the right weight to the most relevant ones. Let us consider for instance two investments A and B. The"rst allows a "rm to achieve a high improvement in the variable d
1 and a little im-provement in the variablee
2. The second, on the contrary, has e!ect only on the variabled
1, that is highly improved. It appears clear that, ceteris paribus, A is the better investment because it allows managers to achieve the same results of B on d
1, ensuring also a little improvement one
2. The AHP is able to rank precisely these investments, whereas FLA, weighting the performance achieved by B on the two variables, assigns a better rank to B.
According to these issues the AHP performs better because it allows us to evaluate more careful-ly the di!erent investments. In contrast, the fuzzy linguistic approach gives too much importance to the less signi"cant performances, achieving, in this, not always achieving correct results.
Ease of use. Both the techniques are very easy to use, but we think that the FLA would be the easiest. Indeed with FLA we only have to assign some linguistic assessments to the variables under evalu-ation, whereas with the AHP we have to do pairwise comparisons among these variables which represents a time-consuming analysis.
Intuitiveness. If managers have to utilise these
techniques in order to support their decisional pro-cess, it is clear that they have to trust these approaches. Managers will not utilise those tools which they do not trust [12]. This problem is parti-cularly important speaking of AHP and FLA because managers usually do not have a great trust in these two methods, because in most cases they are not able to understand how they work.
In particular, the problems resulting from the implementation of FLA concern:
f the translation of the linguistic assessments in fuzzy numbers; and
f the operations on triangular fuzzy numbers.
If the translation of the linguistic assessments in fuzzy numbers could be rather intuitive, because referring to the natural concept of fuzzy bound-aries, the same is not true speaking of operations on
triangular numbers. In this case, managers often have to do an act of faith in believing how the operations work, because they do not have the competency required to understand them. Hence, by only proving the FLA in some simple cases and verifying ex post the results, managers can gain su$cient trust in its performance.
The AHP is not lacking some problems too. Indeed, we are all able to do pairwise comparisons between variables, but understanding how the pair-wise comparisons are elaborated in order to achieve the"nal ranking is surely more di$cult.
In such a situation the di$culties are related to the use of the matrix algebra. Speci"cally, bcause the matrix algebra is not very intuitive, managers can have some problems in trusting these opera-tions. In this case too, we think that only by verify-ing the results provided by the AHP it is possible to gain the trust essential to utilise properly such a tool.
Hence, it is hard to choose which of these tech-niques is more intuitive. Probably it is not possible to identify the better one, but di!erent managers will have di!erent preferences.
In conclusion, according to the above framework which considers four evaluation parameters (see Table 11), the adoption of the AHP represents a better operating solution for the selection of qual-ity-based investments in small"rms. Indeed, such a technique performs better with respect to the `reliabilityaparameter that is, according to us, the most important of the four.
Acknowledgements
Fig. 5. An example of triangular membership function.
The paper is due to the joint work of the authors; however, Giovanni Toletti wrote Sections 2, 4 and 5 and Giuliano Noci wrote Sections 1 and 3.
Appendix A
A.1. The fuzzy linguistic approach
The FLA based on the concept of linguistic vari-ables [40]. A linguistic variable is a variable whose value is not a number but words or sentences in a natural or arti"cial language. A linguistic variable is characterised by a given set of linguistic values, with each value being a fuzzy set.
A fuzzy set is a collection of elements with smooth boundaries, in which the transmission from membership to non-membership is gradual rather than abrupt. A basic concept of the fuzzy sets the-ory is that an element can belong partially to a fuzzy set. LetXbe the space of elementsx; a fuzzy setAinXis characterised by a membership func-tionkA(x) which associates with each elementxin
X, a real number in the interval [0; 1], which rep-resents the`degree of membershipaofxinA. Thus, ifkA(x)"1 thenxcompletely belongs to the setA;
ifkA(x)"0 thenxdoes not belong toA; in all other cases, i.e. 0(k
A(x)(1, x belongs partially to
A(the nearer the value ofk
A(x) to 1, the higher the
grade of membership of x in A). In particular, a fuzzy numberAis a fuzzy set of the real line R. For the sake of computational e$ciency and ease of data acquisition, triangular membership func-tions are often used. In Fig. 5 such a fuzzy number is reported: it is de"ned by the following member-ship function:
k(x)"
G
(x!a)/(b!a), a)x)b, (x!c)/(b!c), b)x)c,
0, otherwise,
and would normally be de"ned as the triplet (a;b;c). By the extension principle of Zadeh [41], the extended algebraic operations on triangular fuzzy numbers that are used in our approach are the following:
Addition=
(a
1,b1,c1)=(a2,b2,c2)
"(a
1#a2,b1#b2,c1#c2).
Multiplication?
(a
1,b1,c1)?(a2,b2,c2)+(a1a2,b1b2,c1c2)
A.2. Analytic hierarchy process(AHP)
The AHP is a MADM method aimed at integrat-ing several performance measures into a sintegrat-ingle overall score ranking alternative decisions. The main characteristic of this technique is that it is based on pairwise comparison judgements [32}34].
The AHP main steps are:
(1) First the relative importance of the criteria has to be de"ned on the basis of pairwise compari-son assessments. To this aim it is possible to use a scale such that shown in Table 12. For instance, if criterionC
1is judged to be Moder-ately Preferred to criterionC
Table 12
An example of measurement scale for the AHP
Verbal judgement Degree of
preference
Equally preferred 1
Moderately preferred 3
Strongly preferred 5
Very strongly preferred 7
Extremely preferred 9
to be compared (for instancen). Thea
ijvalue of
the matrix represents the relative importance of theith criterion relative to thejth criterion. It is a matter of fact that only (n!1)! of the
n2 values of the matrix are independent and hence, only these values have to be obtained directly from managers. Indeed the other ones are automatically generated considering both re#exivity (ifi"jthena
ij"1) and reciprocity
(a
ij"1/aji). The relative values forming the
matrix (A) are translated in absolute priority weightings on the basis of Saaty's eigenvector procedure:
A*=
j"k*=j
where:=
jrepresents the vector of the absolute
values of the importance weightings and k is the highest of the eigenvalues of the matrixA. (2) In the second step the alternatives have to be assessed on a pairwise basis with respect to the criteria using the same procedure as previously described. The output achieved is the absolute ratings of the alternatives with respect to all criteria (A
ij).
(3) Averaging the absolute ratings with respect to each criterion with the corresponding absolute importance weightings it is possible to calcu-late the overall suitability ratings (K
j) of the
alternative investments.
Appendix B
Investments in engineering and/or marketing:
(0.0; 0.2; 0.4)=[(0.0; 0.2; 0.4)?(0.7; 1.0; 1.0)
=(0.8; 1.0; 1.0)?(0.0; 0.0; 0.3)]
"(0.0; 0.2; 0.4)=[(0.0; 0.2; 0.4)=(0.0; 0.0; 0.3)]
"(0.0; 0.2; 0.4)=(0.0; 0.1; 0.35)
"(0.0; 0.15; 0.38).
This fuzzy number can be translated, through the centre of gravity method, into the linguistic vari-able indicating the LOW priority of this invest-ment.
Investments in quality of supplies:
(0.6; 0.8; 1.0)=[(0.8; 1.0; 1.0)?(0.2; 0.5; 0.8)]
"(0.6; 0.8; 1.0)=(0.16; 0.5;0.8)
"(0.38; 0.65; 0.9).
This fuzzy number corresponds to a MEDIUM/ HIGH investment priority.
Investments in certixcation:
(0.0; 0.2;0.4)=[(0.0; 0.0; 0.2)?(0.2; 0.5; 0.8)
=(0.0; 0.2; 0.4)?(0.7; 1.0; 1.0)]
"(0.0; 0.2; 0.4)=[(0.0; 0.0; 0.16)=(0.0; 0.2; 0.4)]
"(0.0; 0.2; 0.4)=(0.0; 0.1; 0.28)
"(0.0; 0.15; 0.34).
For the investments in certi"cation it is possible to deduce a LOW priority level.
Investments in inbound inspection:
(0.3; 0.5; 0.7)=[(0.8; 1.0; 1.0)?(0.2; 0.5; 0.8)]
"(0.3; 0.5; 0.7)=(0.16; 0.5; 0.8)
"(0.23; 0.5; 0.75).
We found that this investment has a MEDIUM priority.
Investments in on line/xnal inspection:
(0.3; 0.5; 0.7)=[(0.8; 1.0; 1.0)?(0.0; 0.3; 0.5)]
"(0.3; 0.5; 0.7)=(0.0; 0.3; 0.5)
"(0.15; 0.4; 0.6).
Investments in technology:
We found that this investment has a MEDIUM priority.
Investments in training:
(0.6; 0.8; 1.0)=[(0.0; 0.0; 0.2)?(0.2; 0.5; 0.8)
We found that this investment has a MEDIUM priority.
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