A two-stage mechanism as a decision support for marketing via customer satisfaction measures

Journal of the Chinese Institute of Industrial Engineers

Vol. 29, No. 4, June 2012, 270–281

A two-stage mechanism as a decision support for marketing via customer

satisfaction measures

Hamed Fazlollahtabara* and Ermia Aghasib

aFaculty of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran; bDepartment ofExecutive Management, Faculty of Human Sciences, University of Guilan, Rasht, Iran

(Received December 2011; revised April 2012; accepted April 2012)

In this article, we propose a two stage decision model to aid the marketing team of a company. Thedecision is based on customers’ satisfaction measures. These measures are related to the differentservices the company offers to its customers. Thus, they constitute a multi criteria evaluation of thecompany’s performances. The first stage of our proposed mechanism is to purify the services withrespect to the criteria. A stochastic multi-criteria acceptability analysis is employed to purify theservices. Then a multi-objective mathematical model is utilized to determine the services with moreprofits. A fuzzy goal programming is applied to solve the multi-objective model. The applicability andvalidity of the proposed mechanism is illustrated in a case study.

Keywords: decision support; multi-objective mathematical model; fuzzy goal programming

1. Introduction

Marketing has received extensive attention fromboth the managers and the experts in recent years.From a managerial viewpoint, top managementincreasingly calls for ‘‘marketing accountability’’pressuring marketers to produce metrics that doc-ument marketing activities [13]. From an academicperspective, the growing interest in marketingmetrics can be attributable to five theoreticalangles [3]. First, according to the control theorysuggesting the need for past information on mar-keting programs as an essential segment of the cycleof analysis, planning, implementation, and control[18,24], marketing metrics were utilized to evaluatepast performance to improve future strategy andexecution. Second, with respect to agency theoryfocusing on contract between a principle and anagent and the need for past data on the extent towhich the principal’s objectives have been met [20],marketing metrics could be used facilitate thecontract between corporate and marketing man-agement [2]. Third, reinforcing the broader questfor a balanced scorecard of performance [22],which puts emphasis on such intangible assets asbrand equity that account for a large and increasingproportion of shareholder value, marketing metricsare used to measure its various dimensions. Fourth,consistent with the literature on market orientation[19,31] that argues for the need of market sensingand appropriate cross-functional responsiveness tothe resulting data, marketing metrics are part of

‘‘marketing sensing’’. Finally, as marketing metrics

become more widespread among firms, institu-

tional theory [30] suggests that their use will

become an institutional norm. Operationally, the

present study focuses on how firms use marketing

metrics as tools for customer relationship manage-

ment (CRM).Gitomer [15] points out that the most important

factor affecting the success of CRM implementa-

tions is top management’s participation.

Furthermore, Fitzgerald and Brown [12] suggest

that the implementation of CRM needs to be

managed by ‘‘executive committees’’ rather than a

single executive. Although researchers have pro-

posed that CEO involvement is critical to CRM

implementation, they have not provided a recom-

mended way for management to help the CRM

implementation. Thus, the purpose of this article is

to identify some success factors contributing to

CRM implementation. The results from the present

study could provide some recommended ways for

executives to participate and support their CRM

implementation projects.Stochastic multi-criteria acceptability analysis

(SMAA) is a recently developed cluster of multiple

criteria decision-aiding (MCDA) approaches.

Different SMAA methods can be employed to

work with the three fundamental MCDA problems

[11]: choosing, ranking, and sorting. The method-

ology considers these problems in a broader sense.

The approach is based on an inverse analysis of the

*Corresponding author. Email: [email protected]

ISSN 1017–0669 print/ISSN 2151–7606 online

� 2012 Chinese Institute of Industrial Engineers

http://dx.doi.org/10.1080/10170669.2012.691118

http://www.tandfonline.com

space of feasible parameter values. One of theadvantages of SMAA rather other MCDA meth-odologies are that it can be used without anypreference information.

The dynamism was categorized into threesubcategories: incompleteness, imprecision, anduncertainty [34]. Incomplete information is that avalue is missing. Imprecise information is that wehave a value for the variable but not with therequired precision. Uncertainty, instead, is a formof dynamism appearing when the observer is takeninto account. It means that the observer givescomplete and precise information, but is unreliableitself. For information and references onapproaches dealing with dynamism, see Stewart[35]. In some models, the decision makers (DMs)did not want to reveal their preference model, andtherefore exact parameter values could not beobtained in others, the alternatives had uncertainor imprecise values for criteria measurements.Therefore, new advances seem necessary to pre-serve the usefulness of the approach.

One way to overcome the weaknesses of theutility function-based approach is through aninverse method: instead of asking parametervalues and giving an answer to the problem inquestion, the values resulting in different outcomesare described. The inverse SMAA method includescomputing multidimensional integrals over feasibleparameter spaces in order to support DMs withdescriptive measures. The method solves variousproblems encountered in the traditional approachallowing to use parameters with dynamism on thevalues. For example, usually different weight elic-itation techniques produce different values; there-fore, deterministic weights are harder to justifythan, for example, weight intervals.

The remainder of our work is organized asfollows. Next we review the related literature. Theproblem is defined in Section 3. Section 4 modelsthe problem in a two stage mechanism. Section 5proposes a solution approach for the proposedmathematical model. The efficiency and validity ofthe proposed model is illustrated in a case study inSection 6. We conclude in Section 7.

2. Literature review

The development of marketing decision supportsystems (MDSS) inaugurated a new era in market-ing activities. They are especially designed to allowmarketing managers to benefit from advances inmarketing theories underlying models. As market-ing models are created, MDSS makes them easy tofunction. For example, Lilien and Rangaswamy[27] present a set of marketing models embedded insoftware. Yet, Little [28] stated that ‘‘marketing

managers in companies are not so eager to usemarketing models.’’ Many authors still agree onthis assertion [1,32,38].

Several studies have examined the effectivenessof MDSS models. In a field experiment, Fudge andLodish [14] considered that salespersons usingCALLPLAN outperform their counterparts whodid not use it. In contrast, Chakravarti et al. [7]showed that ADBUDG, Little’s original decisioncalculus model does not help the users to makebetter decisions and is even worse than decisionsbased on intuition. However, McIntyre [29] showedthat using CALLPLAN in an experimental settingimproves DMs’ performance, at least for problemsinvolving constrained budget allocations in simpleand stationary environments. In a marketing strat-egy game, Van Bruggen et al. [39] findings revealthat the availability and the quality of the MDSSimprove DMs’ performance with no negative effecton user confidence, whatever the level of timepressure. Van Bruggen et al. [40] showed that DMsusing MDSS are better able to set the values ofdecision variables to increase performance. Yet,Barr and Sharda [5] proposed that the two poten-tial explanations of the performance improvement:reliance and development effects. The former effectsuggests that decision support system (DSS) usageleads to deferring the decision process to ‘‘let thecomputer do it’’ whilst the latter refers to anincreased understanding of relationships betweenrelevant variables (i.e. the decision model). Theresults of their experimental study indicate that theimprovement in the DMs performance was due tothe efficiency of the DSS than the developmenteffect. In most experimental research in marketing,authors used MDSS that enable users to runsimulations. These MDSS are supplied to market-ing managers with information about the tasks forwhich the tool should be used, but without anyexplanation about the supporting model.Consequently, DMs may see these systems asblack-box MDSS (BMDSS).

The question arises as to whether DMs arewilling to use tools that do not lead them to betterevaluate their own decision making. Similarly,Eisenstein and Lodish [10] mention that the useof a model that users do not understand mightaffect the likelihood of adoption and usage.Consequently, we propose to enhance the trans-parency of MDSS. We argue that DMs should notonly be familiar with the interface of the MDSS butthey should also understand the hypotheses under-lying the decision model, variables and relation-ships between them and data used to quantify theserelationships. Firstly, increasing the transparencyof MDSS may help managers achieve a betterunderstanding of the market. Managers may gain

Journal of the Chinese Institute of Industrial Engineers 271

this understanding not only by decision aid usagebut also by being aware of the MDSS’ underpin-ning model. Secondly, given that managers are notvery inclined to use decision models and that thelatter models usage does not increase their confi-dence in their decision, we investigate whether thesystems’ openness increases DMs confidence.Indeed, some studies look into MDSS characteris-tics. Van Bruggen et al. [40] studied the impact ofMDSS quality on managers’ performance. Yet,researchers in the DSS field [5] believe that DSSspecific parameters may influence the understand-ing of decisions that managers gain from usingsystems.

There are numerous multi-criteria decisionanalysis (MCDA) methods that apply differentapproaches to tackle the difficulties encountered inreal-life decision-making problems. One of theoldest, and the most successful ones, is the utilityfunction-based approach, in which alternatives areevaluated based on utility scores derived using afunction operating on criteria values. The utilityfunction-based approach has been researchedintensively and applied in various models (see[11]). Although the approach has a history ofrelevant applications, it has become apparent thatthe exact parameter values required by earliermethods of the approach were not sufficient in alldecision-making situations.

3. Proposed problem

Here, a company is considered providing severalservices to customers. The services are assessableusing some criteria depending on customers’ satis-faction to be able to weigh the significance of theservices. Customers can express their views aboutthe services based on the criteria.

It is significant for the marketing team of thecompany to evaluate the customers’ opinions onthe received services to analyze them for obtainingthe maximum profit. Therefore, consider c1, . . . , cm,for i¼ 1, . . . ,m, as criteria and s1, . . . , sn, forj¼ 1, . . . , n, as services. We propose a mechanismto assess customers’ satisfaction about the receivedservices. The aim is to purify and determine theservices providing the maximum profit for thecompany. All the services should be analyzed withrespect to the given criteria. Thus, a multi-criteriadecision model is configured. Due to dynamismexists in the market and uncertainty of the realworld data, a stochastic multi-criteria decisionmodel is employed namely SMAA. This way,some of the services are pointed out via acceptabil-ity threshold. Here, amongst those services pointedout via SMAA, the ones providing more profitare chosen applying a multi-objective

mathematical model. The objectives are minimizingthe service cost, minimizing the service deliverytime and maximizing the delivered service quality.To optimize the proposed multi-objective model,fuzzy goal programming (FGP) is employed due toits considerations of uncertainty and flexibility indecision making rather than other multi-objectivemodels. The flowchart of our mechanism is shownin Figure 1.

The significances of this research include thefollowings:

. providing a mechanism as a decision aidfor company’s marketing team,

. considering and including customers’ opin-ions to improve serviceability of thecompany,

. proposing a SMAA to counteract thedynamism of customers’ viewpoints,

. purification of the services via SMAA,

. considering multiple objectives for betterservice provision, and

. obtaining the services provide the maxi-mum profit to the company.

4. Modeling the problem

The discrete decision-making problem refers to aset of n alternatives X¼ {x1, . . . , xj, . . . ,xn}, whichare evaluated on the basis of m criteria{g1, . . . , gi, . . . , gm}. The evaluation of action xj oncriterion gi is denoted gi(xj).

The model considers multiple DMs, eachhaving a preference structure representable throughan individual weight vector w and a real-valuedutility function u(xj;w) that has a commonlyaccepted shape. The most commonly used utilityfunction is the linear one:

uðxj,wÞ ¼Xmi¼1

wi � giðxj Þ: ð1Þ

The weights will be assumed non-negative andnormalized. Therefore, the feasible weight spacewill be

W ¼ w 2 <m : w � 0 andXmi¼1

wi ¼ 1

( ): ð2Þ

The SMAA methods are developed for situa-tions where criteria values and/or weights or othermodel parameters are not precisely known.Uncertain or imprecise criteria values are repre-sented by stochastic variables �ij corresponding tothe deterministic evaluations gi(xj) with densityfunction f�ð�Þ in the space � � <m�n. Similarly, theDMs unknown or partially known preferences arerepresented by a weight distribution with joint

272 H. Fazlollahtabar and E. Aghasi

density function fWðwÞ in the feasible weight

space W.As for the utility function-based approaches,

one should note that the weights are defined asscale factors: the weights rescale the values of

partial utility functions in such a way that the full

swing in the scaled function indicates the impor-

tance of the criterion.

4.1 Stochastic multi-criteria acceptabilityanalysis

The fundamental idea of SMAA is to provide

decision support through descriptive measures

calculated as multidimensional integrals over sto-

chastic parameter spaces. The original SMAA [25]

introduced an analysis measure entitled ‘‘accept-ability index.’’ For this purpose, the set of favor-

able weights Wj ð�Þ is defined as follows:

Wj ð�Þ ¼ w 2W : u �j,w� �

� u �k,wð Þ, 8k¼ 1, . . . ,n� �

:

ð3Þ

Any weight w 2Wj ð�Þ makes the overall utility

of xj greater than or equal to the utility of all other

alternatives. The descriptive measures of SMAA

are computed through Monte Carlo simulation.

This means that they might contain errors, but theerror margins are so small that usually they do not

have to be taken into account (when the number of

Monte Carlo iterations is large enough).

4.1.1 Acceptability index

The acceptability index of an alternative describesthe share of different valuations making an alter-native the most preferred one. It is computed as amultidimensional integral over the criteria distri-butions and the favorable weight space as

aj ¼

Z�2�

f�ð�Þ

Zw2Wj ð�Þ

fWðwÞdwd�: ð4Þ

Acceptability indices can be used to classifyalternatives into stochastically efficient ðaj � 0Þ orinefficient ones (aj near zero, for example, 50.05).A zero acceptability index means that an alternativeis never considered the best with the assumedpreference model. For stochastically efficient alter-natives, the index measures the strength of theefficiency considering simultaneously the dynamismon the criteria measurements and the DMs’ prefer-ences. Scaling the criteria affects the acceptabilityindices. Therefore, scaling must not performedarbitrarily when trying to classify the alternativeson the basis of acceptability indices [26]. Forexample, if the minimum and maximum criterionvalues are chosen as the corresponding scalingpoints, the possible introduction of a new alterna-tive might change these values and, therefore, alsothe acceptability indices to a large extent [4].

4.2 Multi-objective optimization

This way, a purification is performed on theservices as alternatives and those attract customers’

Figure 1. The flowchart of the proposed mechanism.


satisfaction more are determined. Here, the mar-keting team explores the more beneficial servicesoptimizing the objectives of the company. Theobjectives are minimizing the service cost, minimiz-ing the service delivery time and maximizing thedelivered service quality.

Cost of service (COS) is the cost of providing aservice. It can also be used as an adjective (COS) todenote rate structures, analysis, and expensesamong other things. COS pricing is the setting ofa price for a service based on the costs incurred inproviding it. COS pricing can be applied to anindividual customer based on the costs of servingthat customer, or as an average COS for a group ofsimilar customers.

Since we want to minimize the service cost,therefore we consider,

Mathematical notations:

j Counter for services; j¼ 1, 2, . . . , n.ej Amount of investment for the jth

servicesj 1, if service j is selected, 0, otherwiseFj Service transformation function of

s1, . . . , snB Fixed cost

Then, the mathematical model for cost is:

Min Z1 ¼Xnj¼1

sj � ej þ b: ð5Þ

Subject to,

s0 ¼ Fiðs1, . . . , snÞ, ð6Þ

where Fiðs1, . . . , snÞ is a mathematical function forrelating the sj and s0 is an iso-service level being thelocus of the services having same service level.

This model is a constrained nonlinear one. Tosolve the cost minimization problem, we set theLagrangian integrated function (L) as Equation (7)and set the partial derivatives Equations (8) and (9)equal to zero (first order conditions):

L ¼Xnj¼1

sj � ej þ bþ � s0 � Fiðs1, . . . , snÞ� �

, ð7Þ

@L

@sj¼ ej � � � fj ¼ 0, ð8Þ

@L

@�¼ s0 � Fiðs1, . . . , snÞ ¼ 0, ð9Þ

where fj is the marginal cost for each service,fj ¼ @Fi=@sj.

To investigate whether the obtained service isoptimal or not, we check the second order condi-tions. The second order conditions for the minimi-zation of cost require that the relevant Hessian of L

be positive semi-definite (if the Hessian of L is not

positive semi-definite, then we are sure that the

obtained service is not a minimizer). Here, the

Hessian of L is:

r2L� �

ij¼@2L

@si@sj: ð10Þ

To be positive semi-definite, the eigenvalues of

r2L, the �i, must satisfy:

�i � 0, 8i: ð11Þ

If the solution point is so that r2L is positive

definite, that is,

�i 4 0, 8i, ð12Þ

then the point is a local minimizer of L.Service delivery time is the length of time

between the preparation of a service and the

delivery of the service to the end consumer. It is

also sometimes referred to as the delivery period.

Companies keep track of their delivery times for

the purpose of being able to provide accurate

estimates when orders are placed so that consumers

know when to expect a delivery. This tracking is

also used internally to monitor efficiency. When

customers place an order, they are usually provided

with information about the estimated delivery time.

Here, we make use of earliness and tardiness being

penalized for the service delivery time minimiza-

tion. We consider,Mathematical notations:

� weight for total earliness; � � 0� weight for total tardiness; � � 0Ej earliness of service j; j ¼ 1, 2, . . . , n,Tj tardiness of service j; j ¼ 1, 2, . . . , n,Pj processing time of service j;

j ¼ 1, 2, . . . , n,Cj completion time for service j;

j ¼ 1, 2, . . . , n,dj due date of service j; j ¼ 1, 2, . . . , n,

Objective function:

Min Z2 ¼Xnj¼1

� � Ej � sj þXnj¼1

� � Tj � sj, ð13Þ

where

� ¼ Pj � dj�� 2, j ¼ 1, . . . , n, ð14Þ

� ¼ Pj � Cj

�� 2, j ¼ 1, . . . , n: ð15Þ

Equations (14) and (15) imply that the penalty

weights for total earliness and tardiness, respec-

tively, are a loss function of processing time, due

date, and completion time. Here, the difference

between processing time and due date is a penalty


for the earliness and the difference between pro-

cessing time and completion time is considered as a

penalty for tardiness.

Tj ¼ max 0, Cj � dj� �

, j ¼ 1, . . . , n, ð16Þ

Ej ¼ max 0, dj � Cj

� �, j ¼ 1, . . . , n: ð17Þ

Since formulae (16) and (17) are nonlinear, we

linearize them as follows:

Ej � 0, j ¼ 1, . . . , n, ð18Þ

Ej � dj � Cj, j ¼ 1, . . . , n, ð19Þ

Tj � 0, j ¼ 1, . . . , n, ð20Þ

Tj � Cj � dj, j ¼ 1, . . . , n: ð21Þ

Service quality involves a comparison of expec-

tations with performance. Service quality is a

measure of how well a delivered service matches

the customers’ expectations. Generally the cus-

tomer is requesting a service at the service interface

where the service encounter is being realized, and

then the service is being provided by the provider

and in the same time delivered to or consumed by

the customer. The main reason to focus on quality

is to meet customer needs while remaining eco-

nomically competitive in the same time. This means

satisfying customer needs is very important for the

enterprises survive. The outcome of using quality

practices is:

. understanding and improving of opera-

tional processes;. identifying problems quickly and

systematically;. establishing valid and reliable service per-

formance measures; and. measuring customer satisfaction and other

performance outcomes.

To control the quality of various services, the

concept of six sigma is considered as service weight.

The six sigma approach is one of the most widely

known best practices in providing a tolerance for a

parameter [17]. The concept of six sigma originates

from statistical terminology, wherein sigma (�)represents standard deviation. In the recent years, a

few researchers have focused on the application of

six sigma methodology in balancing process [6,21].This approach assumes that the ideal value of

the process mean is between specification intervals,

i.e. ’L 5 ’5 ’U (with 1:5� shift from the mean). It

is implied that six sigma concept with a 1:5� shift

from the mean holds and the probability of

conformance can be shown to be 0.9999966 (or

3.44 ppm). The level of assurance is targeted, but

the terminology is also used to evaluate currentlevel of ’ with the following sigma level (SL)(Table 1).

Analysis of the six sigma approach makes use ofprocess capability indices Cp and Cpk. Processcapability index Cp is defined as,

Cp ¼’U � ’L

SL: ð22Þ

The difference ’U � ’L represents specificationwidth. When Cp¼ 2 and service presence mean iscentered at ð’U � ’LÞ=2 without any shift, then theprobability of conformance is 99.9999998%.

Here, we make use of six sigma concept andEquation (22) to control the variation of theservices offered by the company. Thus, the simpli-fied version of Equation (22) is,

�j ¼ Cp ¼’Usj � ’

Lsj

SL: ð23Þ

Therefore, as we explore maximizing the deliv-ered service quality and considering process capa-bility index as a weight coefficient for any service,we obtain,

Max Z3 ¼Xnj¼1

sj � �j: ð24Þ

The complete multi-objective mathematicalmodel is presented below:

Min Z1 ¼Xnj¼1

sj � ej þ b ð25Þ

Min Z2 ¼Xnj¼1

� � Ej � sj þXnj¼1

� � Tj � sj ð26Þ

Max Z3 ¼Xnj¼1

sj � �j ð27Þ

s.t.

s0 ¼ Fiðs1, . . . , snÞ, j ¼ 1, . . . , n, ð28Þ

� ¼ Pj � dj�� 2, j ¼ 1, . . . , n, ð29Þ

Table 1. The trend of SLs.

SL PPM

1� 691,4622� 308,5383� 66,8074� 62105� 2336� 3.44


� ¼ Pj � Cj

�� 2, j ¼ 1, . . . , n, ð30Þ

Ej � 0, j ¼ 1, . . . , n, ð31Þ

Ej � dj � Cj, j ¼ 1, . . . , n, ð32Þ

Tj � 0, j ¼ 1, . . . , n: ð33Þ

Tj � Cj � dj, j ¼ 1, . . . , n: ð34Þ

�j ¼ Cp ¼’Usj � ’

Lsj

SL, j ¼ 1, . . . , n, ð35Þ

sj 2 f0, 1g, j ¼ 1, . . . , n: ð36Þ

To solve the proposed multi-objective model,fuzzy goal programing technique is employed. Asummary of fuzzy goal programing is given in nextsection.

5. FGP as solution approach

In many goal programming (GP) formulations twoassumptions underline: (1) the DM determines aprecise target for each attribute and (2) the devi-ations regarding the target are penalized with aconstant weight independently of which is thedistance from the target. With these considerations,we have a linear penalty function. However, insome situations the DM does not want to associatea precise target to certain attributes, being satisfiedwith values within a certain target interval.

The use of fuzzy set theory in GP was firstdiscussed by Hannan [16] and Korhonen andWallenius [23]. Rubin and Narasimhan [33] andTiwari et al. [36] have presented various aspect ofdecision problem using FGP. In FGP, the approachis something different from the previous one, it isconsidered that the goals are represented by fuzzysets whose membership functions provide the satis-faction degree regarding the achievement of thetargets. These functions play the same role than thepenalty functions in classic GP problems. In manyapplications it is supposed that the membershipfunctions are linear. The application FGP in realworld decision are found in numerous publication,from the environmental system management [36],the problem of aggregate production planning [9] todecision support for bus operation [8].

In the present work, we use the simple additivemethod developed by Tiwari et al. [37] to solve theFGP model due to its simplicity as compared to theother procedures. The model can be defined asfollows:

Find X

to satisfy Gs Xð Þ � gs, s ¼ 1, 2, . . . ,m: ð37Þ

Subject to,

AX � 0,

X � 0,

where X is an vector of decision variables and

AX� b are system constraints. Let’s consider,

Gs Xð Þ � gs or Gis Xð Þ � gs,

as imprecise forms (fuzzy) of the aspiration level.

According to Tiwari et al. [37] and Zimmermann

[41] a linear membership function (ms) for the each

fuzzy goal s could be expressed as follows:For problem of fuzzy goal as Gs(X)� gs:

i ¼

1 if GsðXÞ4 gs,

GsðXÞ � Ls

gs � Lsif Ls � GsðXÞ � gs,

0 if GsðXÞ5Ls:

8>><>>: ð38Þ

where Ls is the lower tolerance limit for the fuzzy

goal Gs(X).Also, the following expression could be formu-

lated for problem of fuzzy goal as Gs(X)� gs:

i ¼

1 if GsðXÞ5 gs,

Us � GsðXÞ

Us � gsif gs � GsðXÞ � Us,

0 if GsðXÞ4Us:

8>><>>: ð39Þ

where Us is the upper tolerance limit.This additive model of FGP has single achieve-

ment function that is a single objective optimization

problem. The criterion of the objective is to

maximize membership function of decision (ms)

instead of minimizing the deviation (as in conven-

tional GP). Hence, Tiwari et al. [37] formulated for

problem of fuzzy goal form Gs(X)� gs by adding

the membership functions together as:

Maximize VðÞ ¼Xs

s, ð40Þ

Subject to

s ¼GsðXÞ � Ls

gs � Ls, ð41Þ

AX � 0, ð42Þ

s � 1, ð43Þ

X,s � 0, s ¼ 1, 2, . . . ,m: ð44Þ

Note that, in (43) the model is constrained to

have membership values equal or lower than 1

being a classic definition of membership value

pointed out in Zimmermann [41]. We illustrate the

applicability and validity of our mechanism in a

case study.


6. Case study

Here, a case study is conducted in a car company inIran to illustrate the applicability and effectivenessof the proposed mechanism. In this car companyseveral services (j) are offered to the customers.These services support customers before, duringand after purchase process. The services are listedin Table 2, chronologically.

As shown in Table 2, there are 11 services thatthe company offers to the customers in differenttime periods. The services are evaluated using thefollowing criteria (i):

. ease of data access,

. user friendly applications,

. online information sharing,

. information comprehensiveness,

. responsiveness, and

. rapidness in service delivery.

Thus, j¼ 1, . . . , 11 and i¼ 1, . . . , 6. The result ofthe evaluation is expressed via a density functionf�ð�Þ due to uncertainty and dynamism with respectto the time factor. Also, the customers’ uncertainpreferences are presented by fWðwÞ. The densityfunctions for all services evaluation are given byuniform density functions having differentparameters,

f ðxÞ ¼

1

�� 5 x5�

0 o:w:

8<: ð45Þ

Also, the consumer preferences are shown byexponential density functions having variousparameters in different situations,

f ðxÞ ¼

1

e�x x4 0

0 o:w:

8<: ð46Þ

The selection of the density functions forparameters and customer preferences are based onthe previous data which in our case are uniformand exponential, respectively.

We are now able to make use of SMAAtechnique to determine the most effective services.To facilitate the computations Monte Carlo simu-lation was employed. The results of SMAA com-putations are summarized in Table 3.

We consider 0.65 as the threshold to accept a

service, i.e. if a value is lower than 0.65, then the

related service is considered to be not effective for

the customers. Therefore, product information

provision, news teller, product information

update, online purchase process, parts provision,

free checkups, guarantee of repair are chosen as the

services customers consider significant. Now, using

the selected services, we configure the proposed

multi-objective mathematical model.As stated, seven services are qualified to be

considered for profit optimization. The amount of

investment for the seven services are 75, 68, 34, 82,

56, 49, and 63, respectively. Also the service

transformation function being the relation of the

relativeness of the interactions of the services on

each other is s0 ¼ s21 þ s2 � s3 þ ðs24 � s5=3Þ þ ðs6=s7Þ:

The fixed cost is 1500 unit of money. The process-

ing times for the services are 25, 32, 41, 17, 28, 37,

and 43, respectively. Also, the completion times are

37, 59, 63, 48, 52, 45, and 67. And the due dates are

29, 49, 57, 34, 33, 51, and 68. The process capability

indices for services are computed to be 2.33, 2.59,

1.9, 3.3, 2.25, 3.14, and 2.78.Here, to solve the proposed multi-objective

model, fuzzy goal programing technique is

employed. Let g1, g2, and g3 are the goal values

for objectives 1–3, respectively. Also, p1, p2, and p3are the maximum tolerance related to the corre-

sponding objectives. For obtaining g1, g2, and g3,

three sub-problems as Prob. 1, Prob. 2 and Prob. 3

Table 2. Different services offered to the customers.

Before purchase During purchase After purchase

Product information provision Monitoring purchase process Parts provisionNews teller Online purchase process Periodic maintenanceProduct information update Online user error correction Free checkups

Guarantee of repairAfter sale services

Table 3. Computations for SMAA.

Numerical value of aj

Product information provision 0.67News teller 0.72Product information update 0.83Monitoring purchase process 0.57Online purchase process 0.69Online user error correction 0.44Parts provision 0.91Periodic maintenance 0.52Free checkups 0.93Guarantee of repair 0.85After sale services 0.62


with individual objectives 1–3 must be solved as

follows:

Prob. 1. Min Z1

s.t.constraints (28)–(36),

Prob. 2. Min Z2

s.t.constraints (28)–(36),

Prob. 3. Max Z3

s.t.constraints (28)–(36).

Solving the above three problems using

MATLAB 7.0 we obtain Z1¼ 1639, Z2¼ 1892,

and Z3¼ 2324. Also, the maximum tolerance values

determined by DM are p1¼ 800, p2¼ 1500, and

p3¼ 1200 thus, the membership functions for the

objectives are as follows:

1 ¼

1 if Z1ðXÞ � 1639,

2439� Z1ðXÞ

800if 1639 � Z1ðXÞ � 2439,

0 if Z1ðXÞ4 2439:

8>><>>:

ð47Þ

2 ¼

1 if Z2ðXÞ � 1892,

3392� Z2ðXÞ

1500if 1892 � Z2ðXÞ � 3392,

0 if Z2ðXÞ4 3392:

8>><>>:

ð48Þ

3 ¼

1 if Z3ðXÞ � 2324,

3392� Z3ðXÞ

1200if 2324 � Z3ðXÞ � 3524,

0 if Z3ðXÞ4 3524:

8>><>>:

ð49Þ

To obtain the optimal solutions we have to

optimize the following program:

Maximize �, ð50Þ

Subject to (28)–(36),

� ¼2439� Z1ðXÞ

800, ð51Þ

� ¼3392� Z2ðXÞ

1500, ð52Þ

� ¼3392� Z3ðXÞ

1200, ð53Þ

0 � � � 1: ð54Þ

Optimizing the above linear program in

MATLAB 7.0, we obtain � ¼ 0:37 and s2, s5, and

s6 are chosen as the services maximizing profit. This

way, we are able to make use of the proposed

decision support to help the marketing teams for

better segmentation of services and more appro-

priate customer mental mining. Also, the optimi-

zation of services is fulfilled via a multi-objective

mathematical modeling. This model is able to

counteract the dynamism in the market and is

flexible for the adoption of more variables and

objectives.

7. Conclusions

We proposed a two stage decision model to aid the

marketing team of a company based on customers’

satisfaction measures. These measures were related

to the different services the company offers to its

customers. The company’s performance was eval-

uated via SMAA as a purification tool of services

with respect to the criteria. Then a multi-objective

mathematical model was utilized to determine the

services with more profits considering the objec-

tives of minimizing the service cost, minimizing the

service delivery time and maximizing the delivered

service quality. To optimize the proposed mathe-

matical model, FGP was applied. We illustrated all

aspects of our model in a case study conducted at a

car company. The proposed model was able to

counteract the dynamism in the market and was

flexible for the adoption of more variables and

objectives.

Notes on contributors

Hamed Fazlollahtabar has been graduated in MSc ofIndustrial Engineering at Mazandaran University ofScience and Technology, Babol, Iran. He receivedDoctorate awarded from the Gulf University of Scienceand Technology in Quantitative Approaches inElectronic Systems. Currently he is studying PhD ofIndustrial Engineering at Iran University of Scienceand Technology, Tehran, Iran. He is in the editorialboard of WASET (World Academy of ScienceEngineering Technology) Scientific and TechnicalCommittee on Natural and Applied Sciences, reviewercommittee of International Conference on Industrialand Computer Engineering (CIE), and member of theInternational Institute of Informatics and Systemics(IIIS). He has become a member of Iran Elite Council.His research interests are mathematical modeling,optimisation in knowledge-based systems andmanufacturing systems. He has published over 90research papers in international book chapters, journalsand conferences.

Ermia Aghasi has been graduated in MSc ofExecutive Management at the University of Guilan,Rasht, Iran. His research interests are marketingresearch and decision making. He has publishedseveral research papers in international journals andconferences.


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Hamed Fazlollahtabar*Faculty of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

Ermia AghasiDepartment of Executive Management, Faculty of Human Sciences, University of Guilan, Rasht, Iran

; ;

* [email protected]


A two-stage mechanism as a decision support for marketing via customer satisfaction measures

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