e ciency assessment of iranian handmade carpet company by network...

Scientia Iranica E (2018) 25(1), 483{491

Sharif University of TechnologyScientia Iranica

Transactions E: Industrial Engineeringhttp://scientiairanica.sharif.edu

Research Note

E�ciency assessment of Iranian handmade carpetcompany by network DEA

S.H. Zegordi� and A. Omid

Faculty of Industrial & Systems Engineering, Tarbiat Modares University, Tehran, Iran.

Received 11 April 2014; received in revised form 5 November 2015; accepted 12 November 2016

KEYWORDSData envelopmentanalysis;E�ciency;Multistage;Multi-objective;Network;Undesired outputs.

Abstract. Di�erent categories of Iranian handmade carpet are produced each year. Dueto resource limitation, it is so important for managers to allocate more resources to themost e�cient categories. Therefore, the main purpose of this illustration is to considermost e�cient types of carpet in production and sales stages. To do so, di�erent categoriesof Iranian handmade carpet are considered as DMUs. This study utilizes network DEAfor constructing a model to analyze total and partial e�ciencies of Iranian HandmadeCarpet Company (IHCC), simultaneously. IHCC consists of three main departments thatare working jointly to maximize productivity of the �rm; therefore, the case of IHCC is amulti-stage system with shared intermediate variables, extra inputs to the second stage,and undesired outputs. The novelty of this paper is the methodology used for calculatingthe e�ciency, which is based on multi-objective programming. Results of experimental dataof IHCC are summarized in order to prepare some brilliant management strategies basedon partial and total e�ciency scores of di�erent carpet categories. Because of the lack offamiliar researches in the area of carpet industry e�ciency measurement, this research willprovide valuable information for decision makers.© 2018 Sharif University of Technology. All rights reserved.

1. Introduction

Resource allocation is one of the most important issuesfor companies, especially for an enormous industrysuch as handmade carpet texture. It is importantto note that resource limitations is an inseparableissue in each business, so how to allocate budget andresources among di�erent activities is a crucial task forall managers; if managers allocate the greatest amountof resources to the most e�cient activities, productivityand pro�t of the company will increase. Thus, due to

*. Corresponding author. Tel.: +98 21 82883394;Fax: +98 21 88005040E-mail addresses: [email protected] (S.H. Zegordi);[email protected] (A. Omid)

doi: 10.24200/sci.2017.20006

the shortage of resources, it is so essential to allocateresources to the most e�cient products. Analysisof historical data can also help managers to do thisduty successfully. According to the e�ciency scores ofdi�erent DMUs, experts can make suggestions aboutwhich DMU performs better and has priority for moreinvestigation; additionally, if performance score of aDMU is poor, partial e�ciency scores of sub-processescan help managers to realize which sub-process needsto be strengthened in order to maximize the overallperformance.

In handmade carpet industry, there are di�erentcategories of carpets, which are distinguished by design,color, size, raw material, and the pro�ciency of weavers;Carpet specialists classify these di�erent types of car-pet in some particular categories, which are mostlynamed by the geographic region in which the carpetsare woven. Production costs of these categories are

484 S.H. Zegordi and A. Omid/Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 483{491

di�erent based on di�erent weavers' wages dependingon gender and geographic region; in addition, di�erentkinds of raw materials with di�erent prices are usedsuch as wool, silk, u�, lint, etc.

From a managerial point of view, performance ofthe carpet industry is the aggregated e�orts of di�erentdepartments, involving both the production and thesales departments. Sales department consists of twomajor markets: internal market and external market,which work jointly to maximize the productivity ofthe company. Besides, there is changeable demand fordistinct kinds of carpet in the internal and externalmarkets; some are sold better in the local marketsand some are better to be exported. Hence, it is soimportant to perceive which category is more e�cientin production and marketing.

Therefore, if we assume each category of hand-made carpets as a DMU; it is so crucial for decisionmakers to know which DMU works e�ciently, sinceit can help managers to allocate more budgets to therespective category for the next year. In addition,partial e�ciency can bene�t managers a lot. Ifmanagers get access to the partial e�ciency scoresof di�erent departments, they can understand whichcomponent is ine�cient. Thus, specialists will focuson this department and, by empowering it, and willenhance the overall e�ciency of the DMU.

To the knowledge of the authors, there is noresearch done yet in the �eld of measuring the per-formance of handmade carpet texture industry. Thisstudy provides new methodology for measuring thee�ciency of a network structure, which is based onmulti-objective programming, to maximize total andpartial e�ciencies, simultaneously; therefore, for the�rst time, a method is applied to a handmade carpetcompany case.

For ease of notation, Section 2 begins with re-viewing relevant literature; then, in Section 3, weintroduce our approach to model multi-stage system ofIranian Handmade Carpet Company (IHCC). Section 4provides illustrative example of IHCC; besides, resultsof e�ciency scores, which are measured by means of theproposed network DEA methodology, are summarized.Then, in Section 5, discussions about the results aredeveloped. Conclusions are given in the last section.

2. Literature review

Data Envelopment Analysis (DEA) was introduced in1978 for measuring relative e�ciency of peer DecisionMaking Units (DMUs) [1]. DEA has been widelyrecognized as an e�ective technique for measuring therelative e�ciency of a set of DMUs that apply mul-tiple inputs to produce multiple outputs, with manytheoretical developments and practical applicationsbeing reported (for example, the review of Cook and

Seiford [2]; Emrouznejad et al. [3]; Liu et al. [4,5]; andZhou et al. [6]).

Although DEA has been applied in many di�erent�elds, DMUs have traditionally been seen as blackboxes with inputs and outputs, but without any con-sideration of what is happening inside the DMU [7].Traditional DEA models failed to measure the e�orts ofdi�erent processes and sub-processes within the orga-nization [8]. Another issue that should be noted is thatignoring the operations of the component processesmay end in misleading results; a number of exampleshave been presented to show that an overall systemmay be e�cient even if all component processes arenot [9]. More signi�cantly, there are cases in which allthe component processes of a DMU perform worse thanthose in another DMU, yet they have better systemperformance [10]. To overcome this, many studies inthe area of network structure e�ciency measurementhave been done; Kao published a literature reviewarticle about network data envelopment analysis thatclassi�ed models used in network systems in an appro-priate manner [11]; some develop models to measuree�ciencies under speci�ed conditions, some examinethe properties possessed by certain models, and othersapply existing models to solve real-world problems.Cook et al. reviewed a number of models for thebasic two-stage system, which had only two processesconnected in series, with the second only consuming allthe outputs from the �rst stage [12]. Conversely, quitea few researches focused on general multi-stage networkwith extra inputs and outputs. As an instance, Toneand Tsutsui proposed a Slacks-Based Measure (SBM)model to measure the system and process e�ciencies ofa network system with extra inputs and outputs [13].Kao transformed the nonlinear model into a linearone using a variable substitution technique [14]. Inaddition, for network structures with more than twostages, Kao proposed the relational network DEAmodel [15]. Hiseh and Lin utilized relational networkdata envelopment analysis to construct a model to an-alyze the e�ciency and e�ectiveness of an internationaltourist hotel [16]. Liu and Lu enhanced the network-based approach, which was a novel method to increasediscrimination in data envelopment analysis [17]. Liet al. modeled a two-stage structure by assumingthe inputs to the second stage, including both theoutputs from the �rst stage and additional inputs tothe second stage [18]. Recently, Liu et al. tried tosystematically examine two-stage DEA models withundesirable input-intermediate-outputs [19]. Besides,Matin and Azizi introduced a uni�ed general modelfor e�ciency evaluation of network production sys-tems when arbitrary relations between individual sub-processes were allowed [20].

In addition, some studies proposed decompositionapproach for measuring the e�ciency of network struc-

S.H. Zegordi and A. Omid/Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 483{491 485

ture; as an instance, Chen et al. developed additivee�ciency decomposition approach for measuring thee�ciency of two-stage network process [21], same asthe study by Cook et al., which represented the overalle�ciency of an open multistage process as an additiveweighted average of the e�ciencies of the individualcomponents [22]. In this regard, Kao and Liu devel-oped a multi-period e�ciency measurement in DEA tocalculate overall and period e�ciencies of a DMU at thesame time. In their methodology, the overall e�ciencywas a weighted average of the period e�ciencies [23].

Some other new studies focused on network DEAproblems from multi-objective point of view, such asthe research done by Kao et al. which proposed theMulti-Objective Programming (MOP) method for solv-ing Network DEA (NDEA) models. In the proposedmethod, the divisional e�ciencies (within an organiza-tion) and the overall e�ciency of the organization wereformulated as separate objective functions in the multi-objective programming model [24]. Despotis et al. alsoused multi-objective programming approach for solvinga network DEA problem [25]. This paper wishes toprovide some information about the researches done inthe area of carpet industry e�ciency assessment; tothe best of the authors' knowledge, no relevant studieshave been done in this area yet. Based on the literatureprovided above, this research also considers networkDEA problem as a multi-objective problem, henceassuming the e�ciency of each stage as an objectivethat should be optimized simultaneously.

3. Methodology

In this investigation, DMUs are not treated as a black-box; instead, the proposed modeling considers inter-nal structure of Iranian Handmade Carpet Company.Thus, the overall performance and the e�ectiveness ofIHCC's sub-processes are measured.

3.1. Model constructionOur model disentangles the major Iranian HandmadeCarpet Company's activities and places them intothe network DEA model. Through the modeling,we consider the handmade carpet industry as a boxthat can be broken into two main stages, the �rstone is production stage and the second is marketingstage; marketing stage is divided into two parallelsub-processes named, internal and external markets,which use the desired outputs of the �rst stage as theirown inputs and proportionally cleave inputs betweenthemselves.

The production department uses raw material,weavers' wages, and some other expenses such as de-signing costs and transportation expenses as its inputs,which are shown by xij (i = 1; � � � ;m), and producecarpets (measured by area) as its output. Since

human error is an unavoidable factor in the handmadecarpet industry, there are some carpets which are notacceptable for carpet company. Thus, some carpets areperfect, called desired outputs, which enter the secondstage as inputs (denoted by ztj (t = 1; � � � ; n)) andsome others are imperfect, called undesired outputs(Urj (r = 1; � � � ; l)), which are sent out of the systemas wastage. A part of these desired outputs enterthe external sales department (denoted by �tjztj (t =1; � � � ; n)) as inputs and the rest enter the internal salesdepartment (denoted by �tjztj (t = 1; � � �n)). Thepro�t earned from each market is the output of thesesub-processes (y1j for external market sub-process andy2j for internal market sub-process). Additionally,external sales department has its own inputs, whichare independent from the �rst stage that relates toexpenses for customs clearance and transportation, soit is considered as an independent input to the externalsales sub-process (denoted by Hdj (d = 1; � � � ; p)).Since the internal sales expenses are much less thancustoms and transportation costs, they can be ignoredin the modeling.

Figure 1 illustrates the divisions and componentsof handmade carpet industry. This study aims toevaluate the e�ciency of the overall organization ande�ectiveness of major departments' operations.

Consider that there are k DMUs, where eachDMUj (j = 1; � � � ; k) consists of two main stages,named as production stage and sales stage, as shownin Figure 1. Suppose that each DMUj(j = 1; � � � ; k)has m inputs denoted by xij (i = 1; � � � ;m) to thewhole process as well as n desired outputs denotedby ztj (t = 1; � � � ; n) from the �rst stage, which thenbecome inputs to the second stage and are referred toas intermediate measures. Additionally, suppose thateach DMUj (j = 1; � � � ; k) has l undesired outputsdenoted by Urj (r = 1; � � � ; l) from the �rst stage,which are put out of the system as losses. Thedesired outputs from the �rst stage (ztj) are sharedas inputs between two sub-processes of the secondstage; the proportion of these inputs measured by �tj isdedicated to the �rst sub-process while the remainingmeasured by �tj is dedicated to the second one, so�tj + �tj = 1. Furthermore, we assume that the�rst sub process of second stage has extra inputs fromoutside of the system, denoted by Hdj (d = 1; � � � ; p).Eventually, ysj is the outputs of the sth sub-process ofthe second stage. These parameters are also illustratedin Figure 1.

Consistent with the two-stage frameworks com-monly used in the existing literature, the overall orga-nization e�ciency can be calculated as the product ofthe e�ciency of two stages as follows [26]:

EK = EK1:EK2; (1)

where EK1 and EK2 are the e�ciencies of production


Figure 1. Multi-stage structure of Iranian Handmade Carpet Company (IHCC).

stage and sales stage, respectively. Based upon theConstant Return to Scale (CRS) model [1], the CRSe�ciency score for DMUj in the �rst and second stagescan be calculated, respectively, by the following twoequations:

EK1 =Pt wtjztj �Pr urjUrjP

i vijxij; (2)

EK2 =Ps usjysjP

t wtjztj +Pd hdjHdj

: (3)

As can be clearly seen, e�ciency of each stage isde�ned as the ratio of the weighted sum of outputsto the weighted sum of inputs. The rationale for thenegative sign of the second term in the numerator ofe�ciency of the �rst stage is that the outputs Urj areundesirable and to be minimized; thus, they should bedecreased in the production process. Besides, it shouldbe considered that

Ps usjysj =

Pu1jy1j +

Pu2jy2j .

Thus, the model can be illustrated as follows:

max

0@Pt wtjztj�Pr erjUrjPivijxij

�PsusjysjP

twtjztj+

PdhdjHdj

1A ;(4)

subject to:Ps usjysj �Pr erjUrjPi vijxij +

Pd hdjHdj

� 1; (5)Pt wtjztj �Pr erjUrjP

i vijxij� 1; (6)P

s usjysjPt wtjztj +

Pd hdjHdj

� 1; (7)Pu1jy1jP

t �tjwtjztj +Pd hdjHdj

� 1; (8)

Pu2jy2jP

t �tjwtjztj� 1: (9)

For a speci�c DMUj , Constraint (5) considers thesystem as a whole and represents that the weightedsummation of outputs of the whole process is smallerthan or equal to that of its inputs. As it was mentionedbefore, since Urj is undesired outputs, it should bedecreased and that is why it has the negative signin this constrain. Similarly, Constrain (6) is same asConstraint (5), with the di�erence that it considers the�rst stage as a box.

Constrain (7) represents e�ciency of the wholesecond stage, which is smaller than or equal to one.Constraints (8) and (9) represent the relative e�cien-cies of each sub-processes of the second stage to besmaller than or equal to one. As can be clearly seen,Constraints (5) and (7) are redundant, since Constraint(7) can be obtained by Constraints (8) and (9); inaddition, Constraint 5 can be obtained by Constraints(6), (8), and (9). Based on relational model [9], weassume that the same factor has the same multiplier,no matter how it is used.

The purpose of this issue is to determine optimalvalues of the variables wtj , erj , usj , vij , and hdjfor each DMUj(j = 1; � � � ; k) such that the overalle�ciency of the whole system is maximized. It isblindingly evident that this modeling results in anonlinear objective function, which cannot be solvedwith linear programming approaches and needs somechanges to become solvable. In the following, multi-objective methodology is used to solve this problem.

3.2. Multi-objective methodology for NDEAIn the multi-objective approach, the e�ciency of eachsub-process in addition to e�ciency of the whole pro-cess is considered as a di�erent objective that shouldbe optimized. Therefore, if the e�ciency of each sub-process is assumed as the ratio of weighted outputs tothe weighted inputs, the objective functions will be asfollow:


EPj =Pt wtjztj �Pr erjUrjP

i vijxij;

EEj =Pu1jy1jP

�tjwtjztj +PhjHj

;

EIj =Pu2jy2jP�tjwtjztj

;

Ej =Pu1jy1j +

Pu2jy2j �Pr erjUrjP

i vijxij +PhjHj

; (10)

where each of EPj , EEj , EIj , and Ej is an objectivethat should be optimized. EPj , EEj , EIj , and Ejare the e�ciencies of production sub-process, externalsales sub-process, internal sales sub-process, and totale�ciency, respectively. It should be considered that anappropriate model is the one that optimizes all theseobjectives simultaneously.

As mentioned, the main objective of e�ciencyevaluation by means of multi-objective network DEAis to maximize all of the above e�ciency equationssimultaneously. On the other hand, since each ef-�ciency equation in Constraint (10) is a fractionalobjective, a methodology is used to transform thisfractional objective into a linear one. As mentionedbefore, maximizing each equation is the main objectiveof the model. Maximizing a fractional equation meansto maximize its numerator and, at the same time,to minimize its denominator. Therefore, objectivefunctions of Eq. (10) can be rewritten as follows:

max

8>>><>>>:Pt wtjztj �Pr erjUrjPu1jy1jPu2jy2jPu1jy1j +

Pu2jy2j �Pr erjUrj

(11)

min

8>>><>>>:Pi vijxijP�tjwtjzj +

PhdjHdjP

�tjwtjztjPi vijxij +

PhdjHdj

(12)

As much asPt wtjztj , which is the output of the

�rst stage and simultaneously the input to the secondstage, plays two roles, it needs reconsideration. WhilePt wtjztj is the output of the �rst stage, it should

be maximized and, conversely, while it is the input tothe second stage, it should be minimized. Therefore,because of these dual characteristic of this componentin the model, it should be equal to a �xed value inorder to solve the problem. As a result, Constraint(13) Should be added to the constraints of the model:X

t

wtjztj = 1: (13)

Until now, the fractional multi-objective problem hasbeen transformed into a linear multi-objective prob-lem. In order to solve this multi-objective problem, amethod for transforming the multi objective probleminto one objective problem is needed, which has theability to optimize all objectives simultaneously.

Zimmermann [27] applied Bellman and Zadeh'smax-min operator [28] to solve the multi-objectivelinear programming model. This operator enjoyedcomputation simplicity and some other advantages;however, it was not a compensatory operator. Hence,it did not assure a Pareto-optimal solution [30]. Ap-plying Bellman and Zadeh's max-min operator [28], theoptimal solution can be obtained by:

max�;

� �Xt

wtjztj �Xr

erjUrj ;

� �Xu1jy1j ;

� �Xu2jy2j ;

� �Xu1jy1j +X

u2jy2j �Xr

erjUrj ; (14)

min�;

� �Xi

vijxij ;

� �X�jw1jzj +X

hjHj ;

� �X�jw2jzj ;

� �Xi

vijxij +X

hjHj : (15)

Subject to:Xs

usjysj�Xr

erjUrj�Xi

vijxij�Xd

hdjHdj�0;(16)X

t

wtjztj �Xr

erjUrj �Xi

vijxij � 0; (17)

Xs

usjysj �Xt

wtjztj �Xd

hdjHdj � 0; (18)

�u1j 00 u2j

��y1jy2j

��tj�tj

�wtjztj�

�hj 00 0

��HjLj

��0;

(19)Xt

wtjztj = 1: (20)


In the constraint set above, the summation of weightedoutputs is smaller than the summation of weightedinputs. It can be clearly seen that the proposedmethodology converts the nonlinear Constraint set(5) to (9) into the linear programming format bymeans of Charnes and Cooper transformation [31]. Asmentioned before, Constraint (16) can be obtainedby summation of Constraints (17) and (18), so it isredundant. Besides, Constraint (18) can be obtainedby summation of two constraints summarized in Con-straint (19), so this one is redundant, too.

Li utilized Bellman and Zadeh's max-min oper-ator and proposed a two-phase approach [29] usingmax-min operator as phase I; The optimal solution ��obtained by phase I was supplemented with the con-straints of the problem as the minimum solution valuein phase II. The two-phase approach was a combinationof max-min operator and averaging operator. Sinceaveraging operator had full-compensation property, thesolution made by two-phase approach was an e�cientone [30]. Therefore, using this two-phase approach ismore bene�cial than only using max-min operator ofBellman and Zadeh:

max�1 + �2 + �3 + �4

4;

�� 1 �Xt

wtjztj �Xr

erjUrj ;

�� 2 �Xu1jy1j ;

�� 3 �Xu2jy2j ;

�� 4 �Xu1jy1j +X

u2jy2j �Xr

erjUrj ;

0 � �u � 1 u = 1; 2; 3; 4: (21)

In this approach, the optimal value �� resulting fromthe max-min operator in Model (14) is considered asthe lower bound of all �u. Therefore, it assures thevalue of each e�ciency score is at least equal to ��:

min�1 + �2 + �3 + �4

4;

�� 1 �Xi

vijxij ;

�� 2 �X�jw1jzj +X

hjHj ;

�� 3 �X�jw2jzj ;

�� 4 �Xi

vijxij +X

hjHj ;

0 � �u � 1; u = 1; 2; 3; 4: (22)

In the same manner, the optimal value, ��, resultingfrom the max-min operator in Model (15) is consideredas the upper bound of all �u.

Finally, overall e�ciency of the system and therelative e�ciencies of sub-processes can be calculatedfrom Eq. (10) where EPj , EEj , EIj , and Ej are thee�ciency ratios of production, internal sales depart-ment, external sales department, and total e�ciency,respectively.

4. Empirical study

This paper presents an illustrative example with realdata of Iranian Handmade Carpet Company (IHCC).Iranian Handmade Carpet Company has more than80 years of experience in the �elds of weaving, pro-ducing, and trading hand-woven carpets. Iran CarpetCompany is the major center of hand-woven carpets inIRAN with the following speci�cations: 10000 weavers,500 branches in villages and rural areas, and 100branches in major cities. Data of IHCC are gatheredin a period of two years from the beginning of 2012to the end 2013 and the average is summarized inTable 1. For establishing the main departments inaddition to main parameters of input, intermediate,and output, broad consultations are done with IHCC'sspecialists, including production managers, marketingmanagers, and sales managers. Upon the consultationsdone with carpet specialists, we assume 15 DMUs asthe main carpet industry's DMUs, which are basedon the di�erent categories of carpets such as Tabrizcarpet, Yazd carpet, Isfahan carpet, etc. For eachDMU, we assume three inputs, named raw material ex-penses (X1j); weavers' wages (X2j); and other expensesrelated to plan, design, and the equipment needed forweaving a carpet (X3j), which are measured by currentcurrency of Iran. The amount of perfect carpets wovenby weavers is measured by area (m2), which is assumedas desired output of the �rst stage (Ztj) that enters thesecond stage. Besides, undesired or imperfect carpetsare denoted by Uj , which are sent outside the system.The proportion of the desired outputs, denoted by�tjztj , enters the external markets and the remain-ing, denoted by �tjztj , enters the internal markets.Consider that �tj and �tj are the parameters of themodel and �tj + �tj = 1. In addition, independentinputs to the external markets are denoted by Hj . Thepro�t earned from each market is the outputs of thesub-processes, denoted by y1j and y2j for external andinternal sales sub-processes, respectively. The dataset for a one-year period is summarized in Table 1.The results calculated by both models are reported inTable 2, where the �rst four columns represent theresults of the �rst methodology and the remainingshow the results of the second methodology. The �rstand 5th columns of Table 2 show the overall e�ciency


Table 1. Data set of Iranian Handmade Carpet Company (IHCC's archives, 2012-2013).

DMUFirst stage's inputs Intermediate variables Second stage's inputs Second stage's outputs

Rawmaterial

Wages Otherexpenses

Desiredoutput

Undesiredoutput

� � Customs andtransportation

Externalmarkets'earning

Internalmarkets'

pro�tDep1 56 190 4.1 470 24 0.30 0.70 22 103 28Dep2 282 298 6.8 1280 75 0.47 0.53 58 579 80Dep3 38 122 5.8 800 61 0.23 0.77 26 285 317Dep4 82 262 23 310 19 0.16 0.84 8 86 36Dep5 18 208 15 610 21 0.18 0.82 5 172 87Dep6 129 295 30 1120 71 0.34 0.66 53 314 58Dep7 79 132 29 600 13 0.25 0.75 22 169 66Dep8 54 128 21 460 12 0.26 0.74 18 128 59Dep9 63 98 15 710 30 0.31 0.69 32 198 36Dep10 43 85 13 360 12 0.14 0.86 8 99 26Dep11 76 129 17 530 19 0.19 0.81 16 148 26Dep12 68 120 25 860 34 0.17 0.83 19 241 90Dep13 85 124 2.7 370 28 0.15 0.85 12 103 161Dep14 95 75 7.9 250 12 0.23 0.77 7 69 20Dep15 54 55 9.3 320 30 0.13 0.87 5 88 13

Table 2. Results of e�ciency measurement.

DMUFirst approach

Totale�ciency

Productione�ciency

External salese�ciency

Internal salese�ciency

Dep1 (Isfahan) 0.51 0.64 0.56 0.55Dep2 (Tabriz) 0.84 0.68 1.00 0.79Dep3 (Zabol) 0.78 1.00 0.53 1.00Dep4 (Ghom) 0.59 0.45 0.71 0.59Dep5 (Naeen) 0.81 1.00 0.87 0.71Dep6 (Kerman) 0.44 0.33 0.52 0.22Dep7 (Ilam) 0.56 0.58 0.62 0.58Dep8 (Birjand) 0.64 0.75 0.65 0.61Dep9 (Kashan) 0.47 0.76 0.54 0.54Dep10 (Yasouj) 0.60 1.00 0.72 0.62Dep11 (Yazd) 0.48 0.61 0.57 0.54Dep12 (Hamedan) 0.56 0.66 0.63 0.68Dep13 (Shahrkord) 1.00 1.00 1.00 0.99Dep14 (Kashmar) 0.63 0.91 0.73 0.21Dep15 (Bijar) 0.53 1.00 0.68 0.19

scores obtained by the �rst and second approaches,respectively. In addition, partial e�ciency scores ofall departments are summarized in Table 2.

5. Discussion

The results summarized in Table 2 can be used to de-velop bene�cial management strategies for future years.For instance, Shahrkord, Tabriz, Naeen, and Zabolcarpets have higher total e�ciency scores among all 15departments. Thus, during the production planningand resource allocation in the following year, moreresources will be allocated to these special categories

of handmade carpet in order to maximize the pro�tand productivity of the company.

One of the high-priority policies of Iranian Hand-made Carpet Company is conducting the productionprocedures with regards to export's needs; conse-quently, it is so important for IHCC's decision mak-ers to know what category of carpets has the moste�ciency in external markets. In other words, bydistinguishing those kinds of carpet that can bringmore pro�t for the company through export, IHCC canincrease its income properly, especially now that thevalue of Dollar has increased greatly in relation to Rial.Based on the information summarized in Table 2, the


most e�cient categories of Iranian handmade carpetfor export include the Tabriz, Naeen, and Shahrekordcarpets. In other words, these categories of carpetsare the best categories for export and have the highestexternal sales e�ciency scores.

In addition to export, internal sale is so im-portant for IHCC. Since, if IHCC's managers getaccess to scienti�c information about the e�ciency ofdi�erent carpet categories in internal markets, theycan make logical decisions on the production plan forthe amounts of di�erent categories in future years.In addition, about 40% of IHCC's income is earnedthrough internal markets in average; therefore, e�-ciency assessment of di�erent categories in domesticmarkets is so important. By means of the methodologyprovided in this study and the e�ciency assessment inTable 2, it can be concluded that Zabol, Shahrkord,and Tabriz are the most e�cient categories in internalmarkets.

In addition, by focusing on partial e�ectivenessof di�erent departments, most e�cient carpets amongproduction departments can be classi�ed as Zabol,Naeen, Yasuj, Shahrkord, and Bijar. It means thatthe production departments of these DMUs producethe maximum amounts of desired output in proportionto their inputs relative to other DMUs.

In comparison, the model proposed by this paperworks better than the previous ones because of twomain reasons. The �rst reason is related to the resultsobtained from experimental data. As Table 2 indicates,results show that a DMU will be e�cient if and only ifall of its departments are e�cient. As an illustration,consider the third DMU, which is e�cient in productionand internal sales; however, the external sales depart-ment of this DMU does not work properly and it hasan e�ciency score of 0.53. Thus, the consequence isthat total e�ciency score of this DMU must be lessthan one, because all departments of this DMU arenot e�cient; this is true, because the proposed modelmeasured the amount of 0.78 for total e�ciency score.In fact, a DMU is e�cient only if all of its' departmentsare e�cient and this reasonable result can be obtainedfrom the proposed MOP-NDEA approach. Besides, forthe 13th DMU, which is e�cient in production, internalsales, and external sales departments, total e�ciencyscore is measured as 1, showing that this DMU iscompletely e�cient.

The second reason is related to the manner ofsolving the problem. By means of MOP in NDEA,the partial and total e�ciencies can be optimized in acohesive manner.

6. Conclusion

The main objective of this paper was to assess theperformance of handmade carpet industry for the �rst

time. To achieve this goal, this study measured the ef-�ciency and e�ectiveness of Iranian Handmade CarpetCompany (IHCC), which is a multi-stage system withextra inputs, undesired outputs, and shared variables.Because of network structure of the system, overalle�ciency equation resulted in a nonlinear function. Inorder to convert this nonlinear function to a linearone, a new approach for assessing the overall e�ciencyand partial e�ectiveness of each sub-processes wasintroduced.

In this research, multi-objective programmingwas used in order to solve a network DEA problem.By means of MOP in NDEA, the partial and totale�ciencies could be optimized in a cohesive manner.This approach considered the network DEA problemas a multi- objective one and aimed to maximizetotal and partial e�ciencies of the network structure,simultaneously, by solving just one model. Resultscalculated from empirical data of IHCC distinguishedthe most e�cient departments and prepared some bril-liant information for decision makers to make strategicdecisions in future. Further researches can exploreother multi-objective network DEA models for mea-suring the performance of more complex multi-stagenetworks with undesired outputs in variable return-to-scale mode. In addition, due to the importance ofcarpet industry, more investigations in this area areneeded.

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Biographies

Seyed Hessameddin Zegordi is Professor of Indus-trial Engineering in the Faculty of Industrial & SystemsEngineering at Tarbiat Modares University, Tehran,Iran. He received his PhD degree from the Departmentof Industrial Engineering and Management at TokyoInstitute of Technology, Japan, in 1994. He holds anMSc degree in Industrial Engineering and Systems fromSharif University of Technology, Iran, and a BSc degreein Industrial Engineering from Isfahan University ofTechnology, Iran. His research interests include math-ematical modeling for production planning problems,location & layout design, metaheuristics, supply chainmanagement, quality management, and productivity &performance measurement.

Azadeh Omid is a PHD student at Tarbiat ModaresUniversity, Department of Management. She receivedBSc degree in Mechanical Engineering from Iran Uni-versity of Science and Technology in 2011, and MScdegree in Industrial Engineering from Tarbiat ModaresUniversity, Tehran, Iran, in 2013. Her researchinterests include applications of operations research,productivity and performance management, supplychain management, multi-objective optimization, androbust optimization.

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