Computers & Industrial Engineering 61 (2011) 550–560

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Computers & Industrial Engineering

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Order partitioning and Order Penetration Point location in hybridMake-To-Stock/Make-To-Order production contexts q

H. Rafiei ⇑, M. RabbaniDepartment of Industrial Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran

a r t i c l e i n f o

Article history:Received 23 May 2010Received in revised form 19 April 2011Accepted 22 April 2011Available online 29 April 2011

Keywords:Fuzzy analytic network processHybrid Make-To-Stock/Make-To-OrderOrder partitioningOrder Penetration PointProduct delivery strategyProduction planning

0360-8352/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.cie.2011.04.010

q This manuscript was processed by Area Editor Mo⇑ Corresponding author. Tel.: +98 21 88021067; fax

E-mail addresses: hrafiei@ut.ac.ir (H. Rafiei), mrab

a b s t r a c t

Hybrid Make-To-Stock (MTS)/Make-To-Order (MTO) is one of the product delivery strategies which haverecently attracted practitioners’ and academicians’ interest to meet requirements of today competitiveenvironment. Two important decisions involved in hybrid MTS/MTO context are order partitioning anddetermining Order Penetration Point (OPP) location. In this paper, a model is developed to first decideon which product is manufactured upon MTS, which one upon MTO and which one upon hybrid strategy.Then, a fuzzy analytic network process (ANP) is utilized to locate the OPP for the products which aredecided to be manufactured upon hybrid strategy. Finally, a real industrial case study is reported to showapplicability of the proposed model.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

In today growing competitive markets, a manufacturing com-pany’s survival depends increasingly on how best it can design,manage and restructure its production system to deal with productdiversity, improve delivery reliability, customize products, providesuitable production flexibility and reduce system costs. To copewith these issues, manufacturing companies often use differentproduction systems based upon a strategic question: How muchdo customer orders influence production strategy? Order Penetra-tion Point (OPP) or Customer Order Decoupling Point (CODP) wasintroduced by taking into consideration both customers and pro-duction-line issues (Hoekstra & Romme, 1992). OPP is defined asthe point in the production value chain at which a specific orderis linked to a specific product. Therefore, this point divides theproduction activities into forecast-driven (downward the OPP)and customer-order-driven activities (upward the OPP) (Olhager,2003). Regarding different stages in production flow line at whichOPP is located, diverse production strategies can be obtained. Fig. 1shows different locations of OPP and the corresponding productionenvironments. The scope of this paper includes MTS, MTO and hy-brid MTS/MTO production strategies.

ll rights reserved.

hamad Y. Jaber.: +98 21 88013102.

ani@ut.ac.ir (M. Rabbani).

1.1. Production strategies

Based on market demands’ response policy, production systemscan be classified into two major categories: MTS and MTO. MTSproduction strategy is based upon forecasts of product demandsand production is accomplished without considering specificationsof customer orders. Hence, considerable holding costs or stock-outcosts are inevitable in markets with fluctuating demands. Also, nocustomization can be performed on MTS products, as orders occurwhile products are fully processed and stocked in warehouses ofthe firm (Mu, 2001). Furthermore, in highly competitive industries,products have limited shelf life; therefore, finished products in apure MTS system are subjected to risk of obsolescence. Importantissues and measures in MTS environment are usually higher fillrate, demand forecasting, lot sizing, average inventory levels, etc.(Soman, van Donk, & Gaalman, 2004).

In contrary to MTS, MTO policy is fully structured with respectto customer orders. In an MTO environment, manufacturing of aspecific product is not initiated, unless a specific order is receivedfrom a customer. Although this system eliminates finished-goodsinventories and reduces firm’s exposure to financial risk, it usuallyresults in long customer lead times and large order backlogs(Zaerpour, Rabbani, Gharegozli, & Tavakkoli-Moghaddam, 2008).Important issues considered in MTO systems are average responsetime, average order delay, due date setting etc. (Soman et al.,2004).

Hybrid MTS/MTO production context is benefited from bothMTS and MTO. In hybrid systems, there are two distinct stages in

Strategy Procurement Processing Delivery

Make-To-Order

(Pull system) OPP

Hybrid MTS/MTO

(Hybrid push-pull system) OPP

Make-To-Stock

(Push system) OPP

Fig. 1. Different production strategies; dashed and solid lines represent forecast-driven and customer-order-driven activities, respectively (Hoekstra & Romme, 1992;Olhager, 2003).

H. Rafiei, M. Rabbani / Computers & Industrial Engineering 61 (2011) 550–560 551

a common production line for each product; common and differen-tiation stages. During common stage, all products are processedthrough the same work centers with the same job descriptionsand semi-finished products are completed in differentiation stagewith respect to customer orders and associated customizations.The two above-mentioned stages are separated by a stocking pointcorresponding to each product. Compared with MTS, hybrid MTS/MTO environments yield higher level of customization, lesswork-in-process inventories, less backlog or loss-sales costs, lessholding cost, higher flexibility etc., while some characteristics, likeunder load utilization and longer lead times are embedded to thisproduction strategy. To tradeoff between MTS and MTO as two ex-treme systems, hybrid systems have been adopted by practitionersand academicians in recent years. As discussed by Soman et al.(2004), since MTS/MTO system is a combination of two productionsystems, a variety of conflicting issues are arisen in hybrid MTS/MTO and it is difficult to handle all of these issues simultaneously.In this regard, a hierarchical decision-making structure is a reason-able approach to solve the issues involved. This paper focuses ondetermining appropriate product delivery strategy for differentproducts in a manufacturing system (MTS/MTO partitioning). Next,OPP locations of products are determined with respect to theirdecided delivery strategies (OPP location). To make the two abovestrategic decisions in MTS/MTO systems, a comprehensive deci-sion-making structure is proposed for the first time. The proposedstructure results in three delivery strategies: MTS, MTO and hybridMTS/MTO. As there are inter-related decision criteria to locateOPPs, an ANP model is proposed. The proposed ANP model com-pensates deficiencies of the previous models by considering in-ter-relations and both qualitative and quantitative criteria.Moreover, the proposed ANP is equipped with fuzzy sets theoryto tackle ambiguity and uncertainty of input judgments. To doso, next sections are structured as followings. Section 2 briefly re-views the previously performed researches. The fuzzy ANP is elab-orated in Section 3, while the proposed decision-making structureis presented in Section 4. Section 5 provides a real case study andfinally, some remarks and future research directions are concludedin Section 6.

2. Literature review

Due to long use of MTS systems, many instances have been de-voted to how to plan and schedule the products in the productionsystem to meet their forecasted demands. There are considerableamount of works in the literature considering production planningand scheduling techniques for MTS systems, especially in

MRP-based systems (e.g. see Vollmann, Berry, Whybark, & Jacobs,2005). Of particular interest, the Hierarchical Production Planning(HPP) approach has been one of the most applied methodologiesfor MTS companies because of its several advantages in practice(e.g. see Omar & Teo, 2007). In contrary to MTS systems, the pro-duction system in MTO firms activates only when a new order isreceived. Hence, production planning and scheduling issues are to-tally different from those of MTS firms. The main objective in MTOenvironments is to manage the deliveries of arriving orders toreach shorter and more reliable delivery lead times. To achieve thisgoal, firms should focus on order due dates and their manufactur-ing lead times (Corti, Pozzetti, & Zorzini, 2006).

Literature review on MTS/MTO systems reveals that there isonly a handful related researches in the literature body. This con-firms that research on MTS/MTO systems is still in its infantstages (Soman et al., 2004). To the best of our knowledge, the pa-per by Soman et al. (2004) is the most notable one in MTS/MTOliterature. They proposed a comprehensive HPP framework thatcovers important production management decisions for MTS/MTO situations in food processing. This framework consists of athree-level decision-making structure. Decisions of the first levelare related to determining which products to be manufacturedupon the order and which products to be manufactured uponstock. At the second level, demand and capacity are balanced.The relevant decision at this level is allocation of productioncapacity to both MTS and MTO products. At the third level, thereare scheduling and controlling decisions by which production or-ders are sequenced and scheduled. With respect to this level ofthe proposed HPP (the third level), Chang, Pai, Yuan, Wang, andLi (2003) developed a heuristic production activity control modelto schedule and control wafer manufacturing in a hybrid waferfabrication environment (MTS and MTO). For MTO orders, theydeveloped a rigid order release plan and dispatching control. Also,they proposed a method to fill up an appropriate level of capacityby processing MTS orders. Mu (2001) developed a mathematicalmodel as a decision tool to design hybrid MTS/MTO systems byoptimizing the economic base stock level and location. Also, heshowed how to determine the optimal point separating MTSand MTO operations for both balanced and unbalanced flow lines.Rajagopalan (2002) proposed a non-linear integer program withservice level constraints for MTS/MTO partitioning problem. Hedeveloped a heuristic procedure to solve this problem. With re-spect to this level, another work was performed by Ertay(1998). He developed a simulation model to compare pull andpush system in cellular manufacturing. Finally, Zaerpour et al.(2008) presented a hybrid fuzzy AHP-SWOT model towards orderpartitioning. They considered sixteen criteria categorized in four

552 H. Rafiei, M. Rabbani / Computers & Industrial Engineering 61 (2011) 550–560

classes; strengths, weaknesses, opportunities, and threats, ofwhich two first classes reflect internal status of firm and twoother classes cover external and environmental factors.

One of the most important strategic issues in MTS/MTO systemsis locating the OPPs of the products. Olhager (2003) presented sev-eral factors in three major classes that influence position of theOPP. Also, he discussed benefits and drawbacks of shifting OPPdownward and upward in the value chain, since different compet-itive priorities are attributed for the pre-OPP and the post-OPPoperations. Moreover, he proposed a model to identify the properproduct delivery strategy with respect to demand volume and vol-atility and also the relationship between production and deliverylead times. van Donk (2001) developed a suitable framework fora manager in food processing industries. He adapted the generaldecoupling point (DP) concept to support such decisions. Afteridentification of influencing factors on DP, he discussed the effectsof each factor on the DP for certain product/market circumstances.

Concluding from the literature, two different categories of re-searches have been performed so far. The first category includesmathematical models which were devoted to decisions of the thirdlevel. The main drawbacks of this category are too many mathe-matical limiting assumptions. These assumptions made the modelstoo difficult to comprehend, implement and communicate. Hence,they are actually useless. The second category relates to the re-searches which apply qualitative methods in order to make deci-sions, such as order partitioning and OPP locating. Theseresearches are also useless, because they are so descriptive withoutany explicit applicable model, except the one by Zaerpour et al.(2008). However, their proposed fuzzy AHP-SWOT model is notwell-structured, because it does not consider relationships amongdecision criteria. Moreover, order partitioning and OPP locating aretwo decisions which are completely interrelated. No research pa-pers have evaluated these two decisions integrated. Therefore, tocope with the aforementioned drawbacks, an ANP model is pro-posed in order to model the interrelationship among decision cri-teria in this paper. Moreover, a step-wise model is developedtowards order partitioning and OPP locating. Applying the pro-posed model enhances implementation capabilities of the pro-posed model. Also, it is easily communicated and comprehendedby the managers. Finally, fuzzy sets theory is utilized in the pro-posed ANP, because considered decisions are strategic and theydeal with imprecise data.

Criteria

Sub-criteria

Alternatives

(a)

C3

cycle

Fig. 2. (a) AHP decision hierarchy versus (b) AN

3. Fuzzy analytic network process

ANP is one of Multi-Attribute Decision-Making (MADM) meth-ods which have been recently applied in numerous fields. ANP wasfirstly introduced by Saaty (1996) as a general form of anotherMADM method, Analytic Hierarchical Process (AHP) (Saaty,1980). An axiom of the AHP is independency between elementsin every level of the associated hierarchy, while ANP can modelthe interrelationship (dependencies) between decision factors aswell as alternatives, or between them in a more complex manner.Moreover in this paper, fuzzy sets theory (Zadeh, 1965) is aug-mented to the ANP due to the uncertainty and ambiguity of thepreference-based comparisons of decision-makers. Broad scopeand applicability of both fuzzy sets theory and ANP made fuzzyANP an applicable robust tool which has been challenged in diversedisciplines; such as Ertay, Kahraman, and Ruan (2005) and Kahr-aman, Ertay, and Büyüközkan (2006) in quality function deploy-ment, Dagdeviren, Yüksel, and Kurt (2008) in safety systems, Linand Hsu (2008) in performance management, Tseng, Liu, and Chin(2008) in clean technology, and Wu, Lin, and Chen (2009) in loca-tion problem. Followings describe elaborately general steps of theadopted fuzzy ANP which is used in Section 4.

3.1. Network formation

In this step, decision criteria are grouped in some clusters. Clus-ters are formed with respect to some issues, such as nature and im-pact of criteria. As well as the clusters of decision criteria, aseparate cluster is devoted to the alternatives. In addition to theclustering, dependency relations are drawn among the criteria.Fig. 2 demonstrates schematic of AHP and ANP in a comparativeform. In this figure, an arrow shows dependency relation; i.e. ele-ment at the end of the arrow is dependent to one at the beginning.Dependencies can be either between two elements in the samecluster (inner dependency or loop) or between two distinct clusters(outer dependency or cycle).

3.2. Local comparison

Elements of the same cluster which are dependent to an ele-ment (from the same cluster or another cluster) are comparedpair-wisely, leading to a comparison matrix which is related to

C4

C2

C1

loop

(b) P network structure (Saaty & Vargas, 2006).

Table 1Triangular fuzzy comparison scale (Chang, 1996).

Linguistic scale Triangular fuzzyscale

Triangular fuzzy reciprocalscale

Just equal (1, 1, 1) (1, 1, 1)Equally important (1, 5/2, 4) (1/4, 5/8, 1)Weakly more important (2, 4, 6) (1/6, 1/3, 1/2)Strongly more important (3, 5, 7) (1/7, 5/21, 1/3)Very strongly more

important(4, 6, 8) (1/8, 3/16, 1/4)

Absolutely moreimportant

(5, 7, 9) (1/9, 7/45, 1/5)

Fig. 3. Schematic of unweighted supermatrix.

H. Rafiei, M. Rabbani / Computers & Industrial Engineering 61 (2011) 550–560 553

the independent (control) element. Since most of the decisionsmade in diverse contexts involve expert preferences, it is inevitableto utilize fuzzy sets theory to overcome the uncertainty andambiguity of the comparisons. Having fuzzy sets theory appliedto the comparison process, resulted comparison matrices bearfuzzy elements. In this paper, fuzzy comparison matrices areformed based upon the fuzzy comparison scale presented by Chang(1996) (Table 1). It is noted that triangular fuzzy numbers areadopted, because comparisons are usually expressed as an approx-imation of a single value. Afterwards, to obtain relative weights ofelements compared pair-wisely in the matrix, a prioritization tech-nique is needed. In this paper, fuzzy preference method (Mikhailov,2003) is adopted to elicit relative weights of elements in a pair-wise comparison matrix, because this method is fully suitable fordifferent cases and it is flexible enough for different fuzzy num-bers. Supposing wi the relative weight of element i, wi/wj corre-sponds to the relative importance of element i over element j ina perfectly consistent comparison matrix; i.e. aij = wi/wj in whichaij is comparison weight i over j in the relative pair-wise compari-son matrix. Supposing comparison elements as symmetric triangu-lar fuzzy numbers aij = (lij, mij, uij), double-sided inequalities (1)hold. Moreover, relative weights of elements sum one, as depictedin Eq. (2).

lij e6wi

wj

e6uij 8i; j ð1ÞXi

wi ¼ 1 ð2Þ

Based upon (1) and (2), model (3) presents the model adoptedfrom Mikhailov (2003). Model (3) yields optimal wi which presentcompared elements’ total scores. In this model, k represents consis-tency index of the given fuzzy comparison matrix (Mikhailov,2003). For a comprehensive description about how the model isformulated and what its characteristics are, readers are referredto Mikhailov (2003).

Maxk

ðmij � lijÞkwj �wi þ lijwj 6 0ðuij �mijÞkwj þwi � uijwj 6 0X

k

wk ¼ 1

wk > 0 k 2 f1;2; . . . ng

ð3Þ

3.3. Cluster comparison

Similar to the local comparisons, dependent clusters to anycluster are compared pair-wisely from which a cluster comparisonmatrix is formed. Elements of the formed cluster comparison ma-trix will be used in the next step to convert the unweightedsupermatrix to the weighted supermatrix.

3.4. Unweighted and weighted supermatrices formation

Unweighted supermatrix is a supermatrix whose blocks are thematrices comprising relative weights of elements of a cluster withrespect to the elements of the same or other clusters. Fig. 3 demon-strates schematic of unweighted supermatrix. In this figure, Wij isthe block corresponding to the elements of cluster i compared withrespect to the elements of cluster j; i.e. columns of Wij are relativeweights of the elements of cluster i with respect to the heading ele-ment of that column. Also, the column corresponding to any ele-ment of cluster j is zero-valued, iff that element does notinfluence any element of cluster i. Because columns of unweightedsupermatrix might constitute more than one block, sum of columnvalues of the unweighted supermatrix might be greater than one.Hence, the unweighted supermatrix is not column stochastic. Toovercome this issue, values of block Wij are multiplied by elementvalue of cluster comparison matrix corresponding to row i and col-umn j. The resulted supermatrix is weighted supermatrix.

3.5. Final decision

To consider indirect dependencies between elements, theweighted supermatrix is powered until the values of each row con-verge. The converged supermatrix is limiting supermatrix uponwhich the final decision is made; i.e. the row values in front ofthe alternatives represent their relative weights. Therefore, thealternative with the highest row value is selected as the bestalternative.

4. Proposed model

In this section, a comprehensive decision-making framework isproposed to tackle order partitioning as well as OPP locating in hy-brid MTS/MTO contexts. In MTS/MTO environment, the adoptedproduct delivery strategy benefits from the strengths of both pureMTS and pure MTO strategies by processing some operations on aforecast-driven basis and finishing them with respect to receivedorders. Fig. 4 demonstrates the proposed framework. In the firststep, scope of the firm is determined. Next, adopting a pure strat-egy is evaluated for every product. If the strategy is not selected,families of products are formed to simplify the decision-makingprocedure. Then, pure strategy adoption is evaluated for the secondtime for the product families. Finally, the hybrid strategy is decidedfor those product families for which a pure strategy is not yetdecided. Details of the proposed model are described in the follow-ing sections.

4.1. Listing all possible products

As the first step, the scope of the firm’s production system is de-fined. To do so, all products to be manufactured in the firm arelisted. The list comprises current products and the products areplanned to be produced in future. It is highly recommended thatexperts from engineering, marketing, R&D, manufacturing and pro-curement departments attend to decide what products are in-cluded in the list.

Listing all possible products

Family formation

Hybrid MTS/MTO strategy

OPP for hybrid MTS/MTO

Pure MTS or pure MTO strategy?

Pure MTS or pure MTO strategy?

OPP for adopted strategy

OPP for adopted strategy

Yes

Yes

No

No

Fig. 4. Proposed model towards order partitioning and OPP location.

554 H. Rafiei, M. Rabbani / Computers & Industrial Engineering 61 (2011) 550–560

4.2. Pure MTS or pure MTO for listed products

Having all products listed, it is assessed whether a pure productdelivery strategy can be adopted. To decide if pure MTS or pureMTO strategy is applicable, three criteria are selected; demand vol-atility, P/D ratio, and product type. Before describing these criteria,it is noted that production and delivery lead times are both lengthsof time. The former represents the time a product spends in themanufacturing shop to be processed, while the latter is the timeinterval between order receipt and delivery of product to the cus-tomer (Shingo, 1981). The considered criteria are described asfollowings.

4.2.1. Demand volatilityIt specifies how long the demand is reliable. A higher level of

demand volatility shifts production strategy towards MTO, sinceMTO deals with products based upon market and real demandrather than volatile historical data.

4.2.2. P/D ratioThis criterion represents the ratio of production lead time to

delivery lead time. Moving from MTS production strategy towardMTO lengthen production lead time, because in MTO systems pro-duction is not triggered until an order is received. Therefore, P/Dgreater than one leads to MTS strategy.

4.2.3. Product typeIt is much more profitable to produce standard products upon

MTS strategy, since there is no customization for these products.MTO strategy is suitable for orders customized by various custom-ers with diverse requirements and tastes.

If all above three factors result in one of pure MTS or pure MTO,that strategy is adopted for the considered product.

4.3. OPP location for adopted strategy

After deciding on production strategy for some of products, OPPcan be located upon the selected strategy. In the case of MTS

H. Rafiei, M. Rabbani / Computers & Industrial Engineering 61 (2011) 550–560 555

strategy, last work center is determined as OPP, because as de-clared in Section 1.1 and shown in Fig. 1, customer’s requirementsdo not influence production process in MTS production systems(push systems). On the other hand, trigger of an MTO productionsystem is the customer’s requirements upon which production isperformed. Hence, the first work center plays the role of OPP inthe case of MTO strategy.

4.4. Family formation

Family formation is performed for any product for which pro-duction strategy is not yet decided. With respect to the remainedproducts, a hybrid strategy of MTS and MTO is adopted, becauseintroduced criteria in Section 4.2 result in conflicting productionstrategies for the remained products. To have simpler and morecontrollable production structure, the remained products are cate-gorized into product families. Different methodologies have beendeveloped so far to form product families among which some arenoted; descriptive procedures (Wemmerlov & Hyer, 1986), mathe-matical programming (Kusiak, 1987; Satoglu, Durmusoglu, & Ertay,2010; Serinavasan, Narendran, & Mahadevan, 1987), cluster-basedprocedures (Kumar, Kusiak, & Vamelli, 1986; Mitrofanov, 1966),and artificial intelligence (Lozano, Canca, Guerrero, & Garcia,2001; Venugopal & Narendran, 1994). In this paper, the recentmethod proposed by Galan, Racero, and Eguia (2007) is adopted,because their method is compatible with reconfigurable produc-tion lines including hybrid MTS/MTO ones. Moreover, as describedin following sections, criteria Compatibility and Demand can be as-sessed both quantitatively and qualitatively (by means of the scalepresented in Tables 2 and 3). Finally, the method and the criteriaare easy to communicate for the production staff. The proposedalgorithm comprises following five indicators to form families ofproducts. Finally after describing five indicators, the family forma-tion procedure is outlined in Section 4.4.6.

4.4.1. ModularityThis attribute shows at which level products are manufactured

from independent modules, leading to simpler parts and compo-nents. To calculate modularity matrix, product-part matrixPP = [pppq] is formed with m products and n parts presented inrows and columns, respectively using the following equation:

pppq¼1 Part q is included in product p

0 Otherwise

�p¼1;...m; q¼1;...n ð4Þ

Table 3Interaction values corresponding different demand interactions.

Interpretation Interaction value

Not related 0Slightly related 0.3Related 0.5Very related 0.8Highly related 1

Table 2Compatibility values corresponding different compatibility levels(Galan et al., 2007).

Interpretation Compatibility value

Not compatible 0Slightly compatibility 0.3Compatible 0.5Very compatible 0.8Highly compatible 1

Then, product modularity is computed as follows; while wp andup are the number of common parts of product p with the otherproducts and the total number of parts, respectively. Modularityis calculated using the following equation:

Mp ¼wp

/p0 6 Mp 6 1 p ¼ 1; . . . m ð5Þ

Utilizing product modularity, similarity coefficients betweentwo products p and q are calculated by means of Eq. (6), leadingto modularity matrix S = [spq].

Spq ¼ 1� jMp �Mqj 0 6 Spq 6 1; Spq ¼ Sqp p; q ¼ 1; . . . m ð6Þ

4.4.2. CommonalityThis index presents the ratio of common parts to all parts used

in every pairs of products. Forming product-part matrix, Jaccord’scoefficients of each pair of products are calculated using Eq. (7)(McAuley, 1972).

Jpq ¼a

aþ bþ c0 6 Jpq 6 1; Jpq ¼ Jqp p; q ¼ 1; . . . m ð7Þ

a is the number of parts in both products p and q; while b and cpresent the number of parts only included in product p and only in-cluded in product q, respectively.

4.4.3. CompatibilityCompatibility corresponds to the ability of two products to form

a family upon general criteria, such as operations, market, process-ing, etc. Compatibility is categorized as technological and market-ing compatibility. Technological compatibility is evaluated byproduction experts and the marketing compatibility is evaluatedby marketing experts and consumers. Concluding from both tech-nological and marketing compatibility, compatibility matrices areformed using the following table (Galan et al., 2007).

4.4.4. ReusabilityReusability is evaluated based upon the level that existing parts

can be used to manufacture a new product. Regarding product-partmatrix, reusability matrix K = [Kpq] is calculated as:

Rpq ¼cpq

kp0 6 Rpq 6 1; Rpq – Rqp p; q ¼ 1; . . . m ð8Þ

Kpq ¼Rpq þ Rqp

20 6 Kpq 6 1; Kpq ¼ Kqp p; q ¼ 1; . . . m ð9Þ

In Eq. (8), Rpq indicates reusability between product p and prod-uct q, when q is immediately processed after p. In (8), cpq and kp arethe number of common parts between products p and q, and thetotal number of parts in product p, respectively. Eq. (9) makes reus-ability matrix symmetric.

4.4.5. DemandDemand behavior of products is one of the factors to put prod-

ucts into the same family. In this paper, the demand matrix struc-ture proposed by Galan et al. (2007) is manipulated, because ittook into account exact demand of each product. Since rough andaggregated data are utilized in order partitioning, demand interac-tion between products p and q are computed using the concept inTable 2, resulting elements of Table 3. To evaluate demand interac-tions of products, marketing experts are required to express theirjudgments. Another reason to manipulate the demand data is thatthe model presented herein can be utilized to newly decided prod-ucts to be manufactured in the current facilities.

4.4.6. Final family formationTo aggregate five mentioned indicators about each pair of prod-

ucts, it is necessary to specify the weights of indicators. Weighting

Table 4OPP location factors.

Cluster Criterion Code

Market-related Delivery time M1Delivery reliability M2Product customization M3

Process-related Work center processing time K1Process flexibility K2Human resource flexibility K3

Product-related Holding cost N1Backorder cost N2Risk of obsolescence N3

556 H. Rafiei, M. Rabbani / Computers & Industrial Engineering 61 (2011) 550–560

methods which have been noted in literature are fixed point scor-ing, rating, ordinal ranking, graphical weights, and paired compar-isons (Hajkowicz, McDonald, & Smith, 2000). In this paper, it issuggested to compare indicators pair-wisely using 1–9 comparisonscale, resulting in a comparison matrix. The eigenvector of the ma-trix includes weights of each indicator. The final weight of eachpair of products is calculated as the weighted sum of elements cor-respondent to the five above indicators. The weights in weightedsum are the ones assigned to the indicators. The formulation ofthe final weight of p–q pair of products is as follows:

apq ¼X

f

apqf p; q ¼ 1; . . . m ð10Þ

Products p and q are put in the same family with apq greater than athreshold value.

4.5. Pure MTS or pure MTO for product families

With respect to the product families, applying pure MTS or pureMTO production strategies is evaluated regarding three mentionedcriteria in Section 4.2 (demand volatility, P/D ratio, product type).Families for which production strategy is specified go to Section4.6 and the ones for which pure strategies are not decided, go for-ward into Section 4.7.

4.6. OPP location for product families

Similar to the OPP location determined for individual productsin Section 4.3, OPPs are determined for product families for whichpure production strategies are decided. The first and the last work-stations are selected as the OPP for MTO and MTS products,respectively.

4.7. Hybrid MTS/MTO production strategy

A recent approach towards production planning and controlwith respect to coming orders is hybrid MTS/MTO which benefits

• Delivery time • Delivery reliability • Product

customization

• Process flexibility • Work center

processing time • Human resource

flexibility

Fig. 5. ANP network

from both MTS and MTO strategies. In the hybrid strategy, opera-tions before the OPP (buffer) are performed upon forecasts andafter the OPP, the operations are finished due to the received or-ders and with respect to the specifications defined by the custom-ers. In the proposed model, product families for which a pure MTSor pure MTO strategy is not decided are produced upon a hybridproduction strategy in which the OPP is located in the next step.

4.8. Locating OPP for hybrid product families

The most remarking role of OPP location rises in the hybridMTS/MTO, since OPP is pre-defined in two pure production strate-gies. OPP concept was firstly introduced by Hoekstra and Romme(1992) and can be defined as the point in the production valuechain at which a specific order is linked to a specific product (Olh-ager, 2003).

In this step, an ANP structure is developed to select OPPs ofMTS/MTO product families. Alternatives of the developed ANPare the planning points along the production value chain. A plan-ning point is a manufacturing resource or a set of manufacturingresources such as a workstation or a manufacturing cell that canbe regarded as an entity from a production planning point of view(Olhager, 2003). Among the planning points of the production line,

List of planning points of OPP in the production line

• Holding cost • Backorder cost • Risk of

obsolescence

to locate OPP.

Table 5Example of modularity matrix towards family formation.

Pa1 P2 P3 P4 P5 P6

P1 0 0.21 0.17 0.16 0.45 0.32P2 0.21 0 0.7 0.34 0.45 0.17P3 0.17 0.7 0 0.3 0.17 0.16P4 0.16 0.34 0.3 0 0.3 0.24P5 0.45 0.45 0.17 0.3 0 0.3P6 0.32 0.17 0.16 0.24 0.3 0

a Product.

Table 6Example of compatibility matrix towards family formation.

P1 P2 P3 P4 P5 P6

P1 1 0.8 0.8 0.8 0.5 0.6P2 0.8 1 0.7 0.6 0.5 0.8P3 0.8 0.7 1 0.5 0.9 0.9P4 0.8 0.6 0.5 1 0.5 0.8P5 0.5 0.5 0.9 0.5 1 0.5P6 0.6 0.8 0.9 0.8 0.5 1

Table 7Example of overall score matrix towards family formation.

P1 P2 P3 P4 P5 P6

P1 5 3.6 3.1 3.6 2.4 2.9P2 3.6 5 2.7 3.6 4.5 4.1P3 3.1 2.7 5 3.0 4.7 4.3P4 3.6 3.6 3.0 5 3.1 2.9P5 2.4 4.5 4.7 3.1 5 4.4P6 2.9 4.1 4.3 2.9 4.4 5

H. Rafiei, M. Rabbani / Computers & Industrial Engineering 61 (2011) 550–560 557

bottlenecks are not suitable alternatives, because bottlenecks yieldlonger delivery times and more backorder costs. In addition to theindividual resources like work centers, continuous processes aretaken into account as alternatives each of which corresponds tothe point before the planning point. Also, decision criteria uponwhich the ANP structure is constructed are the ones presented inTable 4 with their categorized clusters.

The criteria of Market-related reflect market requirements of afirm producing customized products. Among the considered crite-ria, the first two criteria shift the production system towards MTS,while the third one shifts it towards MTO. With respect to the Pro-cess-related criteria, the first one shifts towards MTS, while the nexttwo shift the production system towards MTO. Finally, the first andthe third criterion of Product-related cluster shift the system to-wards MTO, while the second one does towards MTS.

Since the considered criteria are interrelated, ANP methodologyis adopted to cope with the complexity of the OPP location deci-sion. With respect to the above criteria and a cluster for alterna-tives, ANP network is formed as in Fig. 5. To model theinterrelationships among criteria in Fig. 5, it is necessary to con-sider whether changing a criterion affects any other criteria. Forexample, decreasing Delivery time of a product increases Deliveryreliability of that product. Having the network structured, localcomparisons of the elements of one cluster with respect to anyinfluencing elements are performed as well as cluster comparisonsas elaborated in Sections 3.2 and 3.3, respectively.

Applying model (3) to all pair-wise comparison matrices resultsin relative weights of the elements obtained from comparisonmatrices. Then, unweighted supermatrix is formed by putting to-gether the obtained relative weights as described in Section 3.4.Next, weighted supermatrix is calculated using the procedure de-scribed in Section 3.4. After calculation of weighted supermatrix,it is powered until row values are converged. The resulted superm-atrix is limiting supermatrix upon which location of the OPP isdecided. For more explanation of the fuzzy ANP, readers are re-ferred to Section 3.

5. Industrial case study

The authors were requested to modify and redesign productionsystem of an Iranian company which is one of the most leadingmanufacturers in the field of home appliances. Some site visitsand interviews with managers, workers, engineers and also retail-ers of the company were conducted to diagnose the issues. More-over, data proved decreasing trends of total sale and customersatisfaction. Hence, it was decided to restructure production sys-tem of the company. This report presents a part of the total effortmade in the company. Project team decided to implement the pro-posed model in Section 4. To do so, required data were collectedfrom two types of resources; historical data of the last year andthe data collected during one month of production. Afterwards,the proposed model took three months to be implemented. Follow-ing sections provide description about how steps of the proposedmodel were implemented.

5.1. Listing all possible products

First of all, all products of the company were listed. The com-pany produces 25 products for which family formation should havebeen decided.

Project team and the company management agreed to skipSections 4.2 and 4.3, because running the model for all individualproducts might take a long time and made the production controlof the line much more difficult due to different OPPs of all individ-ual products.

5.2. Family formation

To form families of products, manufacturing staff were trainedabout family formation procedure described in Section 4.4, becausethe procedure cannot be implemented without help of the staff. Asseen in Section 4.4, proposed family formation procedure requirestechnical data and expertise. Hence, solely the staffs have the com-plete information and knowledge of the procedure criteria. Total25 models formed four families of products; washing machine,refrigerator, dishwashing machine, and TV set. Tables 5 and 6 dem-onstrate examples of modularity matrix and compatibility matrixof some products, respectively. It is noted that numerical calcula-tions of family formation are too comprehensive to present in thispaper.

To aggregate judgments related to modularity, commonality,comparability, reusability and demand matrices of products, sumof pairwise judgments were calculated as in Eq. (10). Some ele-ments of the resulted matrix are presented in Table 7.

With respect to the results of Table 7, products 2, 3, 5 and 6have overall scores greater than 4.0 (corresponding threshold)and hence, they are in the same family. Similarly, other productswere evaluated and total 25 products were categorized in fourfamilies: washing machine (5 models), refrigerator (6 models),dishwashing machine (3 models), and TV sets (11 models).

5.3. Pure MTS or pure MTO for product families

Having product families formed numerous meetings with man-ufacturing and marketing managers were conducted to gather dataand their judgments about demand volatility, P/D ratio, and

Table 8Managers’ judgment about alternatives with respect to criteria Risk of Obsolescence.

Aa1 A2 A3 A4 A5 A6

A1 (1, 1, 1) (1/6, 1/3, 1/2) (1/7, 5/21, 1/3) (1/6, 1/3, 1/2) (1/7, 5/21, 1/3) (1/4, 5/8, 1)A2 (2, 4, 6) (1, 1, 1) (1/4, 5/8, 1) (1, 1, 1) (1/4, 5/8, 1) (1, 5/2, 4)A3 (3, 5, 7) (1, 5/2, 4) (1, 1, 1) (1, 5/2, 4) (1, 1, 1) (2, 4, 6)A4 (2, 4, 6) (1, 1, 1) (1/4, 5/8, 1) (1, 1, 1) (1/4, 5/8, 1) (1, 5/2, 4)A5 (3, 5, 7) (1, 5/2, 4) (1, 1, 1) (1, 5/2, 4) (1, 1, 1) (2, 4, 6)A6 (1, 5/2, 4) (1/4, 5/8, 1) (1/6, 1/3, 1/2) (1/4, 5/8, 1) (1/6, 1/3, 1/2) (1, 1, 1)

a Alternative.

Table 9Managers’ judgment about clusters with respect to cluster Market-related.

A M N

A (1, 1, 1) (1/9, 7/45, 1/5) (1/6, 1/3, 1/2)M (5, 7, 9) (1, 1, 1) (3, 5, 7)N (2, 4, 6) (1/7, 5/21, 1/3) (1, 1, 1)

Table 10Cluster comparison matrix.

M N K A

M 0 0 0.285714 0N 0.75 0.877193 0 0K 0 0 0.571429 0A 0.25 0.122807 0.142857 0

Table 11Unweighted supermatrix of the case study.

M1 M2 M3 N1 N2 N3 K1 K2

M1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0M2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0M3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0N1 0.4500 0.0000 0.0000 0.0000 0.4500 0.0000 0.0000 0.0N2 0.4500 0.0000 0.0000 0.0000 0.4500 0.0000 0.0000 0.0N3 0.1000 0.0000 0.0000 0.0000 0.1000 0.0000 0.0000 0.0K1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0K2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0K3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0A1 0.4603 0.4603 0.0579 0.4603 0.0500 0.0579 0.0456 0.5A2 0.1082 0.1082 0.1473 0.1082 0.1167 0.1473 0.1106 0.1A3 0.0517 0.0517 0.2858 0.0517 0.3225 0.2858 0.3355 0.1A4 0.1082 0.1082 0.1473 0.1082 0.1167 0.1473 0.1106 0.1A5 0.0517 0.0517 0.2858 0.0517 0.3225 0.2858 0.3355 0.1A6 0.2199 0.2199 0.0753 0.2199 0.0717 0.0753 0.0623 0.1

Table 12Weighted supermatrix of the case study.

M1 M2 M3 N1 N2 N3 K1 K2

M1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0M2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0M3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0N1 0.4500 0.0000 0.0000 0.0000 0.4500 0.0000 0.0000 0.0N2 0.4500 0.0000 0.0000 0.0000 0.4500 0.0000 0.0000 0.0N3 0.1000 0.0000 0.0000 0.0000 0.1000 0.0000 0.0000 0.0K1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0K2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0K3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0A1 0.4603 0.4603 0.0579 0.4603 0.0500 0.0579 0.0456 0.5A2 0.1082 0.1082 0.1473 0.1082 0.1167 0.1473 0.1106 0.1A3 0.0517 0.0517 0.2858 0.0517 0.3225 0.2858 0.3355 0.1A4 0.1082 0.1082 0.1473 0.1082 0.1167 0.1473 0.1106 0.1A5 0.0517 0.0517 0.2858 0.0517 0.3225 0.2858 0.3355 0.1A6 0.2199 0.2199 0.0753 0.2199 0.0717 0.0753 0.0623 0.1

558 H. Rafiei, M. Rabbani / Computers & Industrial Engineering 61 (2011) 550–560

product types of the above product families. Demands of washingmachine and refrigerator are persistent and do not change drasti-cally over periods of time. Also, there are many standard parts inwashing machine and refrigerator, and the estimated productionlead times of these two product families are longer than their cor-responding delivery lead times. Therefore, the team and the man-agers decided to produce washing machine and refrigeratorfamilies upon MTS production strategy. However, the decisionwas different for dishwashing machine family of products. Demandnature of dishwashing machines is totally distinct from that ofwashing machines, the demand volume and the ordering fre-quency is less than order volume and frequency of washing ma-chines. Additionally, dishwashing machine demands are seasonaland not persistent. Production lead time of dishwashing machineis short, because many sub-assemblies of washing machines areused. Hence, it was decided to produce dishwashing machinesupon MTO strategy. With respect to TV sets, a pure MTS or pureMTO strategy was not decided, because (1) TV is a fashionable

K3 A1 A2 A3 A4 A5 A6

000 0.1763 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.1763 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.6473 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.05790 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.1473 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.28580 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.1473 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.28580 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.07530 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

K3 A1 A2 A3 A4 A5 A6

000 0.1763 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.1763 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.6473 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.05790 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.1473 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.28580 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.1473 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.28580 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000000 0.07530 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Table 13Limiting supermatrix for the case study.

M1 M2 M3 N1 N2 N3 K1 K2 K3 A1 A2 A3 A4 A5 A6

M1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000M2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000M3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000N1 0.0616 0.0000 0.0000 0.0000 0.0616 0.0000 0.0000 0.0616 0.0616 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000N2 0.0616 0.0000 0.0000 0.0000 0.0616 0.0000 0.0000 0.0616 0.0616 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000N3 0.0137 0.0000 0.0000 0.0000 0.0137 0.0000 0.0000 0.0137 0.0137 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000K1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000K2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000K3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000A1 0.0100 0.0000 0.0000 0.4603 0.0100 0.0000 0.0000 0.0100 0.0100 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000A2 0.0050 0.0000 0.0000 0.1082 0.0050 0.0000 0.0000 0.0050 0.0050 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000A3 0.0083 0.0000 0.0000 0.0517 0.0083 0.0000 0.0000 0.0083 0.0083 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000A4 0.0050 0.0000 0.0000 0.1082 0.0050 0.0000 0.0000 0.0050 0.0050 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000A5 0.0083 0.0000 0.0000 0.0517 0.0083 0.0000 0.0000 0.0083 0.0083 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000A6 0.0060 0.0000 0.0000 0.2199 0.0060 0.0000 0.0000 0.0060 0.0060 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Table 14Comparison before and after implementation of the proposed model.

Comparison measure Beforeimplementation

Afterimplementation

H. Rafiei, M. Rabbani / Computers & Industrial Engineering 61 (2011) 550–560 559

product, (2) some of its electrical components are standard, but notall of them, and (3) production lead times of some models are con-siderably less than some others. Hence, TV sets were decided to beproduced based upon hybrid MTS/MTO strategy.

Backordered quantity 30 5Held quantity for more than a month 18 4Received orders (MTO and MTS/

MTO)40 38

On-time delivered orders (MTO andMTS/MTO)

29 35

Late orders percentage 27.5 7.89Average lead time (day) 6 3.2

5.4. OPP location for product families

Since washing machines and refrigerators were decided to beproduced upon MTS production strategy, OPPs of these productswere located at the end of the production line. Moreover, OPP ofdishwashing machines was located at the beginning of the line,because they were processed upon MTO strategy. OPP of TV prod-uct family is not easily determined as done for two other strategies.

5.5. Hybrid MTS/MTO production strategy

Since TV sets were decided to be produced upon MTS/MTO, OPPlocations of TVs should have also been determined among theworkstations in TVs process routes. To do so, an ANP model wasstructured as shown in Fig. 5. To do comparisons between criteriaand clusters, a team of engineering, manufacturing, R&D, market-ing, procurement managers and the CEO were gathered. The teamdecided on the comparisons using the scale presented in Table 1.For example, Tables 8 and 9 show their judgments about alterna-tives (six workstations; Assembly, Axial, Eylet, Radial, Sequence,SMD) with respect to criterion Risk of obsolescence and the clusterswith respect to cluster Market-related, respectively. The weights ofcomparison matrices are elicited using the optimization model de-scribed in Section 3.2. With respect to the data in Table 8, results ofthe proposed optimization (Mikhailov’s) model are 0.0579, 0.1473,0.2858, 0.1473, 0.2858, and 0.0753 for Alternatives 1, 2, 3, 4, 5, and6, respectively. With respect to data of Table 9, results of the opti-mization model are 0.75 and 0.25, for Product-related and Alterna-tives clusters, respectively. After performing all of comparisons, thecluster comparison matrix and the unweighted supermatrix areformed as presented in Tables 10 and 11, respectively. As elabo-rated in Section 3.4, the corresponding weighted supermatrix is re-sulted by multiplying blocks of unweighted supermatrix by theircorresponding elements of the cluster comparison matrix (theweighted supermatrix is presented in Table 12). Final decision ismade by means of limiting supermatrix in Table 13. With respectto the results obtained in Table 13, the first alternative (Assemblyworkstation) has the highest final weight. Therefore, this worksta-tion is chosen to be OPP of the production line for TV sets.

After implementation of the model, the most notable improve-ments are more customer satisfaction and easier management ofthe line because of clearance of the material and data flows of

the product families. Moreover, some quantitative analyses areconducted to compare status of case study before and after imple-mentation of the proposed model. Comparisons were conductedusing data from three months before implementation and the sametime duration after implementation of the proposed model. Sum-mary of the comparisons are presented in Table 14.

6. Conclusion and future research directions

This paper addressed hybrid MTS/MTO product delivery strat-egy in which a part of products are processed upon forecasts andthe remaining is finished with respect to customers’ orders. Twoimportant decisions in this strategy are order partitioning andOPP locating. In this paper, a model is proposed to decide whichproducts are processed upon which strategy; MTS, MTO, and hy-brid MTS/MTO. For products with hybrid strategy, location of theOPP is then determined by means of fuzzy analytic network pro-cess to cope with the dependencies among decision criteria. Final-ly, implementation of the proposed model in a case study isreported to show applicability and validity of the model.

To extend current direction of this paper, it is highly recom-mended to define other decision criteria in both partitioning andOPP location decisions. Also, criteria appropriate for differentindustries can be useful and applicable. Moreover, decisions con-sidered in this paper are at the strategic level of a production sys-tem design and can be completed by extending the proposedmodel to other tactical and operational levels.

Acknowledgements

The authors would like to acknowledge the financial support ofUniversity of Tehran for this research under grant number8109002/1/03. Also, they are grateful to the reviewers for theirvaluable, constructive comments.

560 H. Rafiei, M. Rabbani / Computers & Industrial Engineering 61 (2011) 550–560

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