ORIGINAL ARTICLE

Development of an optimal method for remanufacturing processplan selection

Zhigang Jiang & Zhou Fan & John W. Sutherland &

Hua Zhang & Xugang Zhang

Received: 6 July 2013 /Accepted: 13 March 2014 /Published online: 26 March 2014# Springer-Verlag London 2014

Abstract Remanufacturing represents an activity that oftenoffers significant profit opportunities and can provide substan-tial environmental benefits. Process plan selection is one ofthe most important operational decisions in remanufacturingbecause it directly affects the success rate of remanufacturingas well as cost and quality. There is a need for a decision-making aid which can optimize process plan selection in thepresence of wide-ranging alternatives. In response to thisneed, a decision method has been developed that combinesthe strengths of quality function deployment (QFD) and fuzzylinear regression. In this method, quality function deploymentis employed to not only frame the problem but also to establishrelationships between remanufacturing performance and pro-cess quality characteristics of interest. Fuzzy linear regressionis used to determine the functional relationships betweenremanufacturing performance and process quality character-istics and obtain the optimal solution. If desired, the mostsuitable process plan alternative may be determined. To assessthe usefulness and practicality of the proposed method, anillustrative example is given and the results are discussed.

Keywords Remanufacturing . Process plan . Process qualitycharacteristics . Decision-making

1 Introduction

Environmental legislation, customer expectations, and eco-nomic incentives are the most important factors that motivatemany industries to engage in remanufacturing [1].Remanufacturing not only provides products at lower costsbut also promotes maximum resource utilization and mini-mum waste disposal. The price of a remanufactured item isgenerally30–40 % of the price of a new item [2].

Remanufacturing is a process that recovers used productsfor the purpose of creating “like-new” products using cores ordiscarded products as the primary raw material [3]. The pro-cess involves complete disassembly of the product, followedby a series of reconditioning and recovery processes likerepair, rework and refurbishment operations, and replacementto bring the product into a “like-new” condition [4]. Com-pared with traditional manufacturing, the uncertainties associ-ated with used parts make remanufacturing decisions morecomplicated [5]. For example, the number and timing ofreturning cores is one source of uncertainty. The conditionof used components returned for remanufacturing is yet an-other source of variability. All these uncertainties in theremanufacturing environment complicate the decisions asso-ciated with remanufacturing processes and the development ofprocess plans [6]. Of course, it is the purpose ofremanufacturing to restore the worn, degraded, or damagedcondition of used products to like-new conditions. Changes toremanufacturing processes may affect the process efficiency,quality, and costs of producing these like-new products [7].

This work is grounded in the belief that the selection ofprocess plans in remanufacturing applications has to be care-fully formulated. This motivates the need for decision-makingmethodologies and tools that can assist in the formulation ofremanufacturing process plans [8]. Ideally, such tools cansupport the optimal selection of a remanufacturing processplan as a function of essential requirements, internal

Z. Jiang (*) : Z. Fan :H. Zhang :X. ZhangCollege ofMachinery andAutomation,Wuhan University of Scienceand Technology, 430081 Wuhan, Chinae-mail: jzg100@163.com

J. W. SutherlandDivision of Environmental and Ecological Engineering, PurdueUniversity, West Lafayette, IN 47907, USA

Int J Adv Manuf Technol (2014) 72:1551–1558DOI 10.1007/s00170-014-5783-x

capabilities, and constraints, all directed at achieving the de-sired remanufacturing performance. This paper presents aquality function deployment (QFD) and fuzzy linearregression-based method for remanufacturing process planselection to make full use of experts’ experiences and knowl-edge. The initial part of the paper provides a brief overview ofexisting research work in this area. Then, a framework forselecting a remanufacturing process plan is presented. Thepaper concludes with an illustrative example.

2 Brief review of relevant research

Remanufacturing process planning often leads to improvedproduct/component quality, enhanced remanufacturing rate, re-duced capital investment cost, and better utilization of companyresources. Due to the significant importance of remanufacturingprocess planning, it has received increasing attention.

The existing research in this area can be broadly viewed asbelonging to two different categories: uncertainty integrationand process plan generation. The first category seeks to addressthis issue by incorporating quality uncertainty intoremanufacturing process planning. Zikopoulos and Tagaras[9] incorporate quality uncertainty in a single-periodrefurbishing operation. Denizel et al. [10] considerremanufacturing process planning when inputs have differentand uncertain quality levels and there are capacity constraints.Tang et al. [11] analyzed the effect of uncertainty on the qualityof used parts and the performance of remanufacturing processes.Aksoy and Gupta [12] pointed out that the uncertainty in qualitycannot be neglected in remanufacturing process plan decisions.Li and Tang [13] proposed a Graphical Evaluation and ReviewTechnique (GERT)-based analyt ica l method forremanufacturing process plan decisions, which considered theuncertainty in the quality of incoming used components.

For the second category, process plan generation, researchhas approached the issue from a “design for remanufacturing”perspective. Seliger et al. [14] developed a genericremanufacturing plan for mobile phones. Kernbaum et al. [15]presented an approach for the design, evaluation, and imple-mentation of IT-equipment remanufacturing processes in agiven facility. Cao et al. [16] presented a two-phase decision-making model to find optimal process parameters based onassessments from experts and fuzzy regression theory. Songet al. [17] presented a newmethod based on constrained ordinaloptimization for remanufacturing process planning. Li et al.[18] established a remanufacturing process model based on aGERT network, in which all possible remanufacturing processpathways for used components were described, and a timedistribution for every processing time was defined.

Although significant amount of research has been conduct-ed in remanufacturing process, not much effort was reportedon remanufacturing process plan selection. It has been

observed that the optimal selection of remanufacturing pro-cess plans is generally measured by more than one perfor-mance measure and that these measures are usually in conflict.If a decision-maker is interested in evaluating all objectivessimultaneously, an aggregated weighted function may be de-fined [19]. Some multi-criteria decision-making approachesmay be helpful in selecting the remanufacturing process planwhen multiple performance measures are of interest, e.g.,factor analysis, principal component analysis, analytic hierar-chy process, and Delphi method [20]. However, thesemethods are dependent on the decision-makers’ judgmentbased on their knowledge and experience. These shortcom-ings serve as barriers in addressing practical applications. Keet al. [21] suggested that work be initiated to develop adecision method that provides guidance on the formulationof remanufacturing process plans.

Motivated by the foregoing discussion, this paper presentsan integrated method for remanufacturing process plan selec-tion based on quality function deployment (QFD) and fuzzylinear regression to supplement existing evaluating methods.The proposed approach benefits from the fact that QFD isemployed to not only frame the problem but also to establishrelationships between remanufacturing performance and pro-cess quality characteristics of interest. Fuzzy linear regressionis considered as an alternative decision aid for theremanufacturing process plan decision to determine relation-ships between remanufacturing performance and process qual-ity characteristics. Following the presentation of the proposedmethod for selecting a remanufacturing process plan, themeth-od is demonstrated via a lathe guide remanufacturing example.

3 Remanufacturing process plan selection method

The selection of an effective process plan needs to considerthe quality characteristics of each process stage among thedifferent remanufacturing process plans under considerationand identify the plan with the least remanufacturing time,highest remanufacturing quality, and lowest remanufacturingcosts. It is proposed to combine QFD and fuzzy linear regres-sion to develop a more effective decision-making tool forremanufacturing process plan selection. The proposed selec-tion method can be divided into three sequential phases: (1)establish a QFD-based selection framework, (2) estimate QFDparameters via fuzzy linear regression, and (3) select theoptimal process plan alternative.

3.1 A QFD-based selection framework

QFD is a systematic, graphical approach to understand essen-tial requirements, internal capabilities, and constraints in orderto achieve a desired outcome. This paper employs a QFDapproach to establish relationships between remanufacturing

1552 Int J Adv Manuf Technol (2014) 72:1551–1558

performance and process quality characteristics of interest.For a comprehensive background on QFD, the reader mayrefer to Chan andWu [22]. The application of QFD starts withthe first of its four stages, namely, the construction of a Houseof Quality (HOQ). In this work, we focus on this particularstage, as depicted in Fig. 1.

To construct a HOQ, seven elements must be defined. (1)Identify the WHATs. The desired performance criteria for aremanufacturing process are usually called “WHATs”. Theyestablish the foundation of the HOQ and provide a guidelinefor the providers on attributes that the process plan shouldpossess. (2) Determination of HOWs. Process quality charac-teristics are specified as the “HOWs” of a HOQ. (3) Relativeimportance of the criteria for remanufacturing performance.Criteria often have widely disparate units (e.g., minutes, dol-lars, and kilograms); the relative importance of the decisioncriteria may differ among decision-makers. (4) Preparation ofthe relationship. For this element, the different manners inwhich the WHATs impact the HOWs need to be defined. (5)Inner dependencies among the process quality characteristics.The inner dependencies among process quality characteristicsgiven in the HOQ’s roof matrix measure the extent to which achange in one feature affects another. Analogous to the rela-tionships between the HOWs and WHATs, these can bedetermined using fuzzy regression analysis. (6) Performancevalues of process quality characteristics. The performance

values are usually used as the inputs for an optimizationprocess. (7) Competitive analysis. During the competitiveanalysis, the remanufacturing process plan’s position relativeto its main competitors is identified in terms ofremanufacturing performance.

The objective of remanufacturing process plan selectionbased on QFD is to determine a set of values for processquality characteristics that maximize overall satisfaction. Theoptimization problem can be expressed as follows:

max z y1; y2;…; ymð Þ ð1Þ

subject to

yi ¼ f i x1; x2;…; xnð Þ ; i ¼ 1; 2;…;mxj ¼ g j x1; x2;…; x j−1; x jþ1;…; xn

� �j ¼ 1; 2; ;…n

where z(y1,y2,…,ym) is an individual function, yi is a numer-ical value that describes the degree of satisfaction of theremanufacturing performance as characterized by the ith per-formance criterion (i=1,2,…,m), xj is the optimal value of thejth process quality characteristic (j=1,2,…,n), fi represents thefunctional relationship between the ith criterion and the pro-cess quality characteristics, and gj denotes the functionalrelationship between the jth process quality characteristic andthe other process quality characteristics.

Alternative A

Alternative B

Alternative C

Relativeimportanceofcriteria

AlternativeA

AlternativeB

AlternativeC

WHATs HOWs

Inner dependenceamong the HOWs

Remanufacturingperformance (Criteria)

Process qualitycharacteristics

Relative importanceof criteria

Performance valuesof process quality

characteristics

Relationshipsbetween WHATS

and HOWs

Competitive analysis

Fig. 1 House of quality (HOQ)

Int J Adv Manuf Technol (2014) 72:1551–1558 1553

Using the degree of satisfaction variables, yi, the objectivefunction of Eq. (1) can then be expressed as follows:

z y1; y2;…; ymð Þ ¼Xm

i¼1wi yi−y

mini

� �= ymax

i −ymini

� � ð2Þ

where wi is a weight that describes the relative importance ofthe ith criterion and is defined such that 0<wi≤1, and yimin andyimax are the minimum and maximum possible values for theith criterion. Given this formulation, the optimization problemcan be represented as follows:

max z y1; y2;⋯; ymð Þ ¼Xm

i¼1wi yi−y

mini

� �= ymax

i −ymini

� �s:t: yi ¼ f i x1; x2;⋯; xnð Þi ¼ 1; 2;⋯;m

xj ¼ g j x1; x2;⋯; x j−1; x jþ1;⋯; xn� �

j ¼ 1; 2;⋯; n

ymini ≤yi≤ymaxi

ð3ÞThe information provided in the HOQ can be used to

estimate the parameters of the functional relationships fi andgi. Since the relationships between the criteria and the processquality characteristics and the interactions among the processquality characteristics are imprecise, fuzzy regression servesas a robust alternative for developing the relationships.

3.2 QFD parameter estimation via fuzzy linear regression

Fuzzy linear regression, which was introduced by Tanakaet al. [23], is founded on possibility theory and fuzzy settheory. Fuzzy linear regression has been reported to be a moreeffective tool than statistical regression when the data set isinsufficient to support statistical regression, human judgmentsare involved, or the degree of system fuzziness is high. In thisstudy, fuzzy linear regression is employed to estimate rela-tionships owing to its ability to deal with human expertknowledge, which is an important source of knowledge inthe remanufacturing domain.

The information provided in the HOQ can be used toestimate the parameters of the functional relationships be-tween fi and gi. Generally, a fuzzy linear regression model isformulated as follows:

y ¼fA0 þfA1x1 þfA2x2 þ⋯þfAnxn ð4Þ

Where, y denotes the dependent variable, xj are the inde-

pendent variables, and eAj are the fuzzy parameters expressedas symmetrical triangular fuzzy numbers with centers αj andspreads cj, respectively, having the membership function:

μ eA j a j� � ¼ 1−

α j−a j����

c j0; otherwise

;α j−c j≤a j≤α j þ c j

8<: ð5Þ

where αj and cj represent the center and spread of thefuzzy number eAj , and μ eA j a j

� �denotes the member-

ship of aj in the fuzzy number eAj . Given these defini-tions, the fuzzy linear regression model of Eq. (4) canbe rewritten as follows:

y ¼ α0; c0ð Þ þ α1; c1ð Þx1 þ α2; c2ð Þx2 þ⋯þ αn; cnð Þxnð6Þ

Fuzzy linear regression establishes the fuzzy parameters,eAj , such that the established output has the minimum totalspread while satisfying a target degree of belief, h, where 0≤h<1. The value for h is selected by the decision-maker andmeasures the goodness of fit of the estimated fuzzy linearregression model to the data set. The following linear pro-gramming model is solved to obtain the fuzzy parameters[24]:

min Z ¼Xn

j¼0c jXs

k¼1xjk�� ��� �

s:t:Xj¼0

n

α jxjk þ 1−hð ÞXj¼0

n

c j xjk�� �� !

≥yk; k ¼ 1; 2;⋯; s

Xj¼0

n

α jxjk− 1−hð ÞXj¼0

n

c j xjk�� �� !

≤yk; k ¼ 1; 2;⋯; s

x0k ¼ 1; k ¼ 1; 2;⋯; s

c j≥0; j ¼ 0; 1;⋯; n

ð7Þ

where xjk is the value of the jth independent variable for the kth

observation (here, the value of the kth process plan alternativewith respect to the jth process characteristic), and yk is thevalue of the dependent variable for the kth observation (here,the degree to which the customer need is satisfied for the kth

process plan alternative).Equation (7) aims to determine eAj in a way so as to

minimize the total fuzziness under the condition that eachobservation yk has at least h degrees of belonging to its fuzzyestimate. When no fuzziness is considered in the systemparameters, only the center value estimates obtained fromEq. (7) are used in the optimization problem of Eq. (3) andthe spreads are ignored.

3.3 Selection of optimal process plan alternative

Once the maximum overall satisfaction for remanufacturingperformance and optimal values for process quality character-istics and criteria have been obtained through Eqs. (3) and (7),the deviation of each process plan alternative from the process

1554 Int J Adv Manuf Technol (2014) 72:1551–1558

plan possessing the optimal process characteristic values canbe computed using a weighted distance measure [25], asshown in Eq. (8):

dkp ¼X

iwi max 0; y�i −yik

� �� �� �pn o1=p; p ¼ 1; 2; k ¼ 1; 2;…; s ð8Þ

where wj is the weight of the ith criterion, yi* is the

optimal value of the ith criterion, yik is the value of theith criterion for the kth process plan alternative, and dp

k isthe distance metric for the kth process plan alternativethat is based on the pth-order lower partial moment.The process plan alternative with the minimum distancevalue is selected, and the process plans can be rankedaccording to dp

k in ascending order.

4 Illustrative example

To illustrate the proposedmethod for remanufacturing processplan selection, consider a company that recovers used lathesand remanufactures them. A lathe requires significant capitalinvestment and, therefore, has a large potential forremanufacturing. The performance of remanufactured lathescan be the same as, or even better than, a new lathe. Aremanufactured lathe may require only 40–60 % of themanufacturing cost of a new lathe [26]. One of the keychallenges with used lathes is the need to repair their guides.As an element of a lathe, the main guide failure mode is wear.The remanufacturing process associated with a guide may bedivided into three process stages: cleaning, surface repair, andmachining. In each stage, inspection serves as the first step.The company of interest is assumed to have the technology/equipment in place for cleaning, welding, brush plating, andgrinding. It is desired to provide guidance to the company onwhich process plan should be chosen to remanufacture theguides.

Three process plan alternatives exist to address thedamaged/worn guides: (i) cleaning, micro-arc cold welding,and grinding; (ii) cleaning, plastic paste application, andscraping; (iii) cleaning, brush plating, and grinding. Basedon these alternatives, attention must now be directed at iden-tifying the process quality characteristics and remanufacturingperformance for each alternative.

The process quality characteristics for lathe guideremanufacturing include surface cleanliness, hardness, preci-sion retention, straightness, and parallelism. With the fivetechnology requirements specified, the vector of quality char-acteristics, X=(x1,x2,x3,x4,x5), was defined. Based on discus-sions with key personnel in the company, the minimum andmaximum range of process quality characteristics and the

recommended values for remanufactured guides was set asshown in Fig. 2.

In this case, three primary criteria (time (T), cost (C), andreliability (R)) are employed to measure the remanufacturingperformance. During the process plan decision stage, infor-mation is often incomplete, of unknown accuracy, lacking inprecision, and based on multiple assumptions. Thus, thevalues obtained for each criterion will be subject to significantuncertainty. With this in mind, it is proposed to employ a 5-point scale for each criterion. Each process plan alternativewill be graded in terms of every criterion using this scale. The5-point scale ranges from 1 to 5, with larger numbers indicat-ing better performance, and smaller numbers indicating poorerperformance.

After determining the decision criteria and alternative pro-cess plans, the relative importance of the three criteria isdetermined using the analytic hierarchy process (AHP). InAHP, a pairwise comparison matrix is created based ondecision-maker inputs; the matrix is formed based on com-paring the relative importance or preferences of two criteria. Incomparing two criteria, experts compare every pair of criteriaand make a judgment of the importance of criterion A relativeto criterion B. If criterion A is judged to be far more importantthan criterion B, the relative importance of A relative B is setto 9 (the importance of B relative to Awill be the reciprocal ofthis number, 1/9). A score of 1 refers to equal importancebetween the two criteria [27]. Discussions with the companyprovided data on the pairwise criteria comparisons. Using theAHP method, the importance weights of the criteria werefound to be 0.25 for time, 0.45 for cost, and 0.30 for reliability.Furthermore, the consistency ratio of the pairwise compari-sons has been examined; the ratio was calculated as 0.0272,which is less than a 0.10 threshold and indicates that thepairwise comparisons are sufficiently consistent with oneanother.

The process quality characteristics and remanufacturingperformance data related to three process plan alternativesare illustrated in the HOQ of Fig. 2. Below the relationshipmatrix, objective criteria, i.e., data related to theremanufacturing performance for each of the three processplan alternatives, are listed. The rightmost part of the HOQ,which captures the experts’ perspectives, presents the dataresulting from the competitive analysis of the process planalternatives with respect to company demands.

For the process quality characteristics with widelydisparate units, normalizing is an effective way to putall parameters on equal footing and make them dimen-sionless. The measures can be calculated using thefollowing equations:

x j0 ¼ x j−xmin

xmax−xminfor measures where larger is better

ð9Þ

Int J Adv Manuf Technol (2014) 72:1551–1558 1555

x j0 ¼ xmax−x j

xmax−xminfor measures where smaller is better

ð10Þ

where xj′ is the normalized value for the jth measure, and xj is

the untransformed value for jth measure. For measures wherehigher values are more desirable (e.g., surface cleanliness,hardness, and precision retention), the normalized values canbe calculated with Eq. (9). For measures where smaller valuesare desired (e.g., straightness and parallelism), normalizedvalues can be calculated with Eq. (10). Following this pro-cessing, all the data are transformed to a 0–1 scale. It is notedfor the normalized values that larger numbers indicate better

performance, and smaller numbers indicate poorerperformance.

The normalized values of the process quality characteristicsthen form the matrix, F:

F ¼0:500 0:450 0:657 0:857 0:7500:250 0:750 0:543 0:571 0:6000:750 0:250 0:486 0:286 0:500

24 35

With identified relationships and related data avail-able, a quantified relationship between the process char-acteristics and different criteria is calculated for every

Table 1 Parameter estimationsαj(cj) by employing fuzzy linearregression for h=0.5

Intercept x1 x2 x3 x4 x5

y1 (3.48, 0.64) (−0.8, 0)y2 (4.847, 0) (6.714, 0) (−8.134,0)y3 (3.297, 0) (3.923, 0) (−2.834, 0)x2 (−0.102, 0.433) (1.170, 0) (0.324, 0)

x3 (0.411, 0) (−0.071, 0)x4 (−1.290, 0.095) (3.340, 0)

T(y1)

C(y2)

R(y3)

Process plan (i)

Process plan (ii)

Process plan (iii)

x1 x2 x3 x4 x5

√

√ √

√ √

Criteria

Process qualitycharacteristics

√ √

Minimum level

Maximum level

Unitsa 7-point

scale

WeightsProcessplan (i)

Processplan (ii)

Processplan (iii)

Min Max

Fig. 2 House of quality forremanufacturing process planselection

1556 Int J Adv Manuf Technol (2014) 72:1551–1558

process plan alternative. The h value, which is between0 and 1, is referred to as the degree of fit of theestimated fuzzy linear model to the given data set. Aproper value of h accurately reflects the decision-makers’ beliefs regarding the range of possibility distri-bution of fuzzy parameters. Herein, fuzzy linear regres-sion minimized the total sum of spreads of the estimat-ed values for a certain h level.

In this paper, the h value was set to 0.5 as in a number ofprevious works on fuzzy regression. The parameter estima-tions obtained by employing Eq. (7) are summarized inTable 1.

An example was used for application of Eq. (7), as pre-sented in Fig. 2, y1 is associated with x1, thus employingEq. (7) related fuzzy linear programming model for h=0.5 iswritten as follows:

min Z ¼ c0 þXj¼1

n

c jXk¼1

s

xjk�� �� !

¼ c0 þ 1:450c1

s:t: :

0:5c0 þ 0:225c1ð Þ þ α0 þ 0:45α1≥2:80:5c0 þ 0:225c1ð Þ−α0−0:45α1≥ −2:80:5c0 þ 0:375c1ð Þ þ α0 þ 0:75α1≥3:20:5c0 þ 0:375c1ð Þ−α0−0:75α1≥ −3:20:5c0 þ 0:125c1ð Þ þ α0 þ 0:25α1≥3:60:5c0 þ 0:125c1ð Þ−α0−0:25α1≥ −3:6

8>>>>>><>>>>>>:

The solution for this linear program is α0=3.48,α1=−0.8,c0=0.64,c1=0.

When the normalized data for process quality char-acteristics and parameter estimations obtained by fuzzy

linear regression are considered, Eq. (3) can be rewrittenas follows:

max z ¼ 0:25 � y1−1ð Þ5−1

þ 0:4 � y2−1ð Þ5−1

þ 0:35 � y3−1ð Þ5−1

¼ 0:063 y1 þ 0:100 y2 þ 0:086 y3− 0:25

s:t: y1 þ 0:8x1 ¼ 3:48

y2− 6:714 x4 þ 8:134 x5 ¼ 4:847

y3− 3:923 x2 þ 2:834 x3 ¼ 3:297

x2−1:170x3 ¼ −0:1020:071x2 þ x3−0:324x4 ¼ 0:411

−3:34x3 þ x4 ¼ −1:290≤xi≤1; i ¼ 1; 2;⋯; 5

1≤y j≤5; j ¼ 1; 2; 3

The results of the above linear programming model areshown in Table 2. Table 2 presents the optimal values ofprocess quality characteristics for achieving maximum satis-faction values.

After obtaining the optimal values for remanufacturingperformance criteria, the process plan alternative thatminimizes the weighted sum of deviations from themaximum achievable values for remanufacturing perfor-mance can be obtained. Given the optimal values (yi

*)for the remanufacturing performance criteria, the criteriaimportance weights (wi), and the scores of each processplan with respect to each criterion (qik), Eq. (8) can beused to calculate the performance for each plan. Theseare shown in Table 3.

According to the results in Table 3, plan (ii) that has thesmallest score (0.1889) and is therefore the best plan. Thus,remanufacturing process plan (ii) appears to be the mostsuitable remanufacturing process plan alternative. The resultof the model application shows that, once a complete set ofperformance attributes for process plan selection, along withthe set of alternatives and their level are laid out, an effectivejustification process around multi-criteria decision model canbe performed.

Table 2 Optimal values of process quality characteristics

Z* y1* y2* y3* x1* x2* x3* x4* x5*

0.701 3.274 4.226 3.746 0.646 0.524 0.561 0.176 0.273

Table 3 Calculation forremanufacturing processes planselection

Criterion score, qik Plan (i) Plan (ii) Plan (iii) Target value, yi* Criterion weight, wi

Time 2.8 3.2 3.6 3.274 0.25

Cost 4.5 3.8 2.7 4.226 0.4

Reliability 3.2 4.7 2.9 3.746 0.35

d1−=max{y1

*−q1k,0} 0.474 0.074 0

d2−=max{y2

*−q2k,0} 0 0.426 1.526

d3−=max{y3

*−q3k,0} 0.546 0 0.846

Z ¼ ∑i¼1

3

wid−i

0.3096 0.1889 0.9065

Int J Adv Manuf Technol (2014) 72:1551–1558 1557

5 Summary and conclusions

Remanufacturing process plan decisions can often make thedifference between successful and unsuccessfulremanufacturing. A decision-making method has been pre-sented for process plan selection that utilizes a QFD frame-work and fuzzy linear regression. This approach addresses theoften overlooked issues of the fuzziness of remanufacturingperformance criteria and the inherent complexity associatedwith the process plan decision. This paper utilized a multiple-stage, hybrid solution procedure that combines the strengthsof QFD and fuzzy linear regression into a systematic decision-making tool. The usefulness and practicality of the proposedmethod was demons t ra ted us ing a la the gu ideremanufacturing example.

The lathe guide example demonstrates the importance ofconsidering process quality characteristics in theremanufacturing process plan decision procedure. In the ab-sence of process quality characteristics, a remanufacturingprocess plan selection would be created that does not consideractual benefits. In general, it may be concluded that adecision-making method that integrates process quality char-acteristics is more effective than other approaches. A futureresearch direction may embed the proposed methodologywithin an intelligent decision support system frameworkwhere the model can be interfaced with human experts, data-bases, and computer software.

Acknowledgments The work described in this paper was supported bythe National Natural Science Foundation of China (51205295), WuhanYouth Chenguang Program of Sc ience and Technology(2014070404010214), and Science Foundation of Hubei Education ofChina (13 g157). These financial contributions are gratefully acknowl-edged. The authors also thank anonymous reviewers whose reviews helpimprove the manuscript.

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