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Journal of Intelligent & Fuzzy Systems 24 (2013) 163–174 DOI:10.3233/IFS-2012-0542 IOS Press
Optimal machine tools selection using quality function deployment and fuzzy multiple objective decision making approach Selc¸uk Perc¸ina,∗ and Hokey Minb a Department b Department
of Business Administration, Karadeniz Technical University, Trabzon, Turkey of Management, College of Business Administration, Bowling Green State University, Bowling Green,
OH, USA
Abstract. Machine tool selection is one of the most important strategic decisions in production planning because it directly affects production rates, costs, accuracy, flexibility, and design. Improperly selected machines can negatively affect the manufacturer’s overall manufacturing capability. Considering the significance of machine tool selection to production planning, there is a great need for a systematic decision-aid tool which can optimize the machine tool selection decision in the presence of wide-ranging alternatives. In response to such a need, we propose a hybrid decision-aid tool that combines the strengths of quality function deployment (QFD), fuzzy linear regression, and zero-one goal programming. QFD is utilized for incorporating the customer service needs into machine tool selection by examining the causal relationships between customer needs and technical tool requirements. Fuzzy linear regression is then used to determine such causal relationships which cannot be expressed in clear and precise manners. Finally, zero-one goal programming (ZOGP) is used to select the most desirable machine tool alternative. To verify the usefulness and practicality of the proposed method, we applied it to solve actual machine tool selection problem encountered by a steel automobile part manufacturer in Ankara, Turkey. Keywords: Machine tool selection, quality function deployment, fuzzy regression, decision making
1. Introduction The proper selection of machines tools can boost manufacturing throughputs and quality of finished products, while reducing manufacturing costs. Due to the strategic importance of machine tool selection to ∗ Corresponding
author. Selc¸uk Perc¸in, Department of Business Administration, Karadeniz Technical University, 61080, Trabzon, Turkey. Tel.: +90 462 3773473; Fax: +90 462 3257281; E-mails:
[email protected],
[email protected] (Selc¸uk Perc¸in),
[email protected] (Hokey Min).
manufacturing operations, it has received widespread attention from both practitioners and academicians alike. Generally speaking, the machine tool selection decision is concerned with the determination of machine tool combinations in such a way that production setup time is minimized, machine is fully utilized, a defect rate (or rework and scrap) is minimized, and machining cost is minimized given a set of alternative tool characteristics (e.g., tool size, power, tolerance, positioning accuracy, spindle speed). The optimal selection of machines tools often leads to improved product diversity/quality, enhanced manufacturing flexibility,
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reduced capital investment cost, and better utilization of company resources [4, 10, 23]. However, due to inherent complexity involved in machine tool selection, machine tool selection has been one of the most onerous decision making processes. Such complexity stems from the diverse but conflicting nature of tool selection criteria. For example, a machine tool that can help increase a variety of parts to be manufactured may increase set-up/changeover time. Reflecting this complex and multiple-objective nature, many prior studies adopted Multiple Criteria Decision Making (MCDM) methods to solve the machine tool selection problem. The MCDM methods proposed by prior studies include: Analytical Hierarchy Process (AHP) [9, 20, 35], scoring method [12], and multiple-criteria weighted average (MCWA) [2]. Additionally, integrated MCDM methods such as AHP with simulation techniques [3], AHP with the Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) approach [10], and AHP with Expert systems [29] are used in evaluating machine tool selection decisions. However, the aforementioned MCDM methods failed to reflect the vagueness and imprecision associated with the description of machine tool characteristics. For instance, machine tool rigidity cannot be easily described in a crisp manner, because the meaning of rigidity may differ from one manufacturing process to another. As such, Fuzzy MCDM approaches were proposed for machine tool selection problems [36]. To elaborate, Wang et al. [34] proposed a fuzzy MCDM model to select the appropriate machines for a flexi¨ ble manufacturing system (FMS). Aya˘g and Ozdemir [4] presented a fuzzy version of AHP for a machine ¨ ut et al. [23] presented a tool selection problem. On¨ fuzzy AHP based Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) approach to machine tool selection. More recently, Tuzkaya et al. [32] suggested an integrated fuzzy Analytic Network Process (ANP) with fuzzy PROMETHEE approach for the machine or equipment selection problems. Also, a fuzzy TOPSIS approach is developed by Yurdakul and ˙Ic¸ [36] to solve the machine tool selection problem. Similarly, fuzzy goal programming approaches were proposed by Prakash et al. [24] and Chan and Swarnkar [7] for machine tool selection. Furthermore, fuzzy information processing principles such as fuzzy axiomatic design [18], and utility models such as multiattribute utility theory (MAUT) [28], and evolutionary approaches such as heuristics [5] and genetic algorithm [21] were utilized to determine the most suitable
machine tool alternative in the presence of linguistic variables. Despite numerous merits, most of the past literature on machine tool selection neglected the critical role customers played in designing new products and the subsequent selection of appropriate machine tools. That is to say, machine tools that do not reflect specific customer needs and desires cannot manufacture products meeting customer technical requirements. To fill the void left by prior literature, this paper proposes a Quality Function Deployment (QFD) which translates customer needs and desires into machine tool characteristics for each stage of product design and development, while examining the causal relationship among the multiple machine tool selection criteria. Once QFD is utilized for determining the relationships between the customers’ needs and machine tool characteristics, fuzzy linear regression is employed to link those relationships to machine tool selection decisions. Afterward, the zero-one goal programming (ZOGP) model is used to determine the most suitable machine tool among a set of alternatives. In other words, this paper proposes a three-stage, integrated fuzzy decision making methodology for machine tool selection based on the combinations of QFD, fuzzy linear regression, and ZOGP. This proposed methodology aims at (1) translating customer needs into machine tool characteristics, (2) capturing vague and imprecise relationships among the machine tool selection criteria, and (3) minimizing the weighted sum of deviations from the maximum satisfaction values of customer needs. The rest of the paper is organized as follows. Section 2 explains the research methodology and presents the details of QFD and fuzzy linear regression. In Section 3, a real case application is given to show the effectiveness of the proposed hybrid QFD and fuzzy multiple objective decision making methodology. Finally, the last section contains concluding remarks and suggestions for future research.
2. Research methodology Customer service is the lifeblood of any business success. As such, the assurance of service that makes customer special is one of the best ways to win the heart of customers and enhance customer loyalty. The same service principle should be applied to the development of products which is often affected by machine tool selection. Thus, machine tool selection should factor into customer needs (CNs). One of the systematic ways to incorporate customer needs into machine tool
S. Per¸cin and H. Min / Optimal machine tools selection
characteristics is the use of QFD which is designed to link customer needs with manufacturing processes and translate customer needs into actions and designs. Given that some customer needs such as “ease of use,” “easy to clean,” “soft and comfortable,” “flexible,” and “high level of safety” are somewhat difficult to define in a clear manner, the inherent vagueness of customer needs should be taken into consideration when products are designed and machine tools relevant to product design are selected. This is why fuzzy linear regression is justified to determine the functional relationships between customer needs and machine tool characteristics. Indeed, a number of pioneering researchers such as Kim et al. [16], Chen et al. [8] and Fung et al. [11] utilized fuzzy linear regression to reflect the vague and imprecise voice of customers in their QFD analyses of production planning. More recently, Karsak [14] made a similar attempt to evaluate robotic systems. Sener and Karsak [27] developed a fuzzy regression based optimization approach for setting target levels in software quality function deployment. Also, Karsak and ¨ gul [15] adopted a fuzzy linear regression in selectOzo˘ ing the most suitable ERP system, while Alptekin and Karsak [1] used the same methodology in selecting elearning products. Going a step further beyond these earlier attempts, we would combine and then integrate three techniques: (1) QFD, (2) fuzzy linear regression, and (3) ZOGP to develop a more effective decision-aid tool for machine tool selection. These techniques will be discussed in greater detail in the following subsections.
(b)
(c)
(d)
(e)
(f)
2.1. QFD Put simply, QFD is a technique which transforms customer needs (CNs) or the voice of customers (VOC) into engineering characteristics using the matrix called house of quality (HOQ) [13]. HOQ basically summarizes what customer wants in terms of customer attributes and their relative importance to product characteristics. As shown in Fig. 1, the horizontal portions (rows) of HOQ matrix contain customer attributes reflecting what a customer needs, whereas its vertical portions (columns) describe detailed engineering characteristics technically required by the customer (see, e.g., Kim et al. [16]). A typical HOQ contains the following components [1, 27]: (a) Customer needs (WHATs): These are parameters that directly or indirectly influence customer requirements expressed in voices of customers. The needs and desires of customers are generally
(g)
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dubbed as customer attributes, customer needs (CNs) or customer requirements. Technical requirements (HOWs): These are referred to as the voice of the company, design requirements, engineering characteristics, product characteristics or technical requirements (TRs). They also provide the means for measuring CNs. In this paper, technical requirements are dubbed as CNC characteristics (CNCs). Relative importance of the CNs: These are the relative importance of CNs perceived by the customers and measured through a pair-wise comparison scale generally used in analytic hierarchy process (AHP). Relationships between WHATs and HOWs: A relationship between WHATs and HOWs demonstrates how well the CNCs satisfy the CNs. CNs tend to be subjective and vague, thus, the determination of the strengths of these relationships between the CNs and CNCs require expert knowledge. In this paper, we used fuzzy linear regression to examine functional relationships between WHATs and HOWs. Inner dependencies among the CNCs: The inner dependencies, given in the roof matrix, are used to identify the relationships among CNCs and then are estimated using fuzzy linear regression. Competitive analysis: The rightmost part of the HOQ, which provides the customer perceptions, shows the degrees of satisfaction of CNs. This part of the QFD also provides benchmarking information for the company’s products and its main competitors’ products in meeting the most important customer needs. Overall priorities and target values of CNCs: The relative importance of the CNs and target values of the CNCs are generally used as inputs for determining the parameter estimation and selecting the most suitable CNC alternative.
2.2. Fuzzy linear regression Unlike traditional regression analysis where deviations (residuals) between observed and estimated values are assumed to be random, fuzzy linear regression treated the residuals as imprecise values caused by uncertainty. Thus, fuzzy linear regression can handle the interval values of response (dependent) variables [30]. Considering the inherent vagueness associated with the customer needs in QFD, fuzzy linear regression is suitable for estimating the extent of functional
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x x
Roof matrix
x x
CNC-E
CNC-C
CNC-D
CNC-B
Relative importance
CNC Characteristics (CNCs) (HOWs) Customer Needs(CNs) (WHATs)
CNC-A
x
Customer needs 1 Customer needs 2
CNC-A CNC-B CNC-C CNC-D CNC-E
Relationships between WHATs and HOWs
Target values of the CNCs
Competitive analysis
Fig. 1. The house of quality matrix.
relationships between WHATs and HOWs of the HOQ. In the proposed fuzzy linear regression model, its main objective is to maximize customer satisfaction which can be mathematically expressed as follows [8, 14–17]: max z(y1 , y2 , . . . , ym ) =
m
wi (yi − yimin ) (yimax − yimin )
˜0 +A ˜ 1 xi1 + A ˜ 2 xi2 + . . . + A ˜ n xin yi = A
i=1
subject to: yi = fi (x1 , x2 , . . . , xn ), i = 1, 2, . . . , m
yimin and yimax represent the minimum and maximum possible values, respectively, for the ith CN. Using the benchmarking data set available in the HOQ, one can estimate the parameters of the functional relationships between fi and gj . Generally, a fuzzy linear regression model is formulated as [30]:
(1)
xj = gj (x1 , x2 , . . . , xj−1 , xj+1 , . . . , xn ), j = 1, 2, . . . , n yimin ≤ yi ≤ yimax i = 1, 2, . . . , m where wi represents the relative importance weight of the ith CN and is defined such that 0 < wi ≤ 1 and m i=1 wi = 1, yi indicates the customer perception of the degree of satisfaction of the ith CN (i = 1, 2, . . . , m), xj is the normalized target value of the jth CNCs (j = 1, 2, . . . , n), fi represents the functional relationship between the ith CN and the CNCs, gj denotes the functional relationship between the jth CNCs and other CNCs, z represents the degree of overall customer satisfaction for (y1 , y2 , . . . , ym ) and
(2)
where yi denotes the ith observed value of the dependent variable, xij is the jth independent variable for the ith ˜ j are the unknown fuzzy parameters observation and A with center αj and spread cj, respectively. The problem in the fuzzy linear regression model is to determine ˜ j such that the membership value fuzzy parameters A can be defined as ⎧ ⎨1 − |αj −aj | , αj − cj ≤ aj ≤ αj + cj cj µA˜ j (aj ) = (3) ⎩0, otherwise Therefore, the degree of membership of any real number in the interval is defined by an associated membership function. Accordingly, the fuzzy linear regression model can be rewritten as [15]: yi = (α0 , c0 ) + (α1 , c1 )xi1 + (α2 , c2 )xi2 + . . . + (αn , cn )xin
(4)
Fuzzy linear regression aims to determine fuzzy param˜ j by minimizing the total spread in the predicted eters A
S. Per¸cin and H. Min / Optimal machine tools selection
value of dependent (response) variable yi while satisfying the target degree of h. The h value is determined by the decision maker. It is a value between 0 and 1 and is chosen as the degree of fit of the estimated fuzzy linear regression model to the data set [17]. The fuzzy parameters of the fuzzy linear regression model can be estimated by solving the following formulation [14, 31]: min Z =
n j=0
(cj
u xjk ) k=1
subject to: n
αj xjk + (1 − h) (
j=0 n j=0
n
cj xjk ) ≥ yk
(5)
j=0
αj xjk − (1 − h) (
n
cj xjk ) ≤ yk
j=0
x0k = 1, k = 1, 2, . . . , u cj ≥ 0, j = 0, 1, . . . , n where xjk is the value of the jth independent variable for the kth observation (here, the normalized value of the jth CNCs for the kth CNC machining center alternative), and yk is the value of the dependent variable for the kth observation (here, the customer perception of the degree of satisfaction of the customer need for the kth CNC machining center alternative). Formulation (5) aims to determine fuzzy parameters ˜ j in such a way that it minimizes the total fuzziness A in the predicted value of dependent variable yi while each yi has a degree of membership of at least h that belongs to its fuzzy estimate [1, 17].
167
division employs experts in various fields such as casting, melting, moulding and welding sections. The Alpha Steel now has more than 90 full-time employees and wants to position itself as one of the industry leaders in manufacturing automobile parts in Turkey. The company supplies automobile spare parts to the forged steel industry sector. The Alpha Steel currently produces tractor axles assembly products, stabilizer chains, all type of nuts, bolts, linkage pins, clevises, connection parts, and steel equipments. It serves both domestic and foreign markets (e.g., Europe, Asia, and the United States) all across the world. The company has also set up the quality management system in the automotive sector and received the certificates of ISO/TS 16949:2002 and DIN EN ISO 9001:2000. The company now seeks to sustain its competitive advantage by improving the efficiency of its machining operations and its responsiveness to changing customer demands. Therefore, various types of CNC machining centers are needed for manufacturing automobile parts. The Alpha Steel’s managers believe that the establishment of a new CNC machine center will be the key to their company’s business success. The Alpha Steel recently sets the business goals of expanding machining capability, reducing production costs, enhancing product quality, and shortening lead time. To achieve such goals, the Alpha Steel started making a capital investment in the new CNC machining center which requires the optimal selection of new machine tools. Therefore, we can conclude that the new CNC machining center selection is one of the most important strategic decision problems in this automobile part manufacturer. To help the Alpha Steel make a wise investment decision, we proposed the three-step solution procedure shown in Fig. 2. 3.1. Building the HOQ for new CNC machining center selection
3. A real case application In this section, a real case with actual data is solved using the proposed methodology to demonstrate its practicality and usefulness. For illustrative purposes, a capital investment decision involving new CNC machining centers of a steel manufacturer (referred to as “Alpha” Steel hereafter) in Turkey is taken into consideration. The Alpha Steel was founded in 1986 in Ankara, Turkey. Between 1986 and 2010, it grew rapidly thanks to the manufacturing boom in Turkey. The Alpha Steel now occupies 11,500 m2 together with the machining centers division and a production capacity of 3,500 tons annually. The company’s machining
To establish the new CNC machining center, the Alpha Steel formed a project team comprised of four engineers and three managers who have expertise in this project. One of the authors of this study was brought in as an external consultant who conducted a lot of faceto-face interviews with this project team. Based on a series of these interviews, we identified a number of multiple decision criteria (pertaining to CNs and CNCs) and alternative CNC machining centers. In addition, the authors identified various customer requirements by examining the past literature such as prior studies conducted by Arslan et al. [2], Yurdakul [35], Aya˘g and ¨ ¨ ut et al. [23], Da˘gdeviren Ozdemir [4], Aya˘g [3], On¨
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Step 1: Building the HOQ Use face-to-face interviews to collect the required data on decision criteria (CNs and CNCs) and illustrate these data in the HOQ Calculate the relative importance weights of CNs by applying the AHP Determine the degrees of satisfaction of CNs for CNC alternatives Obtain target values of CNCs for five CNC alternatives
Step 2: Fuzzy linear regression analysis Use a linear normalization procedure to normalize the data concerning the target values of CNCs Identify the relationships between the CNs and CNCs and among the CNCs Use fuzzy linear regression to estimate the parameters of functional relationships between the CNs and CNCs and among the CNCs Formulate a linear programming model to determine the new target values of CNCs
Step 3: ZOGP Formulate a ZOGP model to determine the best CNC alternative which minimizes the weighted sum of deviations from the maximum satisfaction values of CNs
Fig. 2. A flow diagram of the research methodology for machine tool selection.
[10], Yurdakul and ˙Ic¸ [36], and Tuzkaya et al. [32]. By combining the interview results and literature reviews, we identified eight customer requirements: cost, flexibility, productivity, service quality, user friendliness, safety and environment, adaptability, and reliability. Costs represent primarily the cost of acquiring and operating the new CNC machining centers. Flexibility means the ability to adapt the system to optimal conditions. It depends on the number of products, set-up time, easy manufacturing and maintenance, and machining speed, etc. Productivity is related to the efficient utilization of input resources for improving the design and functionality of the machining center. Productivity is a function of different machine properties such as power, machine set-up time and machining speed as well as the ability to eliminate non-value adding activities such as idle and down time. Service quality is a gauge of the customer satisfaction level. It also covers all maintenance activities to be performed based on customers’ expectations. User friendliness means ease of use and ease of understanding operations without too much technical expertise and skills. It also includes the reduced training and regular maintenance time by shortening the adaptation process of the different CNC
machines for end-users. Safety means the level of safety hazards associated with the new CNC machining center and its shop floor environment, and the availability of adequate protective equipment (e.g., safety goggles, helmets) for workers. Adaptability is the degree of all the machines’ ability to work together simultaneously. Finally, reliability provides effective operations by improving machining time. It also reduces service and maintenance costs, working hours, and energy consumption. The company also considered eight CNCs to be evaluated as TRs for the appropriate CNC machines. The eight CNCs criteria are: power, maximum tool diameter, machine set-up time, table size, operating time, machining speed, positioning accuracy, and warranty period. After determining the decision criteria, five main CNC alternatives denoted as CNC-A, CNC-B, CNC-C, CNC-D and CNC-E are selected based on company’s demands and experts’ experiences. Then, the required data utilized in the evaluation of CNC selection were collected from the project team and were illustrated in the HOQ. Figure 3 shows the detailed representation of the HOQ for the CNC machining center selection study. After determining the decision criteria and alternative CNC machines, the relative importance of eight CNs is determined using the AHP. In AHP, pairwise comparison matrices, based on comparing the relative importance or preferences of two elements, are generated by verbal judgments such as high, medium and low or by choosing a number on a comparison scale of 1 to 9. In this study, the values in each pairwise comparison matrix are defined on a scale of 1 to 9, where a score of 1 refers to equal importance between the two elements and 9 denotes absolutely greater importance of one element over the other one [25]. After employing the pairwise comparisons of CNs, corresponding relative weights are obtained as (wj ): (0.16)-cost, (0.28)flexibility, (0.08)-productivity, (0.11)-service quality, (0.14)-user friendliness, (0.06)-safety and environment, (0.08)-adaptability, (0.09)-reliability. Furthermore, the consistency ratio of the pairwise comparisons have been examined and proved to be consistent by indicating below the suggested 0.10 threshold. Target values of CNCs for each of the five CNC alternatives have been obtained from the project team and the degrees of satisfaction of CNs has been scaled from 1 to 5, where 1 and 5 represent the worst (“least satisfied”) and the best (“most satisfied”) scores, respectively [11]. The main objective of the project is to determine the most suitable CNC machining center from the given alternatives by
S. Per¸cin and H. Min / Optimal machine tools selection Table 1 The sensitivity of fuzzy regression solutions for y1 to h
considering functional relationships between CNs and CNCs as well as interactions among CNCs. h
3.2. Parameter estimation based on fuzzy linear regression CNCs values are normalized employing a linear normalization procedure. The normalization data concerning power, maximum tool diameter, table size, machining speed, positioning accuracy and warranty period (j = 1, 2, 4, 6, 7, 8) are estimated as xij /xj∗ for j = 1, 2, 4, 6, 7 and 8 where xj∗ = maxj xij , while data related to machine set-up time and operating time are normalized as xj− /xij , where xj− = minj xij for j = 3 and 5 [14]. The normalized values of CNCs data are computed as follows: ⎡
0.432 ⎢ 0.514 ⎢ ⎢ 0.811 X=⎢ ⎢ ⎢ 0.595 ⎣ 1.000
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
␣0
␣1
␣6
␣7
5.434 5.434 5.434 5.434 5.434 5.434 5.434 5.434 5.434
3.061 3.061 3.061 3.061 3.061 3.061 3.061 3.061 3.061
–7.594 –7.594 –7.594 –7.594 –7.594 –7.594 –7.594 –7.594 –7.594
0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800
c 0 c1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
c6
c7
Z
0.333 0.375 0.428 0.499 0.598 0.749 0.998 1.494 3.005
0 0 0 0 0 0 0 0 0
1.330 1.498 1.711 1.996 2.393 2.996 3.991 5.975 12.018
The solution for this linear program is ␣0 = 5.434, ␣1 = 3.061, ␣6 = –7.594, ␣7 = 0.800, c6 = 0.598. To
0.571 0.643
0.600 0.750
0.781 0.781
0.600 0.750
0.833 0.500
0.400 0.800
0.964 0.571 1.000
0.750 1.000 1.000
0.813 0.781 1.000
0.900 0.750 1.000
0.833 0.833 1.000
0.200 0.400 1.000
The h value, which is between 0 and 1, is referred to as the degree of fit of the estimated fuzzy linear model to the given data set. The estimated parameters in the functional relationships can be obtained by using fuzzy linear regression for a 0.5 value of h [8, 14, 17, 30]. For example, as shown in Fig. 3, y1 is associated with x1 , x6 and x7 , and thus employing formulation (5), related linear programming model for h = 0.5 is given as [8, 15]:
169
⎤ 0.750 ⎥ 0.750 ⎥ ⎥ 0.750 ⎥ ⎥ 0.750 ⎥ ⎦ 1.000
examine how the selection of h influences the values of centers and spreads, several different values of h are selected. Then, fuzzy linear regression was employed using CNs and CNCs values as the data set. The corresponding results for the first CNs y1 are given in Table 1. The fuzzy parameters are estimated according to certain h levels. One can realize that h influences both the values of centers (␣j ) and spreads (cj ) of
Min Z = 5.000c0 + 3.351c1 + 4.000c6 + 2.800c7 s.t. :
␣0 +0.432␣1 + 0.833␣6 + 0.400␣7 + 0.500c0 + 0.216c1 + 0.417c6 + 0.200c7 ≥ 1 ␣0 + 0.432␣1 + 0.833␣6 + 0.400␣7 − 0.500c0 − 0.216c1 − 0.417c6 − 0.200c7 ≤ 1 ␣0 + 0.514␣1 + 0.500␣6 + 0.800␣7 + 0.500c0 + 0.257c1 + 0.250c6 + 0.400c7 ≥ 4 ␣0 + 0.514␣1 + 0.500␣6 + 0.800␣7 − 0.500c0 − 0.257c1 − 0.250c6 − 0.400c7 ≤ 4 ␣0 + 0.811␣1 + 0.833␣6 + 0.200␣7 + 0.500c0 + 0.406c1 + 0.417c6 + 0.100c7 ≥ 2 ␣0 + 0.811␣1 + 0.833␣6 + 0.200␣7 − 0.500c0 − 0.406c1 − 0.417c6 − 0.100c7 ≤ 2 ␣0 + 0.595␣1 + 0.833␣6 + 0.400␣7 + 0.500c0 + 0.298c1 + 0.417c6 + 0.200c7 ≥ 1 ␣0 + 0.595␣1 + 0.833␣6 + 0.400␣7 − 0.500c0 − 0.298c1 − 0.417c6 − 0.200c7 ≤ 1 ␣0 + 1.000␣1 + 1.000␣6 + 1.000␣7 + 0.500c0 + 0.500c1 + 0.500c6 + 0.500c7 ≥ 2 ␣0 + 1.000␣1 + 1.000␣6 + 1.000␣7 − 0.500c0 − 0.500c1 − 0.500c6 − 0.500c7 ≤ 2 c0 , c1 , c6 , c7 ≥ 0
(6)
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S. Per¸cin and H. Min / Optimal machine tools selection Table 2 Parameter estimations αj (cj ) by employing fuzzy linear regression for h = 0.5 Intercept
y1 y2 y3 y4 y5 y6 y7 y8 x1 x2 x3 x5 x6
x1
5.434 4.072 4.147 4.008 –4.049 5.302 –2.108(0.566) 5.542(2.550) –0.587 0.091 0.463(0.325) 0.453 0.585(0.342)
x2
x3
x4
x5
3.061 11.203(1.352)
6.420(0.184) 2.182
2.237
x7
x8
0.800
–14.208 5.448
6.135
x6 –7.594(0.598) –9.636
–0.962 7.634 0.117(0.019)
–3.802(0.902) –11.644
6.607(1.199) 6.951 7.256(0.895)
–8.016 2.534
1.652 –6.667 1.158
1.037
–4.234 0.303 –0.063(0.203)
0.500 0.747(0.015) 0.412
0.052 –0.168
Aj . A proper value of h reflects the decision makers’ beliefs regarding the range of possibility distribution of fuzzy parameters [17]. As recalculated in Table 1, the center values remain the same, while the spread values change as h values change. Therefore, the bigger h produces the bigger c6 and Z. Herein; fuzzy linear regression minimized the total sum of spreads of the estimated values for a certain h level. In this paper, the h value is set to 0.5 and Table 2 presents the results of the parameter estimations. Therefore, the parameters of functional relationships between CNs and CNCs (fi ) and the parameters of functional relationships among
–0.245
g6 , g7 and g8 are given as shown in Table 2. Also, as represented in Table 2, x4 , x7 and x8 are correlated with no other CNCs, and thus g4 , g7 and g8 are zero. After calculating the degrees of satisfaction of CNs (yi ) by employing the fuzzy linear regression analysis, the new target values (xj ) for CNCs can be obtained. Therefore, the parameters of functional relationships among CNCs, gj , are calculated using the formulation (5). As shown in Fig. 3, x1 is associated with x2 , x5 and x6 , and thus linear programming model for h = 0.5 is written as
Min Z = 5.000c0 + 3.750c2 + 4.000c5 + 4.000c6 s.t. :
␣0 + 0.571 ␣2 + 0.600␣5 + 0.833␣6 + 0.500c0 + 0.286c2 + 0.300c5 + 0.417c6 ≥ 0.432 ␣0 + 0.571 ␣2 + 0.600␣5 + 0.833␣6 − 0.500c0 − 0.286c2 − 0.300c5 − 0.417c6 ≤ 0.432 ␣0 + 0.643 ␣2 + 0.750␣5 + 0.500␣6 + 0.500c0 + 0.322c2 + 0.375c5 + 0.250c6 ≥ 0.514 ␣0 + 0.643 ␣2 + 0.750␣5 + 0.500␣6 − 0.500c0 − 0.322c2 − 0.375c5 − 0.250c6 ≤ 0.514 ␣0 + 0.964 ␣2 + 0.900␣5 + 0.833␣6 + 0.500c0 + 0.482c2 + 0.450c5 + 0.417c6 ≥ 0.811 ␣0 + 0.964 ␣2 + 0.900␣5 + 0.833␣6 − 0.500c0 − 0.482c2 − 0.450c5 − 0.417c6 ≤ 0.811 ␣0 + 0.571 ␣2 + 0.750␣5 + 0.833␣6 + 0.500c0 + 0.286c2 + 0.375c5 + 0.417c6 ≥ 0.595 ␣0 + 0.571 ␣2 + 0.750␣5 + 0.833␣6 − 0.500c0 − 0.286c2 − 0.375c5 − 0.417c6 ≤ 0.595 ␣0 + 1 ␣2 + 1 ␣5 + 1 ␣6 + 0.500c0 + 0.500c2 + 0.500c5 + 0.500c6 ≥ 1 ␣0 + 1 ␣2 + 1 ␣5 + 1 ␣6 − 0.500c0 − 0.500c2 − 0.500c5 − 0.500c6 ≤ 1 c0 , c2 , c5 , c6 ≥ 0
CNCs (gi ) are determined by employing fuzzy linear regression. Thus, the estimated parameters of functional relationships f1 , f2 , f3 , f4 , f5 , f6 , f7 , f8 , g1 , g2 , g3 , g4 , g5 ,
(7) The parameter estimations of this fuzzy linear program are ␣0 = –0.587, ␣2 = 0.117, c2 = 0.019, ␣5 = 1.158, ␣6 = 0.303. By considering the normalized CNCs
S. Per¸cin and H. Min / Optimal machine tools selection
data and parameter estimations, the coefficients in the functional relationships can be obtained by employing the linear programming model given below:
171
business decisions involving the selection of information system projects [19, 26], the public natural resource investment decisions [22], optimum facility planning decisions [6] and the optimal production scheduling applications [33].
Max Z = 0.053y1 + 0.07y2 + 0.027y3 + 0.037y4 + 0.035y5 + 0.015y6 + 0.020y7 + 0.023y8 − 0.279 s.t. :
y1 − 3.061x1 + 7.594x6 − 0.800x7 = 5.434 y2 − 6.420x2 + 2.237x3 + 9.636x6 = 4.072 y3 − 11.203x1 + 2.182x2 + 14.208x5 = 4.147 y4 − 6.607x6 + 8.016x8 = 4.008 y5 − 5.448x3 + 3.802x5 − 6.951x6 = −4.049 y6 + 11.644x5 − 7.256x6 − 2.534x7 = 5.302 y7 − 6.135x1 + 0.962x2 − 1.652x4 = −2.108 y8 − 7.634x2 + 6.667x5 + 4.234x8 = 5.542 x1 − 0.117x2 + 1.158x5 − 0.303x6 = −0.587 x2 − 1.037x1 + 0.063x6 = 0.091 x3 − 0.500x5 = 0.463 x5 − 0.747x1 − 0.052x3 + 0.245x6 = 0.453 x6 − 0.412x1 + 0.168x3 = 0.585 x1 ≥ 0.432 x2 ≥ 0.571 x3 ≥ 0.600 x4 ≥ 0.781 x5 ≥ 0.600 x6 ≥ 0.500 x7 ≥ 0.200 x8 ≥ 0.750 xj ≤ 1, j = 1, 2, ... , 8 1 ≤ yi ≤ 5, i = 1, 2, ... , 8
(8)
3.3. Zero-One Goal Programming (ZOGP) Table 3 presents the target values of CNCs for achieving maximum satisfaction values of CNs. Once those values are determined, the ZOGP is used to select the most suitable CNC alternative. The rationale being that the ZOGP has been successfully used to make various
ZOGP aims to minimize the weighted sum of the prioritized positive and negative deviations from the maximum satisfaction values of CNs and then select the most suitable CNC alternative. This ZOGP can be formulated as:
172
S. Per¸cin and H. Min / Optimal machine tools selection
Min 0.16 d1− + 0.28 d2− + 0.08 d3− + 0.11 d4− + 0.14 d5− + 0.06 d6− + 0.08 d7− + 0.09 d8− s.t. : 1λ1 + 4λ2 + 2λ3 + 1λ4 +2λ5 − d1+ + d1− = 2.85 1λ1 + 5λ2 + 4λ3 + 2λ4 +3λ5 − d2+ + d2− = 3.81 2λ1 + 1λ2 + 2λ3 + 1λ4 +4λ5 − d3+ + d3− = 1.46 4λ1 + 1λ2 + 3λ3 + 3λ4 +2λ5 − d4+ + d4− = 2.65 3λ1 + 1λ2 + 2λ3 + 4λ4 +5λ5 − d5+ + d5− = 2.50 5λ1 + 2λ2 + 1λ3 + 4λ4 +3λ5 − d6+ + d6− = 3.56 1λ1 + 2λ2 + 3λ3 + 2λ4 +5λ5 − d7+ + d7− = 2.81 4λ1 + 1λ2 + 5λ3 + 3λ4 +1λ5 − d8+ + d8− = 2.45 5
λi = 1
i=1
λi ∈ {0, 1}, i = 1, ..., 5 The ZOGP model bases the selection of the CNC alternatives λi on the AHP determined weights of wj for corresponding di− . In formulation (9), λi is the binary decision variable of the ith CNC alternative, and di+ di− , are the positive and negative deviation variables, respectively, for the ith CNs. The results of the above weighted ZOGP model are obtained as λ1 = λ 2 = λ 4 = λ5 = 0, and λ 3 =1. Thus, CNC-C can be seen as the most appropriate machine tool alternative.
4. Concluding remarks and future research directions In this era of fierce global competition, manufacturing prowess alone cannot guarantee business success. Instead, the firm’s ability to manufacture exactly what customers want and desire can be the differentiator in winning the competition. With this in mind, we proposed an integrated fuzzy multiple objective approach that was ingrained in the QFD framework where customer needs are reflected in the machine tool selection process. This approach differs from the conventional wisdom which often overlooked the fuzziness of customer requirements and inherent complexity associated with the capital investment decision such as machine tool selection. Unlike traditional solutions methods for machine tool selection which heavily relied on a single step, one-dimensional solution procedure, we utilized multiple-stage, hybrid solution procedures which
(9)
combined the strengths of the QFD, fuzzy linear regression, AHP, and ZOGP as a systematic decision-aid tool. The usefulness and practicality of the proposed solution procedures were validated by applying it to the real case encountered by the Turkish auto part manufacturers. The key contributions made by this paper are: (1) the adaptation of QFD as a way to translate customer needs and desires into machine tool characteristics; (2) the introduction of fuzzy concepts into the strategic capital investment decision involving uncertainty and vagueness; (3) the use of AHP for prioritizing the set of customer needs and desires expressed in linguistic variables; (4) the adoption of a ZOGP model which could maximize the customer satisfaction level in manufacturing automobile parts; (5) the successful application of the proposed hybrid research methodology to a real case. Despite these contributions, the proposed methodology can be further refined and extended to solve other real world machine tool selection problems in different industries such as consumer electronics and robotics. Also, the other traditional methods such as ANP, TOPSIS, VIKOR etc. can be developed to compare their results with those of the hybrid QFD and fuzzy multiple objective decision making approach. For further research, rather than the stand-alone solution method, the proposed methodology can be embedded within the intelligent decision support system framework where the model can be interfaced with human experts, data warehouses, and computer software.
S. Per¸cin and H. Min / Optimal machine tools selection x
x
x
173
x x
x x x
x x
x
16 19 30 22 37
x x x
x x
x 15 12 10 12 9
10 6 10 10 12
2 4 1 2 5
x 5 4 4 3 3
0.25 0.25 0.26 0.25 0.32
x 3 3 3 3 4
0.14 0.06 0.08 0.09
CNC-E
x x 80 90 135 80 140
x x
0.16 0.28 0.08 0.11
CNC-D
x x
x
x8
CNC-C
x
x7 x
CNC-B
x x
x6 x x
CNC-A
x5
Importance to customers
x4
Warranty period
x3
Positioning accuracy (10-3 mm)
x2
Machining speed (1000 rpm)
Operating time (s)
x
Table size (m2)
x1 x
Cost (y1) Flexibility (y2) Productivity (y3) Service quality (y4) User friendliness (y5) Safety and environment (y6) Adaptability (y7) Reliability (y8) CNC-A CNC-B CNC-C CNC-D CNC-E
Machine set-up time (s)
Customer Needs(CNs)
Max. tool diameter (mm)
Power (kW)
CNC Characteristics (CNCs)
1 1 2 4 3 5 1 4
4 5 1 1 1 2 2 1
2 4 2 3 2 1 3 5
1 2 1 3 4 4 2 3
2 3 4 2 5 3 5 1
Fig. 3. The house of quality for CNC center selection.
Table 3 Final solutions Zmax
y1
y2
y3
y4
y5
y6
y7
y8
x1
x2
x3
x4
x5
x6
x7
x8
0.53
2.85
3.81
1.46
2.65
2.50
3.56
2.81
2.45
0.64
0.72
0.87
1.00
0.81
0.71
1.00
0.75
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