A fuzzy based decision model for nontraditional machining process

A fuzzy based decision model for nontraditional machining process selection

Tolga Temuçin, Hakan Tozan, Özalp Vayvay, Marta Harničárová & Jan Valíček The International Journal of Advanced Manufacturing Technology ISSN 0268-3768 Volume 70 Combined 9-12 Int J Adv Manuf Technol (2014) 70:2275-2282 DOI 10.1007/s00170-013-5474-z

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Author's personal copy Int J Adv Manuf Technol (2014) 70:2275–2282 DOI 10.1007/s00170-013-5474-z

ORIGINAL ARTICLE

A fuzzy based decision model for nontraditional machining process selection Tolga Temuçin & Hakan Tozan & Özalp Vayvay & Marta Harničárová & Jan Valíček

Received: 12 June 2012 / Accepted: 3 November 2013 / Published online: 19 November 2013 # Springer-Verlag London 2013

Abstract Manufacturing systems are processes in which inputs obtained from interior and exterior sources are transformed into an output by gathering inputs in an optimal way to guide the enterprises. Machining process plays a critical role in industry, and thus, directly affects the efficiency of the manufacturing systems. Due to different importance of the conflicting criterions, the multi-criteria decision-making methods are extremely useful in the selection process of the proper machining type. This study provides distinct systematic approaches in fuzzy and crisp environments to deal with the selection problem of proper machining process and proposes a decision support model for the guidance of decision makers to assess potentials of seven distinct nontraditional machining processes, namely laser beam machining, plasma arc machining, water jet machining, abrasive water jet T. Temuçin (*) : H. Tozan Department of Industrial Engineering, Turkish Naval Academy, 34942 Tuzla, Istanbul, Turkey e-mail: [email protected] H. Tozan e-mail: [email protected] Ö. Vayvay Department of Industrial Engineering, Marmara University, Goztepe Campus, 34722 Kadikoy, Istanbul, Turkey e-mail: [email protected] M. Harničárová Nanotechnology Centre, Institute of Physics, Faculty of Mining and Geology, VŠB—Technical University of Ostrava, 17. listopadu 15/2172, 7, 708 33 Ostrava-Poruba, Czech Republic e-mail: [email protected] J. Valíček Institute of Physics, Faculty of Mining and Geology, RMTVC, Faculty of Metallurgy and Materials Engineering, VŠB—Technical University of Ostrava, 17. listopadu 15/2172, 7, 708 33 Ostrava-Poruba, Czech Republic e-mail: [email protected]

machining, electrochemical machining, electrical discharge machining (EDM), and wire–EDM in the cutting process of carbon structural steel with the width of plate of 10 mm. The required data for decision and weight matrices are obtained via a questionnaire to specialists, as well as by deep discussions with experts and making use of past studies. Finally, an application of the proposed model is also performed via the SETED 1.0 software to show the applicability of the model. Keywords Multiple criteria decision-making . Fuzzy set theory . ELECTRE . TOPSIS . PROMETHEE . Nontraditional machining processes

1 Introduction Manufacturing systems are used to transform inputs originated from different sources into outputs to satisfy each one of the stakeholders. However, it is a tough responsibility as each stakeholder has his/her own criterions with different importance, which eventually makes the process a complex decision problem. In this process, the manufacturer, the decision maker (DM), has to choose the method(s) that will enable the creation of the output. Decision-making process can be defined as the procedure to find the best alternative from a set of feasible ones [1]. However, nowadays, it is hard to accomplish the task as complexity of the process has increased in the course of time because of the increased number of inputs. Thus, multi-criteria decision-making (MCDM) methods have evolved to improve the quality of decisions by making the process more explicit, rational, and efficient. These methods are powerful tools, which are widely used for complex problems featuring high uncertainty, conflicting objectives, multi-interests, and perspectives [2–4].

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Advances in industries as in nuclear reactor, automobile, missile, and turbine industries require high strength and temperature-resistant alloys. This forced scientists in the field of material science to develop higher strength materials. However, in the course of time, traditional machining processes would not be sufficient to produce complex shapes in the strengthened materials, such as titanium and stainless steel. Consequently, cutting tool materials are required to be harder because of the increase in the strength of processed materials, which eventually lead to the evolution of nontraditional machining (NTM) processes. Machining processes, especially the NTM ones, play a critical role in the industry, and they directly affect the efficiency of manufacturing systems. For this reason, it is vital to determine the proper machining process in the cutting operations of specific materials. NTM processes, as a branch of machining processes, are characterized by the presence of a large number of viable alternatives, uncertainties concerning the process capabilities, and shortage of the experienced planners [5]. In this context, the illstructured and multi-criteria nature of the NTM process selection problems caused MCDM methods to be widely used in this area [5–8]. Moreover, development of decision support systems (DSS) using specific MCDM methods for NTM process selection problems is a different kind of development in this field [9–14]. The purpose of this study is to propose a decision support model, which can be used to select the best nontraditional machining process option for cutting operations of a specific material and a generic DSS which is used to rank those processes. Criterions for the proposed model, performances of each alternative in terms of each criterion, and weights representing the rate of importance for the mentioned criterions were identified via questionnaires to specialists, deep discussions with experts, and making use of past studies. The remainder of this study is structured as follows. In the second section, the research methods are introduced briefly. The third section is reserved for the developed decision support software. In the fourth section, firstly, the proposed decision support model is introduced and then a case study is performed. Finally, conclusions and further recommendations are highlighted in the last section.

2 Research methods: ELECTRE I, TOPSIS, PROMETHEE II, Fuzzy TOPSIS, and Fuzzy ELECTRE I In this section, ELECTRE I, technique for order preference by similarity to ideal situation (sTOPSIS), PROMETHEE II, Fuzzy ELECTRE I, and Fuzzy TOPSIS methods, which are the methods used as distinct decision support tools in the solution procedure of proper NTM process selection problem, are explained briefly.

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2.1 ELECTRE I ELECTRE I was developed by Bernard Roy in 1968 [15]. The basic concept of the method is to deal with the outranking relations by using pair-wise comparisons of alternatives with respect to each criterion [16]. In this method, the aim is to find the subset called kernel , the set of alternative(s), which are accepted to be the best at the end of the method [17] by utilizing the outranking relations of alternatives. That is why the DM has to focus his/her attention to the kernel as it holds the best alternative(s). The algorithm of the method is described as follows: –

Construct decision (A) and weight (W) matrices: This is the step where each alternative defined by a 1,a 2,…,a i , …,a m is evaluated in terms of each criterion defined by c 1,c 2,…,c j ,…c n to obtain performances a ij (i =1,2,…, m )(j =1,2,…,n), which will eventually enable creation of the decision matrix. Together with the decision matrix, the weight matrix having the weights defined by w 1,w 2, n

…,w j ,…w n for each criterion satisfying

∑ wj ¼ 1

j¼1

–

–

–

–

– – –

must also be constituted. Construct normalized decision matrix (X ): Dependent on the criterions of different units of all kinds, such as $, hour, etc. it can occupy the decision matrix altogether. Existence of this step enables transformation of the decision matrix into a dimensionless form. Construct weighted normalized decision matrix (Y ): In this step, different importance weights determined for each criterion are incorporated into the calculation procedure. Determine concordance (C ik ) and discordance (D ik ) sets: One classification type for a criterion is to determine whether it is a benefit or a cost criterion. The benefit criterion means that a higher value is better, while for any cost criterion the opposite is valid [18]. In case that the alternative a is compared with the alternative b, the discordance set is the one containing the criterions in which the alternative a is worse than the alternative b, and the concordance set is the one containing the remaining criterions. Construct concordance (C) and discordance (D ) matrices: In case that the alternative a is compared with the alternative b, the concordance matrix provides a measure of the outranking character of a , while the discordance matrix provides a measure of the outranked character of a. These matrices contain values for each alternative pair. Construct dominance concordance (F ) and dominance discordance (G ) matrices Construct total dominant matrix (E ) Determine importance sequence of alternatives

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The details, calculation steps, and basic information on ELECTRE I can be found in Yürekli [19].

method uses pair-wise comparisons of alternatives in terms of each criterion to obtain an overall ranking. The algorithm of the method is described as follows:

2.2 TOPSIS

– –

TOPSIS, which was developed by Hwang et al. in 1993 [20], evolved as an alternative to the ELECTRE I. Advantages of this method are the following [21]: – – –

Computation procedure is simple, Method's logic is understandable, and Importance weights are incorporated into the procedure.

As a human, DM tries to reach an ideal solution of any problem. The ideal can be described as a perfect example of what something should be like, but that is not likely to really exist. In this respect, ideal solution is the choice with best performances in each criterion, which is indeed impossible to come true. However, it is impossible to reach an ideal solution. In a case like this, the choice nearest to the ideal solution must be preferred. The method uses the concepts of positive ideal solution and negative ideal solution in order to determine the best choice. The positive ideal solution is the one maximizing the benefit criterion and minimizing the cost criterion, while for the negative ideal solution, the opposite is valid [21]. According to this method, the best alternative is the one, which is nearest to the positive ideal solution and farthest to the negative ideal solution [22]. The algorithm of the method is described as follows: – – – –

– – –

Construct decision (A ) and weight (W) matrices Construct normalized decision matrix (X) Construct weighted normalized decision matrix (Y) Determine Positive and negative ideal solutions: Dependent on the criterion, the PISs are the ones having the best values in each column while the opposite is valid for NISs. Calculate separation measures: In this step, the distances of each alternative from negative ideal solution (S −i ) and positive ideal solution (S *i ) are calculated. Calculate relative closeness to the ideal solution (C *i ): Using the distances from S −i and S *i , the relative closeness to the ideal solution is calculated. Rank preference order: The alternative with the highest C *i is the best choice.

– –

–

–

Construct decision (A ) and weight (W) matrices Determine preference functions for each criterion : Preference function displays the internal relation of the criterion to which it is designated. Brans et al. [24] claims that the method proposes six different preference functions, which are not exhaustive but sufficient in most of the practical cases. The parameters, namely indifference threshold q, preference threshold p, and standard deviation threshold s are used considering the chosen preference function in the criterion. Preference functions, their definitions, and parameters to be fixed are mentioned in [24]. Determine shared preference functions P(a,b): Shared preference functions are determined by binary comparisons of alternatives with respect to each criterion. Determine preference indexes π(a,b): Preference index determines a valued outranking relation on the set K of actions. This relation shown in Fig. 1 is called a valued outranking graph, the nodes of which are the actions of K. Between two nodes, a and b, two arcs exist having the values π(a,b) and π(b,a ). Determine leaving (Φ +) and Entering (Φ −) Flows: For each node in the valued outranking graph, two flows exist as shown in Fig. 2. The first flow presented by the arcs leaving from the node a is called the leaving flow, while the second flow presented by the arcs entering the node a is called the entering flow. In other words, the flow leaving the node a provides a measure of the outranking character of a, while the flow entering the node a provides a measure of the outranked character of a. Determine preorder (Φ (i )): The alternative with the highest Φ (i) is the best choice.

The details, calculation steps, and basic information on TOPSIS can be found in Uygurtürk and Korkmaz [23]. 2.3 PROMETHEE II The third method used in this study is PROMETHEE II, which was developed by Jean Pierre Brans in 1986 [24]. The method is one of the members of the class of outranking methods. Again, as in the ELECTRE methodology, the

Fig. 1 Valued outranking graph

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Fig. 2 Outranking flows

The details, calculation steps, and basic information on PROMETHEE II can be found in Brans et al. [24]. 2.4 Fuzzy logic concept Fuzzy logic notion was first introduced by L. A. Zadeh in 1965 [25]. It is a precise logic of imprecision and approximate reasoning [26]. It provides a simple way to arrive to the definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information [27]. Very often in MCDM problems, the data are imprecise and fuzzy. Contrary to the crisp set theory, the fuzzy set theory is developed to cope with these kinds of indefiniteness. As a result, fuzzy versions of TOPSIS and ELECTRE I that use the fuzzy set theory concept have emerged. 2.4.1 Fuzzy ELECTRE I and Fuzzy TOPSIS Error rate defined for decision and weight matrices helps to obtain a triangular fuzzy number (TFN) from each crisp number. Considering a TFN formed by a triplet a ¼ ða1 ; a2 ; a3 Þg , the most extreme values and the middle fe one can be computed with Eq. (1). a1 ¼ ðcrisp dataÞ− ðcrisp dataÞ  ðerror rate=100Þ a2 ¼ ðcrisp dataÞ a3 ¼ ðcrisp dataÞ þ ðcrisp dataÞ  ðerror rate=100Þ

ð1Þ

Steps for fuzzy ELECTRE I and Fuzzy TOPSIS methods are similar to those of ELECTRE I and TOPSIS, respectively. The details, calculation steps, and basic information on fuzzy ELECTRE I and Fuzzy TOPSIS can be found in Sevkli [28] and Chen [29], respectively.

3 Search Tool for Enhanced Decision The term “Decision Support Systems” appeared for the first time in 1971 when Gorry and Scott Morton published the paper entitled A Framework for Management Information

Systems [30]. Kou et al. [31] define them as interactive computer-based systems supporting decision-making activities. DSS, SEarch Tool for Enhanced Decision (SETED 1.0), presented in this study was developed with use of the Microsoft Visual C Sharp programming language. SETED 1.0 proposes five distinct MCDM methods, which are mentioned in the previous section, to guide the decision maker. The decision maker can get answer for any decision problem in any combination of five methods. This software uses Microsoft Excel for data input. The user has first to enter the alternatives and criterions into the Excel sheet. In this sheet, the orange cells are designed for alternatives, blue cells are designed for benefit criterions, and green cells are designed for cost criterions, respectively. After this step, SETED 1.0 creates the decision and weight matrix frames based on alternatives and criterions. Evaluations for each alternative in terms of each criterion, weights of each criterion and additional data in case PROMETHEE II is one of the chosen methods, have to be located in the frames. The user has to determine the MCDM methods that will be used at solution procedure after the matrices are filled. In case that any of the fuzzy methods is chosen to be used during the procedure, the user has to determine one of the error rates (5, 10, 15, and 20 %) to generate TFNs from the crisp numbers. After this last step, SETED 1.0 completes all computations and displays the results on the screen. According to the results displayed on the screen, the user makes his/her final decision.

4 Proposed decision support model and a case study for machining technology ranking 4.1 Proposed decision support model According to McQuade [32], laser beam and plasma arc machining methods are the most common ones. Valíček et al. [33] claim that water jet machining and abrasive water jet machining are the most rapidly improving technological methods of machining materials. Additionally, when literature is reviewed, electrochemical machining, electrical discharge machining, and wire–EDM can be classified as the most common machining technologies. Therefore, in this study, the concern is mainly focused on these machining technologies. Determination of the criteria for the proposed decision support model was done via questionnaires filled in by specialists, as well as by deep discussions with experts studying at the Faculty of Manufacturing Technologies of The Technical University of Kosice and by making use of the past studies of Sadhu and Chakraborty [8] and Das and Chakraborty [5]. This

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paper considers the following 20 criterions influencing the machining process selection decision: & & &

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& &

Operational cost: Expenses related to the operation of the machining process or to the operation of the machining device, equipment, facility, etc. Initial cost: Expenses incurred at the purchase of the facility and equipment to be used at production of goods. Technology setup: It is related to the space needed to operate the machining technology.

Fig. 3 Structure of the machining process selection decision support model

& &

Depth of thermal effect: Field in millimeters, where heat came out after the machining process. Waviness: It corresponds to the rough cutting zone of the workpiece created by the machining technology as a result of the released kinetic energy. Surface roughness: It is the texture of created surface. Vibration: It means mechanical oscillations around an equilibrium point, which are undesirable because they cause wastes of energy and create unwanted noise.

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Table 1 Decision matrix CRI./ALT.

Alternative machining processes

Data related to PROMETHEE II

LBM PAM WJM AWJM ECM EDM WIRE–EDM WEIGHTS PR.FUNC. q

s

p

Operational cost Initial cost Technology setup Depth of thermal effect Waviness Surface roughness Vibration Noise Air pollutants Radiation Safety Human health Cutting speed Simplicity of operation

4 8 8 4 5 5 3 1 2 10 1 1 9 5

3 6 6 6 4 3 2 6 8 9 1 3 9 5

2 7 5 1 6 6 4 7 1 1 5 9 6 8

2 8 5 2 7 8 6 8 1 1 8 6 7 8

4 7 7 7 2 2 7 7 5 7 7 4 6 4

4 8 6 6 3 3 7 7 5 7 7 4 8 4

6 8 6 6 2 1 7 7 5 7 7 4 6 4

8 8 6 10 8 10 8 5 7 8 8 8 10 7

1 4 3 2 4 1 3 4 2 5 6 1 5 2

– 1 – 1.5 0.5 – – 1 2.5 1.5 – – 1.5 1

– – – – – – – – – – 2.5 – – –

– 2.5 4 – 3.5 – 2.5 3 – 3.5 – – 4 –

Cutting at any spot Process control Usability/flexibility Material removal rate Reflectivity Thermal conductivity

9 5 10 3 1 1

8 6 8 4 2 1

7 7 8 7 10 10

7 7 8 8 10 10

6 5 4 4 2 5

6 5 4 3 3 5

6 5 4 3 2 5

10 5 8 10 8 10

4 6 1 5 4 3

1.5 – – 2 2 –

– 3.5 – – – –

3 – – 3 3 4

&

& & &

Noise, air pollutants, radiation, safety, and human health: They are related to the safety of the machine operators. They also consider the toxicity, machining medium contamination, and other adverse and hazardous effects of the machining process. Cutting speed: It is related to the measurement of the cutting speed in meters per minute for the machining technology. Simplicity of operation: It corresponds to the simplicity of the machining technology measured by required materials, number of personnel, education level, etc. Cutting at any spot: This criterion considers the ability of the machining technology to start or end the process at any point of the work piece.

Table 2 Determined ranks for each method

&

& & & &

Process control: This criterion considers the possibility of process control of machining technology, such as manual mode, auto mode, programmable mode, online programmable mode, etc. Usability/flexibility: This criterion considers the flexibility of cutting equipment in various conditions, such as space, temperature, mobility, etc. Material removal rate: It measures the amount of material removed from the workpiece by a particular machining process per unit of time [8]. Reflectivity: It is the fraction of electromagnetic power, which is reflected in the workpiece. Thermal conductivity: This is a physical property indicating how well heat flows through a material.

ALT./Methods

TOPSIS

ELECTRE I

PROMETHEE II

Fuzzy TOPSIS

Fuzzy ELECTRE I

LBM PAM WJM AWJM ECM EDM WIRE–EDM

3 4 1 2 6 7 5

2 2 1 3 4 5 4

3 4 1 2 5 7 6

3 4 1 2 6 7 5

2 2 1 3 4 5 4

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Figure 3 illustrates the skeleton of the proposed model, including criterions and alternatives. All criterions in the decision support model are subjective criterion, which are evaluated on a scale of 1–10 by specialists and experts in this field. Additionally, safety, human health, cutting speed, simplicity of operation, cutting at any spot, process control, usability/flexibility, and material removal rate are benefit criterions, where higher values are desired, while the remaining criterions are cost criterions, where lower values are preferred.

4.2 Application for machining technology ranking As mentioned previously, water jet machining (WJM), abrasive water jet machining (AWJM), laser beam machining (LBM), plasma arc machining (PAM), electrical discharge machining (EDM), wire–EDM, and electrochemical machining (ECM) are determined as alternative machining processes. According to Shanmugam et al. [34] in WJM technology materials are removed by the effect of a continuous stream of high-energy water. The water jet exerts machining force on the surface during the process. This force is transmitted by the water causing the cut. The process of AWJM technology is pretty much like the process of WJM with one difference. In this process, water is not the only medium acting by pressure on the surface, but instead the mixture of water with abrasives causes the cut. LBM is a thermal material removal process that uses a high-energy light beam to melt and vaporize particles on the surface of the worked material, whereas PAM is a process that uses plasma, fourth state of matter, to cut the worked material by melting it. Like LBM, EDM is a thermal process in which the material is eroded by a series of discharge sparks between the workpiece and tool electrode when they are immersed in a liquid dielectric [35]. In wire–EDM process, a thin wire as an electrode transforms electrical energy to thermal energy for cutting materials [36]. Finally, ECM process is similar in concept to EDM, but unlike EDM, no sparks occur during the process. Carbon structural steel with the width of plate of 10 mm was considered during the evaluation phase of each alternative machining process in terms of criterions. Determination of the weights concerning each criterion, error rate (10 %), and performances of alternatives in terms of each criterion was done via a questionnaire filled in by specialists, as well as by deep discussions with experts studying at the Faculty of Manufacturing Technologies of The Technical University of Kosice. The developed decision matrix is illustrated in Table 1.

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5 Conclusions The method used in manufacturing systems to meet the requirements determined for the output directly affects the output of the system. In this respect, machining processes are crucial segments of manufacturing systems in which the determination of the most appropriate machining process for the cutting operation of a specific material often seems to be a tough decision problem. In this study, ELECTRE I, TOPSIS, PROMETHEE II, as well as Fuzzy ELECTRE I and Fuzzy TOPSIS based on the hybrid DSS were used to rank alternative machining technologies for the cutting process of carbon structural steel with the width of plate of 10 mm. Additionally, a comprehensive decision support model was proposed to assist decision makers at selection of the right machining process for a specific material. The required data for the study was obtained via questionnaires given to experts and by making use of past studies. The results presented in Table 2 showed that WJM was the best alternative, while AWJM is mostly the second one; LBM and PAM are mostly the third and fourth alternatives in the rank. On the other hand, ECM and wire–EDM seem to be on the fifth and sometimes on the sixth rank in the sequence depending on the chosen application method. Finally, it seems that EDM is the worst alternative. Further researches can be performed using other fuzzy MCDM methods, which would take into consideration the influences between alternatives and criterions, such as fuzzy analytic network process. Acknowledgments This research was realized within the framework of IT4 Innovations Centre of Excellence project reg. no. CZ.1.05/1.1.00/ 02.0070 supported by the Operational Programme “Research and Development for Innovations” funded by the Structural Funds of the European Union and from the state budget of the Czech Republic and by the project RMTVC no. CZ.1.05/2.1.00/01.0040.

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