Appraisal of CNC machine tool by integrated MULTI-MOORA-IVGN circumferences: An empirical study

Abstract

Purpose - The primitive purpose of this manuscript is to develop an effective and efficient computer numerical control (CNC) machine tool evaluation index from the perspective of appraisal and benchmarking of preferred candidate machine tool in subjective information scenario. In this reporting, manager has been facilitated from the decision making tool and methodology in order to evaluate the best one and benchmarking the preferred candidate alternative machine tool under the subjective criterion circumstances. Design/methodology/approach - A MULTI-MOORA (multi-objective optimization by ratio analysis) methodology conjunction with grey number has fruitfully applied in evaluated subjective information against criterion module plate form from the prospectus of handling the vagueness, inconsistency, impreciseness and in order to appraisal and benchmarking of the candidate CNC machine tool alternatives. Findings - In today scenario, the subjective evaluation criterion has even ran over the CNC machine tool evaluation module (index) except other valuable area on account of an abatement of consistent data. The authors found out the subjective information is even necessary/mandatory to handling and tackle such an inconsistent, vagueness, impreciseness which associated uncertain criterion. So, the authors found out that the application of grey number conjunction with MULTI-MOORA decision methodology from the prospectus of appraisal and benchmarking of preferred candidate alternatives machine tool. Originality/value - The major contribution of this manuscript to exploration of grey number set conjunction with MULTI-MOORA methodology toward appraisal and benchmarking of preferred CNC candidate machine tool alternative, handled and tackled the evaluated subjective information from expert panel against subjective criterion environment, facilitates the multi-criterion decision making (MCDM) module from the prospectus of best one and ranking order the candidate machine tool alternative under the similar subjective criterion circumstances.

Full text

Translate

Turn on search term navigation

1 Introduction: computer numerical control

In today's world of emerged technology, computer numerical control (CNC) machine tool plays an important role to complete the production task to achieve the targeted goal of organization.

A CNC machine is considered as cost effective equipment that can be used to perform repetitious, difficult and unsafe manufacturing tasks with high degree of accuracy and a proper machine tool lies not only in increased production and delivery, but also in improved product quality, increased product flexibility and enhanced overall productivity ([1] Athawale and Chakraborty, 2010).

A proper machine tool selection has been very important issue for manufacturing firm due to the fact that improperly selected machine tool can negatively drop an affect the overall performance and the productivity of a manufacturing system. In addition, the outputs of manufacturing system (i.e. the rate, quality and cost) mostly depend on what kinds of machine tool selected and implemented.

CNC machines are the workhorses of the precision machining industry. CNC stands for computer numeric control. It is an industry standard programming language designed specifically for controlling high-precision mills, lathes, cutting and grinding machines. It is the progeny of the marriage between computer aided design (CAD) and computer aided machining (CAM) ( source: www.ehow.com/facts_5085202_cnc-machines.html).

CNC is an industry standard programming language designed specifically for controlling high-precision mills, lathes, cutting and grinding machines. It is the progeny of the marriage between CAD and CAM (source: www.ehow.com/facts_5085223_cnc-machines.html).

CNC is one in which the functions and motions of a machine tool are controlled by means of a prepared program containing coded alphanumeric data. CNC can control the motions of the work piece or tool, the input parameters such as feed, depth of cut, speed, and the functions such as turning spindle on/off, turning coolant on/off ( source: www.wings.buffalo.edu/...564/course-notes/cnc%20notes.pdf).

In today's world of emerged technology, the creation of problems of evaluation of most feasible CNC machine tool among numerous number of available choice has been become a critical factor to enhancing the effective utilization of resources, increase productivity and improve system flexibility. The evaluation of most feasible machine tool among the alternatives is a multi-criteria decision making (MCDM) problem.

MCDM is concerned with structuring and solving decision and planning problems involving multiple criteria. The purpose is to support decision makers (DMs) facing such problems. Typically, there does not exist a unique optimal solution for such problems and it is necessary to use DM's preferences to differentiate between solutions. Solving can be interpreted in different ways. It could correspond to choosing the "best" alternative from a set of available ( source: alternatives http://en.wikipedia.org/wiki/Multi-criteria_decision_analysis).

Benchmarking is a process of measuring and comparing to assessing the alternative under the same circumferences ([18] Keehley et al. , 1997). But the selection of best CNC machine tool alternatives are a MCDM problem, which consider the numerous numbers of subjective indices or criteria which entitled the uncertainty, incomplete information, vagueness, impreciseness. So, in such a situation, interval-value grey number is employed which deal with incomplete information, vagueness and helps to select the best alternative among all available alternatives. The purpose of this research is to develop decision making module for CNC machine tool benchmarking, appraisement and assessment from the perspectives to select the best choice from all available choice.

2 Literature review

[2] Duran and Aguilo (2008) proposed analytic hierarchical process (AHP) based on fuzzy numbers multi-attribute method for the evaluation and justification of an advanced manufacturing system. Finally, an example of machine tool selection is used to illustrate and validate the proposed approach. [3] Abdi (2009) explained the rationale for the development of reconfigurable manufacturing systems (RMS), which possess the advantages both of dedicated lines and of flexible systems. [4] Chuu (2009) proposed a new fusion method of fuzzy information to managing the information assessed in different linguistic scales (multi-granularity linguistic term sets) and numerical scales. The flexible manufacturing system adopted in the Taiwanese bicycle industry to demonstrate the computational process of the proposed method.

[5] Liu and Wang (2011) proposed a multiple attribute group decision making (MAGDM) problems in which the attribute weights and attribute values take the form of the generalized interval-valued trapezoidal fuzzy numbers, and introduced a new group decision making analysis method. [6] Korena and Shpitalni (2010) defined the core characteristics and design principles of RMS and described the structure recommended for practical RMS with RMS core characteristics. After that, a rigorous mathematical method is introduced for designing RMS with this recommended structure. [7] Ayag and Ozdemir (2012) introduced modified TOPSIS and the analytical network process (ANP) to present a performance analysis on machine tool selection problem. The ANP method is explored to determine the relative weights of a set of three valuation criteria and the modified TOPSIS method is utilized to rank competing machine tool alternatives in terms of their overall performance.

[8] Chakraborty (2011) explored the application of multi-objective optimization on the basis of ratio analysis (MOORA) method to solve different decision making problems as frequently encountered in the real-time manufacturing environment. Six decision making problems has been solved the obtained results proved the applicability, potentiality, and flexibility of this method while solving various complex decision making problems in present day manufacturing environment. [9] Gadakh (2011) applied MOORA method for solving multiple criteria (objective) optimization problem in milling process. Six decision making problems which include selection of suitable milling process parameters in different milling processes are considered, the obtained results almost match with those derived by the previous researchers which prove the applicability, potentiality, and flexibility of this method in manufacturing environment. [10] Kalibatas and Turskis (2008) explored multi-objective optimization by ratio analysis (MOORA) to solving the inner climate problems. The factors causing the deviation from the standards are identified and rational dwelling alternatives are examined for chosen from the available options.

[11] Kracka et al. (2010) proposed MULTI-MOORA method for assessment of opportunities for construction enterprises in European Union member states. A theory of dominance compared three parts: the ratio system, the reference point and the full multiplicative form and resulted the, countries were ranked according to suitability of their environment for business. [12] Kildiene (2013) applied the MOORA method in construction in order to solve problems related to energy loss in heating buildings. The aimed of his research is to create a technique for the selection of external walls and windows of buildings.

Grey analysis uses a specific concept of information. It defines situations with no information as black, and those with perfect information as white. However, neither of these idealized situations ever occurs in real world problems. In fact, situations between these extremes are described as being grey, hazy or fuzzy. Therefore, a grey system pointed out that a system in which part of information is known and part of information is unknown ( source: http://en.wikipedia.org/wiki/Grey_relational_analysis).

[19] Stanujkic et al. (2012) presented an algorithm by extended the MOORA method for solving decision making problems with interval data to determine the most preferable alternative among all possible alternatives, when performance ratings are given as intervals.

In this research work, we adopted the subjective indices (index) in order to evaluate appraisal and benchmarking of preferred candidate machine tool in subjective information scenario. We followed the average fuzzy rule to aggregated the final priority rating assessed by expert panel against subjective indices/criterion and weights (significant factor) has also evaluated in form of script value via the subjective assessment of experts team and finally we explored the MULTI-MOORA methodology in the proposed evaluation decision module (subjective index) for appraisal and benchmarking to respective candidate alternative CNC machine tool. The result has been summarized the ranking orders provided by different parts of MULTI-MOORA, namely the ratio system, the reference point, finally, a case study has led in order to point out the effectiveness, efficiency and validly of proposed methodology for subjective index (module).

3 Methodology

3.1 Theory of grey numbers: mathematical basis

Grey theory has become a very effective method of solving uncertainty problems under discrete data and incomplete information. Grey theory has now been applied to various areas such as forecasting, system control, and decision making and computer graphics. Here, we give some basic definitions regarding relevant mathematical background of grey system, grey set and grey number in grey theory ([20] Deng, 1982).

Definition 1

A grey system ([55] Xia, 2000) is defined as a system containing uncertain information presented by grey number and grey variables. The concept of grey system is shown in Figure 1 [Figure omitted. See Article Image.].

Definition 2

Let X be the universal set. Then a grey set G of X is defined by its two mappings: Equation 1 [Figure omitted. See Article Image.] μ¯_G (x )>μ_G (x ), x ∈X , X =R , μ¯_G (x ) and μ_G (x ) are the upper and lower membership functions in G , respectively. When μ¯_G (x )=μ_G (x ), the grey set G becomes a fuzzy set. It shows that grey theory considers condition of fuzziness and can flexibly deal with the fuzziness situation.

Definition 3

A grey number is one of which the exact value is unknown, while the upper and/or the lower limits can be estimated. Generally grey number is written as (⊗G =G |_μ^μ¯ ).

Definition 4

If only the lower limit of G can be possibly estimated and G is defined as lower limit grey number: Equation 2 [Figure omitted. See Article Image.]

Definition 5

If only the upper limit of G can be possibly estimated and G is defined as lower limit grey number: Equation 3 [Figure omitted. See Article Image.]

Definition 6

If the lower and upper limits of G can be estimated and G is defined as interval grey number: Equation 4 [Figure omitted. See Article Image.]

Definition 7

The basic operations of grey numbers ⊗x₁ =[x₁ ,x¯₁ ] and ⊗x₂ =[x₂ ,x¯₂ ] can be expressed as follows: Equation 5 [Figure omitted. See Article Image.]

Whitened value

The whitened value of an interval grey number, ⊗x , is a deterministic number with its value lying between the upper and lower bounds of interval ⊗x . For a given interval grey number ⊗x =[x ,x¯ ] the whitened value x₍_λ₎ can be determined as follows ([26] Datta et al. , 2013): Equation 6 [Figure omitted. See Article Image.] Here, λ as whitening coefficient and λ ∈[0,1]. Because of its similarity with a popular λ function formula (6) is often shown in the following form: Equation 7 [Figure omitted. See Article Image.] For λ =0.5 formula (7) gets the following form: Equation 8 [Figure omitted. See Article Image.]

Signed distance

Let ⊗x₁ =[x₁ ,x¯₁ ] and ⊗x₂ =[x₂ ,x¯₂ ] be two positive interval grey numbers. Then, the distance between ⊗x₁ and ⊗x₂ can be calculated as signed difference between its centers ([27] Sahu et al. , 2012) is shown below: Equation 9 [Figure omitted. See Article Image.]

3.2 The MOORA method

MOORA method is introduced by [13] Brauers and Zavadskas (2006) on the basis of previous researches ([51], [52] Brauers, 2004a, b). The method starts with a matrix of responses of different alternatives on different objectives: Equation 10 [Figure omitted. See Article Image.] Here, x_ij as the response of alternative j on objective or attribute i ; i =1,2, ... ,n ; as the objectives or the attributes; and j =1,2, ... ,m as the alternatives.

The MOORA method consists of two parts: the ratio system and the reference point approach [14] (Brauers and Zavadskas, 2010).

The ratio system approach of the MOORA method

[13] Brauers and Zavadskas (2006) proved that the most robust choice for denominator is the square root of the sum of squares of each alternative per objective, and therefore the use of vector normalization method is recommended in order to normalize responses of alternatives. As a result, the following formula: Equation 11 [Figure omitted. See Article Image.] Here, x_ij as the response of alternative j on objective or attribute i ; j =1,2, ... ,m ; m the number of alternatives; i =1,2, ... ,n ; n the number of objectives; x_ij^* as normalized response of alternative j on objective i ; and x_ij^* ∈[0,1].

For optimization based on the ratio system approach of MOORA method, normalized responses are added in case of maximization and subtracted in case of minimization, which can be expressed by the following formula: Equation 12 [Figure omitted. See Article Image.] Here, x_ij^* as normalized response of alternative j on objective i ; i =1,2, ... ,g ; as the objectives to be maximized; i =g +1, g +2, ... ,n ; as the objectives to be minimized j =1,2, ... ,m ; as the alternatives; and y_j^* as the overall ranking index of alternative jy_j^* ∈[-1,1].

After that, the optimal alternative based on the ratio system part A_RS^* can be determined using the following formula: Equation 13 [Figure omitted. See Article Image.]

The reference point approach of the MOORA method

The reference point approach of the MOORA method is based on the ratio system and starts from already normalized responses of alternatives, obtained by formula (11). After considering the most important reference point metrics ([13], [14] Brauers and Zavadskas, 2006, 2010; [53] Brauers et al. , 2008) emphasized that the min-max metric is the best choice among all of them. Therefore, for optimization based on the reference point approach, [13] Brauers and Zavadskas (2006) proposed the following formula: Equation 14 [Figure omitted. See Article Image.] Here, r_i as i th coordinate of the reference point; x_ij^* as the normalized response of alternative j on objective i ; i =1,2, ... ,n ; as the objectives; and j =1,2, ... ,m ; as the alternatives.

For further simpler presentations, we will mark distance from an alternative to the reference point with d and therefore formula (14) gets the following form: Equation 15 [Figure omitted. See Article Image.] where: Equation 16 [Figure omitted. See Article Image.] and: Equation 17 [Figure omitted. See Article Image.] Here, x_ij^* as the normalized response of alternative j on objective i ; r_i as i th coordinate of the reference point; d_ij as unsigned distance of alternative j to the i th coordinate of reference point; i =1,2, ... ,n ; as the objectives; and j =1,2, ... ,m as the alternatives.

Based on the reference point approach of the MOORA method, the optimal alternative A_RP^* can be determined using the following formula: Equation 18 [Figure omitted. See Article Image.]

3.3 The importance given to objectives

When solving real-world problems using MCDM methods, objectives do not always have the same importance, i.e. some objectives are more important than the others. In order to give more importance to an objective, it could be multiplied with a significance coefficient ([24] Brauers and Ginevicius, 2009). Importance given to objectives has influence on ratio system and reference point approach of the MOORA method. In the ratio system approach importance given to objectives is included by modifying formula (12) which gets the following form: Equation 19 [Figure omitted. See Article Image.] Here, s_i as significance coefficient of objective i ; i =1,2, ... ,g ; as the objectives to be maximized; i =g +1,g +2, ... ,n ; as the objectives to be minimized; j =1,2, ... ,m ; as the alternatives; and y¨_j^* as the overall ranking index of alternative j with respect to all objectives with significance coefficients, y¨_j^* ∈[-1,1].

After that, formula (13) still remains to determine the most appropriate alternative based on ratio system approach of the MOORA method.

As the most effective way to include importance given to objectives into reference point approach of the MOORA method, [19] Stanujkic et al. (2012) proposed to adopt formula (16), which after adoption gets the following form: Equation 20 [Figure omitted. See Article Image.] Here, s_i as significance coefficient of objective i ; x_ij^* as the normalized response of alternative j on objective i ; r_i as i th coordinate of the reference point; d_ij as distance of alternative j to the i th coordinate of reference point; i =1,2, ... ,n ; as the objectives; and j =1,2, ... ,m ; as the alternatives.

After that, formula (18) still remains without changes for determining the most appropriate alternative based on the reference point approach of the MOORA method.

3.4 The grey MOORA

The procedure of selecting the most appropriate alternative using the MOORA method involves several important stages that should be considered before an extension of the MOORA method with interval grey numbers, and these are:

- Stage 1: transforming responses of alternatives into dimensionless values;

- Stage 2: determining overall ranking indexes for considered alternatives based on ratio system part of MOORA method; and

- Stage 3: determining distances between considered alternatives and reference point based of the reference point part of MOORA method.

3.4.1 Stage 1: transformation into dimensionless values

For the normalization of responses of alternatives expressed in the form of interval numbers ([25] Jahanshahloo et al. , 2006), suggested the use of the following formula: Equation 21 [Figure omitted. See Article Image.] Formula (21) provides the appropriate form for normalizing responses of alternatives expressed by interval grey numbers. However, in cases of multi-criteria optimizations which require simultaneously the use of crisp and interval grey numbers, the previously mentioned formula give unsatisfactory results. Therefore, we suggest the use of the following formula: Equation 22 [Figure omitted. See Article Image.] Based on formula (22), upper and lower bounds of an interval grey number can be determined using the following formulae: Equation 23 [Figure omitted. See Article Image.] Equation 24 [Figure omitted. See Article Image.]

3.4.2 Stage 2: determining overall ranking index based on ratio system approach of the MOORA method

For optimization based on the ratio system part of the MOORA method we start from the formula: Equation 25 [Figure omitted. See Article Image.] where: Equation 26 [Figure omitted. See Article Image.] Equation 27 [Figure omitted. See Article Image.] Here, y_j^* as the overall ranking index of alternative j ; y_j⁺ and y_j^- as total sums of maximizing and minimizing responses of alternative j to objectives, respectively; s_i as significance coefficient of objective i ; x_ij^* and ⊗x_ij^* ... as the normalized responses of alternative j on different objectives, which are expressed in the form on crisp or interval grey numbers; Ω_C⁺ and Ω_G⁺ assets of objectives to be maximized expressed in the form on crisp or interval grey numbers; Ω_C^- and Ω_G^- are sets of objectives to be minimized expressed in the form on crisp or interval grey numbers. By replacing formulas (26) and (27) in formula (25), we get the following formula: Equation 28 [Figure omitted. See Article Image.] Based on formulas (28), (7) and (9) we get the final and complete formula form: Equation 29 [Figure omitted. See Article Image.] Here, s_i as significance coefficient of objective i ; x_ij^* as the normalized responses of alternative j on objective i and i ∈Ω_C ; x_ij^* and x¯_ij^* as the normalized bounds of interval grey number which represents response of alternative j on objective i and i ∈Ω_G , respectively; Ω_C and Ω_G as sets of objectives expressed in the form of crisp or interval grey numbers, respectively; λ as the whitening coefficient; y_j^* as the overall ranking index of alternative j ; Ω_C⁺ and Ω_G⁺ as sets of objectives to be maximized expressed in the form on crisp or interval grey numbers; Ω_C^- and Ω_G^- are sets of objectives to be minimized expressed in the form on crisp or interval grey numbers; i =1,2, ... ,n ; as the objectives; and j =1,2, ... ,m ; as the alternatives.

In the case of solving complex real-world problems that require simultaneous use of crisp and interval grey numbers, formula (29) provides adequate ability to rank and select the most appropriate alternative.

In the case of solving well-structured problems, the second part of formula (29) which includes the impact of objectives whose responses are expressed using interval grey numbers, has no influence on ranking index and therefore formula (29) can be transformed into following forms: Equation 30 [Figure omitted. See Article Image.] Equation 31 [Figure omitted. See Article Image.] When objectives have different significances. Formulae (30) and (31) have the same meanings as formulae (12) and (19), respectively, in original MOORA method.

On the other hand, in the case of solving semi-structured problems, the first part of formula (29) which represents the impact of objectives whose responses are expressed using crisp numbers, has no influence to the overall ranking index and therefore it can be transformed into one of three following forms:

When objectives have the same significance: Equation 32 [Figure omitted. See Article Image.]

When the DM has no preferences (λ =0.5): Equation 33 [Figure omitted. See Article Image.]

When the DM has no preference and objectives have the same significance: Equation 34 [Figure omitted. See Article Image.]

During problem solution, i.e. ranking of alternatives, the attitude of the DMs can lie between pessimistic and optimistic, and the whitening coefficient λ , allows expression of DMs degree of optimism or pessimism.

In the cases of particularly expressed optimism, the whitening coefficient λ , in accordance with formula (7), takes higher values (λ [arrow right]1) and ranking order of alternatives is mainly based on the upper bounds of intervals with which overall response of each alternative is expressed, y_j₍_λ₌₁₎ =y¯_j^* . On the other hand, in the cases of particularly expressed pessimism, the whitening coefficient λ takes lower values (λ [arrow right]0) and ranking order of alternatives is mainly based on lower bounds of the intervals, y_j₍_λ₌₀₎ =y¯_j^* .

3.4.3 Stage 3: determining overall ranking index based on reference point approach of the MOORA method

The most appropriate alternative based on the reference point approach of the MOORA method when ratings of alternatives are expressed using exact values can be obtained by formula (15). However, this formula should be adopted in cases when the reference point approach of the MOORA method is used to solve complex real-world problems. To explain our approach in details, we start from the min-max metric expressed by the formula: Equation 35 [Figure omitted. See Article Image.] Here, d_ij as distance of alternative j to the i th coordinate of reference point.

In the course of solving many complex real-world problems, responses to the objectives are simultaneously expressed using crisp and interval grey numbers. In this case, the reference point cannot be expressed adequately with "simple" point in n -dimensional space. We believe that the reference grey point is a more appropriate solution, where coordinates of grey reference point may be crisp or interval grey numbers, depending on type of values which is used to express ratings of alternatives to the corresponding objectives. Therefore, for determining d_ij and r_i for objective i in different cases, [19] Stanujkic et al. (2012) proposed the following.

For objective i with crisp responses, the correspondent coordinate of the reference grey point is calculated using formula (17) and distance to the reference point using formula (16) or (20) when objectives have different significances.

For objectives whose responses are expressed using interval grey numbers formulae are more complex, especially when DMs have opportunity to express their attitudes about optimism or pessimism. For these reasons, we start from the following formulae: Equation 36 [Figure omitted. See Article Image.] Equation 37 [Figure omitted. See Article Image.] When objectives have different significances, where: Equation 38 [Figure omitted. See Article Image.] Equation 39 [Figure omitted. See Article Image.] Here, λ as whitening coefficient; d_ij and d¯_ij as distances of alternative j to the i th coordinate of reference grey point; s_i as significance coefficient of objective i ; i =1,2, ... ,n ; as the objectives; and j =1,2, ... ,m ; as the alternatives.

Every coordinate of reference grey point is represented by appropriate interval grey numbers which bounds are determined by using the following formulae: Equation 40 [Figure omitted. See Article Image.] Equation 41 [Figure omitted. See Article Image.] Depending on DMs' preferences, i.e. whitening coefficient value, formulae (36) and (37) may have the following specific forms:

- In the case of extremely pessimistic DM attitude (λ =0): Equation 42 [Figure omitted. See Article Image.]

- In the case of moderate optimism or when the DM has no preference (λ =0.5): Equation 43 [Figure omitted. See Article Image.]

- Finally, in the case of extremely optimistic DM attitude (λ =1): Equation 44 [Figure omitted. See Article Image.]

4 Empirical research

The lathe CNC machine tool evaluation first level index platform has been shown in Table I [Figure omitted. See Article Image.] and flow chart for evaluation of feasible CNC machine tool has been shown in Figure 2 [Figure omitted. See Article Image.]. The decision making model consists of various CNC machine tool selection indices such as productivity (C ₁ ), precision (C₂ ), reliability (C₃ ), product quality (C₄ ), ergonomical aspect (C₅ ) for judging the most feasible alternative machine tool. The model considered the subjective measures indices C₁ , C₂ , C₃ , C₄ and C₅ are beneficial in nature.

Assume that there are four alternative industries. Our objective is to select that alternative where all the indices drop the positive impact with respect to achieving overall goal of organization. [19] Stanujkic et al. (2012) approached a MULTI-MOORA combined with interval-valued grey numbers set (IVGNS) has been explored in perceptive to evaluate the best CNC machine tool alternative.

Assume that a committee of ten DMs (expert group) such as DM1, DM2, DM3, DM4 DM5, DM6, DM7, DM8, DM9, and DM10 has been constructed from academicians, manager of production unit, marketing unit, material purchasing unit and his/her team. Also, there are four alternative machine tool such as A ₁ , A₂ , A₃ , and A₄ . The procedural steps and its implementation results have been summarized as follows.

4.1 Procedural steps

Step 1: gathering information from the expert group in relation to performance rating and importance weights of different evaluation measures/metrics

For evaluating importance weights of CNC machine tool measures/indices for measuring CNC machine tool alternatives. A committee (expert group) of DMs has been formed. The pre-assumed values of priority weight, i.e. the significance extent against individual evaluation indices: C ₁ , C₂ , C₃ , C₄ , and C₅ , are as 0.20, 0.19, 0.17, 0.21 and 0.23, respectively; which have been set by the top management of the enterprise. The expert group has been instructed to express their opinion regarding performance ratings against individual evaluation indices: C₁ , C₂ , C₃ , C₄ , and C₅ , in terms of their subjective preferences (evaluation score) via linguistic terms (Table II [Figure omitted. See Article Image.]), which have been further transformed into interval value grey number. The appropriateness rating (in linguistic terms) against evaluation indices/measures assigned by the DMs have been furnished (Table III [Figure omitted. See Article Image.]), for alternative A ₁ , A₂ , A₃ and A₄ , respectively.

Step 2: normalization

In order to eliminate the impact of different physical dimension to the decision making result, the decision making information is to be normalized. The normalization method basically preserves the property that the ranges of normalized interval-valued grey numbers belong to [0, 1]. Normalization has been carried out by employing equations (22)-(24). The normalized matrix has been found out for evaluating the performance of various indices/measures.

Step 3: the ratio system

The ratio system, the normalized values has been added using (equation (33)), the results are shown in Table IV [Figure omitted. See Article Image.]. In this computation priority weight of individual evaluation measures C₁ , C₂ , C₃ , C₄ , and C₅ (0.20, 0.19, 0.17, 0.21, and 0.23) have been assessed by DM (Figure 3 [Figure omitted. See Article Image.]).

Step 4: reference point approach

Using the normalized values (equations (37)-(41)), coordinates of reference grey point and distances of alternatives (Figure 4 [Figure omitted. See Article Image.]) to reference grey point have been obtained for λ =0, 0.5, 1 (Table V [Figure omitted. See Article Image.]).

5 Managerial implification

Decision making is a tool which provides the support to manager to evaluate the optimum machine tool from the perceptive of enhancing productivity, profit and other goal of organization for long time. The choice of appropriate CNC machine tool choice is a complicated task due to the presence of multiple subjective indices. Which deal with the subjective information which is assessed by group of DM to select alternative in uncertain environment. It is often experienced that evaluation most of the evaluation criterions are subjective in nature. Subjective evaluation information cannot be analyzed mathematically unless and until they are converted into fuzzy/grey numbers. So, grey number facilitate to DM to select the alternative under the incomplete information environment. Here, the grey MULTI-MOORA methodology is effectively and efficiently dealing with uncertain information (e.g. linguistic variables assessed by DMs). Application of this method helped the managers to choose the best alternatives among available alternatives in real-time for organization (Table VI [Figure omitted. See Article Image.]).

Conclusion

This paper began with an emphasis on the need for an effective and efficient CNC machine tool selection. It went further to highlight the benefits accruable from the exploration of a grey interval-valued grey numbers (GIVGN) in CNC machine tool selection and provided multiple-criteria single level appraisement modeling for selection of best CNC machine choice from available choice. This research explored an interval-valued grey set theory combined with MULTI-MOORA method to facilitate solution of multiple indices appraisement plate form in decision making environment. The theory of dominance ([15] Brauers et al. , 2011) has been applied in the proposed evaluation model which summarized the ranking orders provided by different parts of MULTI-MOORA, namely the ratio system, the reference point, finally, the result revealed the most suitable alternative in perceptive of best effective CNC machine tool selection. A case study has showed to point out the effectiveness of methodology:

- exploration of grey number set conjunction with MULTI-MOORA methodology toward appraisal and benchmarking of preferred CNC candidate machine tool alternative;

- handled and tackled the evaluated subjective information from expert panel against subjective criterion environment; and

- facilitated the MCDM module from the prospectus of best one and ranking order the candidate machine tool alternative under the similar subjective criterion circumstances.

References

1. Athawale, V.M. and Chakraborty, S. (2010), "A TOPSIS method-based approach to machine tool selection", Proceedings of the 2010 International Conference on Industrial Engineering and Operations Management, Dhaka, Bangladesh, 9-10 January.

2. Duran, O. and Aguilo, J. (2008), "Computer-aided machine-tool selection based on a fuzzy-AHP approach", International Journal of Expert Systems with Applications, Vol. 34 No. 3, pp. 1787-1794.

3. Abdi, M.R. (2009), "Fuzzy multi-criteria decision model for evaluating reconfigurable machines", International Journal of Production Economics, Vol. 117 No. 1, pp. 1-15.

4. Chuu, J.S. (2009), "Selecting the advanced manufacturing technology using fuzzy multiple attributes group decision making with multiple fuzzy information", International Journal of Computers & Industrial Engineering, Vol. 57 No. 3, pp. 1033-1042.

5. Liu, P. and Wang, M. (2011), "Extended VIKOR method for multiple attribute group decision making based on generalized interval-valued trapezoidal fuzzy numbers", International Journal of Scientific Research and Essays, Vol. 6 No. 4, pp. 766-776.

6. Korena, Y. and Shpitalni, M. (2010), "Design of reconfigurable manufacturing systems", International Journal of Manufacturing Systems, Vol. 29 No. 4, pp. 130-141.

7. Ayag, Z. and Ozdemir, G.R. (2012), "Evaluating machine tool alternatives through modified TOPSIS and alpha-cut based fuzzy ANP", International Journal of Production Economics, Vol. 140 No. 2, pp. 630-636.

8. Chakraborty, S. (2011), "Applications of the MOORA method for decision making in manufacturing environment", International Journal of Advanced Manufacturing Technology, Vol. 54 No. 9, pp. 1155-1166.

9. Gadakh, V.S. (2011), "Application of MOORA method for parametric optimization of milling processes", International Journal of Applied Engineering Research, Vol. 1 No. 4.

10. Kalibatas, D. and Turskis, Z. (2008), "Multi-criteria evaluation of inner climate by using MOORA method", Information Technology and Control, Vol. 37 No. 1.

11. Kracka, M., Brauers, W.K.M. and Zavadskas, E.K. (2010), "Ranking heating losses in a building by applying the MULTIMOORA", Inzinerine Ekonomika - Engineering Economics, Vol. 21 No. 4, pp. 352-359.

12. Kildiene, S. (2013), "Assessment of opportunities for construction enterprises in European Union member states using the MULTIMOORA method", 11th International Conference on Modern Building Materials, Structures and Techniques (MBMST), Procedia Engineering, Vol. 57, pp. 557-564.

13. Brauers, W.K.M. and Zavadskas, E.K. (2006), "The MOORA method and its application on privatization in a transition economy", Control and Cybernetics, Vol. 35 No. 2, pp. 445-469.

14. Brauers, W.K.M. and Zavadskas, E.K. (2010), "Project management by MULTIMOORA as an instrument for transition economies", Technological and Economic Development of Economy, Vol. 16 No. 1, pp. 5-24.

15. Brauers, W.K.M., Balezentis, A. and Balezentis, T. (2011), "MULTIMOORA for the EU member states updated with fuzzy number theory", Technological and Economic Development of Economy, Vol. 17 No. 2, pp. 259-290.

18. Keehley, P., Medlin, S., MacBride, S. and Longmire, L. (1997), Benchmarking for Best Practices in the Public Sector, Jossey-Bass, San Francisco, CA.

19. Stanujkic, D., Magdalinovic, N., Jovanovic, R. and Stojanovic, S. (2012), "An objective multi-criteria approach to optimization using MOORA method and interval grey numbers", Technological and Economic Development of Economy, Vol. 18 No. 2, pp. 331-363.

20. Deng, J.L. (1982), "Control problems of grey system", System and Control Letters, Vol. 5, pp. 288-294.

24. Brauers, W.K.M. and Ginevicius, R. (2009), "Robustness in regional development studies: the case of Lithuania", Journal of Business Economics and Management, Vol. 10 No. 2, pp. 121-140.

25. Jahanshahloo, G.R., Lotfiand, F.H. and Izadikhah, M. (2006), "An algorithmic method to extend TOPSIS for decision-making problems with interval data", Applied Mathematics and Computation, Vol. 175 No. 2, pp. 1375-1384.

26. Datta, S., Sahu, N.K. and Mahapatra, S.S. (2013), "Robot selection based on grey-MULTIMOORA approach", Grey Systems: Theory and Application, Vol. 3 No. 2, pp. 201-232.

27. Sahu, N.K., Datta, S. and Mahapatra, S.S. (2012), "Establishing green supplier appraisement platform using grey concepts", Grey Systems: Theory and Application, Vol. 2 No. 3, pp. 395-418.

51. Brauers, W.K.M. (2004a), "Multi-objective optimization for facilities management", Journal of Business Economics and Management, Vol. 5 No. 4, pp. 173-182.

52. Brauers, W.K.M. (2004b), Optimization Methods for a Stakeholder Society: A Revolution in Economic Thinking by Multi-Objective Optimization, Vol. 73, Kluwer Academic Publishers, Dordrecht.

53. Brauers, W.K.M., Zavadskas, E.K., Peldschus, F. and Turskis, Z. (2008), "Multi-objective optimization of road design alternatives with an application of the MOORA method", Proc. of the 25th Int. Sym. on Automation and Robotics in Construction, Lithuania, pp. 541-548.

54. Qi, J. (2010), "Machine tool selection model based on fuzzy MCDM approach", International Conference on Intelligent Control and Information Processing, China, pp. 282-285.

55. Xia, J. (2000), Grey System Theory to Hydrology, Huazhong University of Science and Technology Press, Wuhan.

Appraisal of CNC machine tool by integrated MULTI-MOORA-IVGN circumferences: An empirical study

Content area

Abstract

Full text