Selection of Best Intelligent Manufacturing System (IMS) Under Fuzzy Moora Conflicting MCDM Environment

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Selection of Best Intelligent Manufacturing System (IMS)

Under Fuzzy Moora Conflicting MCDM Environment

Uttam Kumar Mandal

, Bijan Sarkar

1_{Department of Production Engineering, National Institute of Technology, Agartala, India} 2_{Department of Production Engineering, Jadavpur University, Kolkata, India}

Abstract: The selection decisions are complex, as intelligent manufacturing system selection is more challenging today. There is a need for simple, systematic, and logical methods or mathematical tools to guide decision makers in considering a number of selection attributes and their interrelations and in making right decisions. Although a large number of mathematical approaches are now available to evaluate, select and rank the alternative intelligent manufacturing system for a given engineering application, this paper explores the applicability and capability of Multi-objective optimization on the basis of ratio analysis (MOORA) method for as intelligent manufacturing system selection. The MOORA method based on ratio analysis and dimensionless measurement will accomplish the job of ranking the intelligent manufacturing system in a non-subjective way. Furthermore, the method uses fuzzy logic to convert the qualitative attributes into the quantitative attributes.

Keywords—Intelligent Manufacturing System (IMS), MOORA Method, AHP and Fuzzy Numbers.

I. INTRODUCTION

Recently, many efforts have been made to develop advanced manufacturing systems that provide rapid response and dynamic reconfigurable structures to facilitate flexible and efficient use of manufacturing resources in rapidly changing environments. Using computational intelligence features such systems are known as intelligent manufacturing systems (IMS).

IMS is a system which improves productivity by systematizing the intellectual aspect involved in manufacturing and flexibility by integrating the entire range of corporate activities (from order booking through design, production, and marketing) so as to foster the optimum in the relationship between men and intelligent machines An intelligent manufacturing process has the ability to self-regulate and/or self-control to manufacture the product within the design specifications.

The different manufacturing systems are Lean manufacturing system (A1), Agile manufacturing system

(A2), Le-agile manufacturing system (A3), Flexible

manufacturing system (A4), Computer integrated

manufacturing system (A5), Holonic manufacturing system

(A6), Bionic manufacturing system (A7), and Fractal

manufacturing system (A8). Lean concepts work well

where demand is relatively stable and hence predictable and where variety is low.

Conversely, in those contexts where demand is volatile and the customer requirement for variety is high, a much higher level of agility is required. Leanness may be an element of agility in certain circumstances, but it will not enable the organization to meet the precise needs of the customers more rapidly. „„Lean‟‟ works best in high volume, low variety and predictable environments..

Agility is being defined as the ability of an organization to respond rapidly to changes in demand, both in terms of volume and variety. The lean and agile paradigms though distinctly different, can be and have been combined within successfully designed and operated total supply chains. „„Agility‟‟ is needed in less predictable environments where demand is volatile and the requirement for variety is high.

The agility and leanness depends upon the total supply chain strategy, particularly considering market knowledge, via information enrichment, and positioning of the de-coupling point. Combining agility and leanness in one Supply Chain via the strategic use of a de-coupling point has been termed „„le-agility‟‟. Therefore le-agile is the combination of the lean and agile paradigms within a total supply chain strategy by positioning the decoupling point so as to best suit the need for responding to a volatile demand downstream yet providing level scheduling upstream from the market place.

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CIM is the designation used to describe the complete automation of the factory by integration of business and manufacturing functions through application of technology. All of the processes and activities are controlled in a hierarchy of computer systems and the information that circulates is exclusively in the digital form. However the planning and scheduling of tasks are centralized and the production are almost sequential. A CIM system implicates high investments, long lead times and complex structures that can take us to the generation of rigid systems.

The fractal concepts have origins in mathematics and theory of chaos and indicate new ideas to handle with the inflexibility and rigidity of the actual organizations. The fractal manufacturing system is an open system, and the main characteristic is the self-similarity between their small components, known as fractal entities or fractal units.

The word „bionic‟ is a combination formed from biology and electronic. Bionics is the application of methods and systems found in nature to the new technology systems. The biological life originates the bionic theory applied to the manufacturing systems. The structures and behavior observed in live beings from the cell level to the biological beings (plants, animal, etc) it is applicable to enterprises. The BMS make a parallelism among these biological characteristics and the essential needs for the futures production systems.

The holonic manufacturing theory grew from concepts developed by the philosopher Arthur Koestler when trying to define the hybrid nature of the structures of living organisms and social groups. He proposed the term Holon based on the Greek word holos (whole) and the suffix on

(part). The main goal is to reach an intelligent manufacturing system that deals to continuous market changes that require expressive changes in the production system; i.e. systems that can adapt to the new situation easier than a competing system, gaining benefit from this:

 Adapting faster than the competition gives a higher benefit in using new opportunities,

 Having a lower cost/effort for adaptation allows profiting from smaller, temporal opportunities.

Keeping in view of the above research works on manufacturing selection, a novel decision making method is proposed in this paper for manufacturing selection for a given intelligent manufacturing system.

The aim of the present paper is to propose a novel MOORA method to deal with the manufacturing system selection problems considering both qualitative and quantitative attributes. A ranked value judgment on a fuzzy conversion scale for the qualitative attributes is introduced. The proposed method helps the decision maker to arrive at a decision based on either the objective weights of importance of the attributes or his/her subjective preferences or considering both the objective weights and the subjective preferences.

II.MULTI-OBJECTIVE OPTIMIZATION ON THE BASIS OF

RATIO ANALYSIS (MOORA)METHOD

Multi-objective optimization (or programming), also known as multi-criteria or multi attribute optimization, is the process of simultaneously optimizing two or more conflicting attributes (objectives) subject to certain constraints. The MOORA method, first introduced by Brauers (2004) is such a multi-objective optimization technique that can be successfully applied to solve various types of complex decision making problems in the manufacturing environment. The MOORA method (Brauers, et al. 2006, 2008, 2009, Kalibatas, et al. 2008, Lootsma, 1999) starts with a decision matrix showing the performance of different alternatives with respect to various attributes (objectives).

Step 1: The first step is to determine the objective, and to identify the pertinent evaluation attributes.

Step 2: The next step is to represent all the information available for the attributes in the form of a decision matrix. The data given in equation (1) are represented as matrix Xmxn. Where xij is the performance measure of i th alternative on j th attribute, m is the number of alternatives, and n is the number of attributes. Then a ratio system is developed in which each performance of an alternative on an attribute compared alternatives is concerning that attribute.

Develop the initial decision matrix, X.

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Where xij is the performance value of ith alternative on jth criterion, m is the number of alternatives compared and n is the number of criteria.

The decision table, given in Table 3, shows alternatives, Ai (for i = 1, 2, . . . , n), attributes, Bj (for j = 1, 2, . . . , m), weights of attributes, wj (for j = 1, 2, . . . , m) and the measures of performance of alternatives, xij (for i = 1, 2, . . . , n; j = 1, 2, . . . , m). Given the decision table information and a decision making method, the task of the decision maker is to find the best alternative and/or to rank the entire set of alternatives.

Table-3: Multi-attribute decision matrix table

Identify the selection attributes for the considered manufacturing selection problem and short-list the manufacturing system on the basis of the identified attributes satisfying the requirements. The attributes are of two types, beneficial (i.e. higher values are desired) and non-beneficial (i.e. lower values are desired).

Step 3: Brauers et al. (2008) concluded that for this denominator, the best choice is the square root of the sum of squares of each alternative per attribute. This ratio can be expressed as given in below;

………eqn(2)

Where xij is a dimensionless number which belongs to the

interval [0, 1] representing the normalized performance of ith _{alternative and j}th _attribute.

Step 4: For multi-objective optimization, these normalized performances are added in case of maximization (for beneficial attributes) and subtracted in case of minimization (for non-beneficial attributes). Then the optimization problem becomes:

……….eqn (3)

Where g is the number of attributes to be maximized, (n-g) is the number of attributes to be minimized, and yi is the normalized assessment value of i th alternative with respect to all the attributes. In some cases, it is often observed that some attributes are more important than the others. In order to give more importance to an attribute, it could be multiplied with its corresponding weight (significance coefficient) (Brauers et al. 2009). When these attribute weights are taken into consideration, Equation- 3 becomes as follows:

[j =1, 2, 3...n]..eqn (4)

Where wj is the weight of j th attribute, which can be

determined applying analytic hierarchy process (AHP) or entropy method.

Step 5: The yi value can be positive or negative depending of the totals of its maxima (beneficial attributes) and minima (non-beneficial attributes) in the decision matrix. An ordinal ranking of yi shows the final preference. Thus, the best alternative has the highest yi value, while the worst alternative has the lowest yi value.

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Qualitative measures of

Selection attribute Number Fuzzy Assign Crisp score Exceptionally low M1 0.04556

Extremely low M2 0.13647

Very low M3 0.22738

Low M4 0.31825

Below average M5 0.40916

Average M6 0.50000

Above average M7 0.59095

High M8 0.68186

Very high M9 0.77278

Extremely high M10 0.863654

Exceptionally high M11 0.95456 Table-4: values of the selection attribute

Figre-2: Linguistic terms to fuzzy numbers conversion (11-point scale)

III. CASE STUDY:SELECTION OF BEST MANUFACTURING SYSTEM BY USING MOORA METHOD

Prepare the decision matrix for evaluating the weight factor by applying the AHP method. Selection the criteria and alternatives of intelligent manufacturing system with respect to benefit and cost (non-benefit) criteria.

Basically, we consider the eight types of intelligent manufacturing system i.e. known as alternatives. The different criteria are to be considered as quality, cost, lead time, service level, product variety and robustness. Finally, each and every product should be minimum cost and minimum lead time with the best quality, product variety,

very good service level and maximum robustness. The different alternatives are Lean manufacturing system (A1), Agile manufacturing system (A2), Le-agile manufacturing system (A3), Flexible manufacturing system (A4), Computer integrated manufacturing system (A5), Holonic manufacturing system (A6), Bionic manufacturing system (A7), and Fractal manufacturing system (A8).

Criteria Criterion Benefit criteria

Non-benefit criteria

C1 Quality  (+) -

C2 Cost -  (-)

C3 Lead time  (-)

C4 Service level  (+) -

C5 Product

variety  (+) -

C6 robustness  (+) -

Table-4: criteria’s of the intelligent manufacturing system

Now, we are generating the primary decision matrix from the AHP method introduced by T.L.Satty and his scale.

(+)C1 (-)C2 (-)C3 (+)C4 (+)C5 (+)C6

C1 1 9 5 3 5 7

C2 1/9 1 2 3 4 3

C3 1/5 1/2 1 2 3 2

C4 1/3 1/5 1/3 1 1/5 1/7

C5 1/5 1/3 1/2 5 1 1/3

C6 1/7 1/2 1/2 1/3 5 1

Table-5: AHP matrix from the Satty scale

λmax = 6.048, R.I = 1.98(6-2)/6 = 1.32, C.I = (6.048- 6)/2 = 0.024, C.R = 0.024/1.32 = 0.0182

C.R =0.0182 < 0.1 different alternatives are Lean manufacturing system (A1),

Agile manufacturing system (A2), Le-agile manufacturing system (A3), Flexible manufacturing system (A4), Computer integrated manufacturing system (A5), Holonic manufacturing system (A6), Bionic manufacturing system (A7), and Fractal manufacturing system (A8).

The weight factors we are getting from the above matrix;-

[C1]W=0.5071, [C2]W=0.1751,[C3]W=0.1275, C4]W=0.0364,

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Main decision matrix of the intelligent manufacturing system given in below:-

(+)C1 (-)C2 (-)C3 (+)C4 (+)C5 (+)C6

A1 High Very High High High Low Low

A2 High High High Very High Very High Very High

A3 High Very High High Very High High High

A4 Very High Very low Extremely high Extremely high Below average

Below average

A5 High Below

average Above average Exceptionally high average Above Above average

A6 Very High High Below average Very High High Very High

A7 Extremely high Extremely low

Above average Above average Very High High

A8 Exceptionally

high Average Extremely high Low Extremely high Extremely high

Table-6: Relation in between alternatives-criteria‟s from fuzzy scale (by word)

Main decision matrix of the intelligent manufacturing system given in below in terms of crisp number:-

(+)C1 (-)C2 (-)C3 (+)C4 (+)C5 (+)C6

A1 0.68186 0.77278 0.68186 0.68186 0.31825 0.31825

A2 0.68186 0.68186 0.68186 0.77178 0.77178 0.77178

A3 0.68186 0.77278 0.68186 0.77178 0.68186 0.68186

A4 0.77278 0.22735 0.86365 0.86365 0.40916 0.40916

A5 0.68186 0.40916 0.59095 0.95456 0.59095 0.59095

A6 0.77128 0.68186 0.40916 0.77128 0.68186 0.77128

A7 0.86365 0.13646 0.59095 0.59095 0.77128 0.68186

A8 0.95456 0.50000 0.86365 0.31827 0.86365 0.86365

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(+)C1 (-)C2 (-)C3 (+)C4 (+)C5 (+)C6

m ∑( Xij) 2

i=1

4.7112 2.6125 3.9934 4.3641 3.4883 3.4883

m SQRT∑( Xij)2

i=1

2.17053 1.6162 1.99825 2.08925 1.86762 1.86762

Weight Factor 0.5071 0.1751 0.1275 0.0364 0.0765 0.0774

Table-8: Relation in between alternatives-criteria‟s summation and square root of summation.

Normalized decision matrix of the intelligent manufacturing system given in below:-

(+)C1 (-)C2 (-)C3 (+)C4 (+)C5 (+)C6

Weight Factor 0.5071 0.1751 0.1275 0.0364 0.0765 0.0774

A1 0.28437 0.47815 0.34123 0.32640 0.17040 0.17040

A2 0.28437 0.42189 0.34123 0.36992 0.41378 0.41378

A3 0.28437 0.47815 0.34123 0.36992 0.36510 0.36510

A4 0.35603 0.14067 0.43220 0.41320 0.21908 0.21910

A5 0.28437 0.25316 0.29573 0.45694 0.31642 0.31642

A6 0.35603 0.42189 0.20476 0.36992 0.36510 0.41378

A7 0.39789 0.08443 0.29573 0.28288 0.41378 0.36510

A8 0.43978 0.30937 0.43220 0.15235 0.46243 0.46243

Table-9: Relation in between alternatives-criteria‟s normalized decision matrix

Now, we formulated the weighted normalized decision matrix from the normalized decision matrix from the equation-[3] and equation-[4]:-

(+)C1 (-)C2 (-)C3 (+)C4 (+)C5 (+)C6

Weight Factor 0.5071 0.1751 0.1275 0.0364 0.0765 0.0774

A1 0.14420 0.08372 0.04351 0.01188 0.01304 0.01389

A2 0.14420 0.07387 0.04351 0.01346 0.03165 0.03203

A3 0.14420 0.08372 0.04351 0.01346 0.02793 0.02826

A4 0.18054 0.024631 0.05510 0.01504 0.01677 0.01696

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A6 0.18054 0.07387 0.02611 0.01346 0.02793 0.03203

A7 0.20177 0.01478 0.03770 0.01030 0.03165 0.02826

A8 0.22301 0.05417 0.05510 0.00554 0.03538 0.03579

Table-10: Relation in between alternatives-criteria‟s weighted normalized decision matrix

Now, value of the alternative-1 [A1]

0.14420 - 0.08372 - 0.04351 + 0.01188 + 0.01304 + 0.01389 = 0.0551

Similarly, the value of alternative-2 [A2]

0.14420 - 0.07387 - 0.04351 + 0.01346 + 0.03165 + 0.03203 = 0.10397

Value of alternative-3 [A3]

0.14420 - 0.08372 - 0.04351 + 0.01346 + 0.02793 + 0.02826 =0.08663

Value of alternative-4 [A4]

0.18054 - 0.024631 - 0.05510 + 0.01504 + 0.01677 + 0.01696 =0.14956

Value of alternative-5 [A5]

0.14420 - 0.04433 - 0.03370 + 0.01663 + 0.02421 + 0.02449 = 0.12749

Value of alternative-6 [A6]

0.18054 - 0.07387 - 0.02611 + 0.01346 + 0.02793 + 0.03203 = 0.15398

Value of alternative-7 [A7]

0.20177 - 0.01478 - 0.03770 + 0.01030 + 0.03165 + 0.02826 = 0.21943

Value of alternative-8 [A8]

0.22301 - 0.05417 - 0.05510 + 0.00554 + 0.03538 + 0.03579 = 0.19042

Relative and maximum relative significance values generating from the equation:-

Alternatives S I (Value) Rank

A1 0.0551 8

A2 0.10397 6

A3 0.08663 7

A4 0.14956 4

A5 0.12749 5

A6 0.15398 3

A7 0.21943 1*

A8 0.19042 2

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This generalized criterion is directly proportional to the relative effect of the values and weights of the considered criteria [23]. The COPRAS, TOPSIS and VIKOR methods are more efficient in dealing with the tangible attributes but they cannot deal very well if the criteria values are expressed qualitatively. Whereas, AHP can also deal with tangible as well as non-tangible attributes, especially where the subjective judgments of different individuals constitute an important part of the decision-making process. But in some cases, unmanageable number of pair-wise comparisons of attributes and alternatives with respect to

As the number of Table 12 compares the performance of COPRAS, EVAMIX, TOPSIS, VIKOR and AHP, MOORA, SAW, ELECTRE methods with respect to calculation/computation time, simplicity, transparency, possibility of graphical interpretation and type of the information [35].

Transparency is one of the important factors that need to be addressed for selecting a particular MCDM method for a specific problem. Different decision-making methods have different levels of transparency.

It is always recommended and desirable not an important part of the decision-making process. But in

some cases, unmanageable number of pair-wise comparisons of attributes and alternatives with respect to each of the attributes may result. As the number of alternatives increases, the amount of calculations rises quite rapidly and computational procedures become quite elaborate.

Table 12 compares the performance of COPRAS, EVAMIX, TOPSIS, VIKOR and AHP, MOORA, SAW, ELECTRE methods with respect to calculation/computation time, simplicity, transparency, possibility of graphical interpretation and type of the information [32].

To use a highly complex MCDM method with lack of transparency (as in case of AHP) as it makes very difficult for the decision maker to identify any mistake made during the calculation process which may often lead to a very high degree of risk involvement by misleading the entire selection process.

A final decision can be taken keeping in view of the practical considerations. All possible constraints likely to be experienced by the user have to be considered. These include constraints such as manufacturing lead-time constraints, manufacturing process constraints, economic constraints, management constraints, social constraints, and political constraints.

MCDM methods Calculation

time

Simplicity Transparency flexibility

MOORA Less Simple Good Very High

EVAMIX Moderate Moderately Critical Low

ELECTRE Moderate Moderately Critical Low

TOPSIS & AHP

High Moderately Good High

VIKOR Less Simple Very good Moderate

MADM Moderate Moderately Critical High

COPRAS less Simple Very good High

SAW Less Simple Good High

Table-12: Comparison of the different MCDM method

If the first choice of intelligent manufacturing system as decided by the results of those MOORA methods that have a very significant positive Spearman‟s rank correlation coefficient cannot be considered due to certain constraints, then the user may opt for the second choice manufacturing system. If the second choice manufacturing system also

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V.CONCLUSIONS

The decision maker can easily apply MOORA method to evaluate the alternatives and select the most suitable manufacturing system, while being completely unaware of the physical meaning of the decision-making process. Moreover, this method allows for the formulation of a reduced performance criterion which is directly proportional to the relative effect of the compared criteria values. On the other hand, the main advantage of MOORA method is that unlike the other MCDM methods, it employs separate mathematical models to benefit the non-benefit and very good graphical qualitative criteria of the decision matrix. Due to this added advantage, in MOORA method, the chance of losing information is very small. The MOORA method, which is quite flexible and easy to comprehend, also segregates the subjective part of the evaluation process into criteria weights including decision using a combined multiple attribute decision-making method.

ACKNOWLEDGMENT

The authors wish to thank Jadavpur University, Kolkata, India and Indian Institute of Management (IIMC), Kolkata, India for their valuable literature supports in making this research successfully.

REFERENCES

[1] R. Booth, Agile manufacturing, Engineering Management Journal 6 (2) (1996) 105-112.

[2] C. Ward, What is Agility, Industrial Engineering, November (1994) 14-16.

[3] J. Stevens, Integrating the supply chain, International Journal of Physical Distribution and Materials Management 19 (8) (1989) 3-8. [4] M.M. Naim, The book that changed the world. Manufacturing

Engineer, February (1997) 13-16.

[5] S. Hoekstra, J. Romme, Integral Logistics Structures: Developing Customer Oriented Goods Flow, McGraw-Hill, London, 1992. [6] T. Hill, Manufacturing Strategy, 2nd Ed., MacMillan, London, 1993. [7] P.T. Kidd, Agile Manufacturing: A Strategy for the 21st _{Century. IEE}

Agile Manufacturing Colloquium 1995, pp. 1/1-1/6.

[8] J.P. Womack, D.T. Jones, D. Roos, the Machine That Changed the World, Rawson Associates, New York, 1990.

[9] G. Stalk Jr, T.M. Hout, Competing Against Time: How Time-Based Competition Is Reshaping Global Markets, The Free Press, New York, 1990.

[10] G.N. Evans, M.M. Naim, D.R. Towill, Process costing} the route to construction re-engineering. Mouchel centenary conference, in: M.B. Leeming, B.H.V. Topping (Eds.), Innovation in Civil and Construction Engineering, Civil-Comp Press, Edinburgh, 1997, pp. 153-162.

[11] R.H. Hayes, G.P. Pisano, beyond world class: The new manufacturing Strategy. Harvard Business Review, January} February (1994) 77-86.

[12] H.J. GruKnwald, L. Fortuin, Many steps towards zero inventories, European Journal of Operational Research 59 (1992) 359-369. [13] J.P. Womack, D.T. Jones, Lean Thinking: Banish Waste and Create

Wealth in Your Corporation, Simon & Schuster, New York, 1996. [14] S.L. Goldman, R.N. Nagel, K. Preiss, Agile Competitors and Virtual

Organizations: Strategies for Enriching, Van Nostrand

[15] Chan JWK, Tong TKL. Multi-criteria material selections and end-of-life product strategy: grey relational analysis approach. Mater Des 2007; 28:1539–46.

[16] Rao RV. A decision making methodology for material selection using an improved compromise ranking method. Mater Des 2008; 29:1949–54.

[17] Zavadskas EK, Kaklauskas A, Turskis Z, Tamošaitien J. Selection of the effective dwelling house walls by applying attributes values determined at intervals. J Civil Eng Manage 2008; 14:85–93. [18] Kaklauskas A, Zavadskas EK, Trinkunas V. A multiple criteria

decision support on-line system for construction. Eng Appl Artif Intell 2007; 20:163–75.

[19] Zavadskas EK, Turskis Z, Tamošaitieneÿ J, Marina V. Multi-criteria selection of project managers by applying grey criteria. Technol Economic Develop Economy, Baltic J Sustain 2008; 14:462–77. [20] Kaklauskas A, Zavadskas EK, Raslanas S, Ginevicius R, Komka A,

Malinauskas P. Selection of low-e windows in retro.t of public buildings by applying multiple criteria method COPRAS: a Lithuanian case. Energy Build 2006; 38:454–62.

[21]Zavadskas EK, Kaklauskas A, Peldschus F, Turskis Z. Multi-attribute assessment of road design solutions by using the COPRAS method. Baltic J Road Bridge Eng 2008; 2:195–203.

[22] Martel JM, Matarazzo B. Other outranking approaches. In: Figueira J, Salvatore G, Ehrgott M, editors. Multiple criteria decision analysis: state of the art surveys. Springer: New York; 2005. p. 197–262. [23] Hajkowicz S, Higgins A. A comparison of multiple criteria analysis

techniques for water resource management. Euro Journal of Operational Research 2008; 184:255–65.

[24] Chung E-S, Lee KS. Identification of spatial ranking of hydrological vulnerability using multi-criteria decision making techniques: case study of Korea. Water Res Manage doi: 10.1007/s11269-008-9387-9. [25] Ustinovichius L, Zavadskas EK, Podvezko V. Application of a

quantitative multiple criteria decision making (MCDM-1) approach to the analysis of investments in construction. Control Cybern 2007; 36:251–68.

[26] Jeffreys I. The use of compensatory and non-compensatory multi-criteria analysis for small-scale forestry. Small-scale Forest Ecol Manage Policy 2004; 3:99–117.

International Journal of Emerging Technology and Advanced Engineering

310 [28] Triantaphyllou E. Multi-criteria decision making methods: a

comparative study. Dordrecht: Kluwer Academic Publishers; 2000. [29] Pérez J, Jimeno JL, Mokotoff E. Another potential shortcoming of

AHP. TOP: Off J Spanish Soc Stat Oper Res 2006; 14:99–111. [30] Ginevic¡ius R, Podvezko V. Multi-criteria graphical–analytical

evaluation of the financial state of construction enterprises. Baltic J Sustain 2008; 14:452–61.

[31] Edwards W, Newman JR. Multiattribute evaluation. In: Arkes HR, Hammond KR, editors. Judgment and decision making: an interdisciplinary reader. Cambridge: Cambridge University Press; 1986.

[32] Farag M. Quantitative methods of materials selection. In: Kutz M, editor. Handbook of materials selection; 2002.

[33] Triantaphyllou E. Multi-criteria decision making methods: a comparative study. London: Springer-Verlag; 2000.

[34] Rao RV. Decision making in the manufacturing environment using graph theory and fuzzy multiple attribute decision making methods. London: Springer-Verlag; 2007.

[35] Torrez JB. Light-weight materials selection for high-speed naval craft. PhD thesis, Massachusetts Institute of Technology; 2007. [36] Ashby MF, Brechet YJM, Cebon D, Salvo L. Selection strategies for

materials and processes. Mater Des 2004; 25:51–67.

[37] Ashby MF. Materials selection in mechanical design. New York: Pergamon Press; 1995.

[38] Zha XF. A web-based advisory system for process and material selection in concurrent product design for a manufacturing environment. Int J Adv Manufacturing Technology 2005; 25(3– 4):233–43.

[39] Jalham IS. Decision-making integrated information technology (IIT) approach for material selection. Int J Comput Appl in Technol 2006; 25:65–71.

[40] Jee DH, Kang KJ. A method for optimal material selection aided with decision making theory. Mater Des 2000; 21(3):199–206. [41] Shanian A, Savadogo O. A material selection model based on the

concept of multiple factor decision making. Mater Des 2006; 27:329– 37.

[42] Shanian A, Savadogo O. A non-compensatory compromised solution for material selection of bipolar plates for polymer electrolyte membrane fuel cell (PEMFC) using ELECTRE IV. Electro-chim Acta 2006; 51:5307–15.

[43] Shanian A, Savadogo O. TOPSIS multiple-criteria decision support analysis for material selection of metallic bipolar plates for polymer electrolyte fuel cell. J Power Sour 2006; 159:1095–104.

[44] Rao RV. A material selection model using graph theory and matrix approach. Mater Sci Eng A 2006; 431:248–55.

[45] Manshadi BD, Mahmudi H, Abedian A, Mahmudi R. A novel method for materials selection in mechanical design: combination of non-linear normalization and a modified digital logic method. Mater Des 2007; 28:8–15.

[46] Chan JWK, Tong TKL. Multi-criteria material selections and end-of-life product strategy: a grey relational approach. Mater Des 2007; 28:1539–46.

[47] Rao RV. A decision making methodology for material selection using an improved compromise ranking method. Mater Des 2008; 29:1949–54.

[48] Chatterjee P, Athawale VM, Chakraborty S. Selection of materials using compromise ranking and outranking methods. Mater Des 2009; 30:4043–53.

[49] Fayazbakhsh K, Abedian A, Manshadi BD, Khabbaz RS. Introducing a novel method for materials selection in mechanical design using Z-transformation in statistics for normalization of material properties. Mater Des 2009; 30: 4396–404.

[50] Saaty TL. Fundamentals of decision making and priority theory with AHP. Pittsburg: RWS Publications; 2000.

[51] Brauers, W. K. M., and Zavadskas, E. K., (2009). Robustness of the multi-objective MOORA method with a test for the facilities sector, Technological and Economic Development of Economy: Baltic Journal on Sustainability, 15(2), pp 352–375.

[52] Brauers, W. K. M., and Zavadskas, E. K., (2006). The MOORA method and its application to privatization in a transition economy, Control and Cybernetics, Systems Research Institute of the Polish Academy of Sciences, 35(2), pp 445–469.

[53] Brauers, W. K. M., (2008). Multi-objective contractor‟s ranking by applying the MOORA method, Journal of Business Economics and Management, 4, pp 245–255.

[54] 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, Proceedings of the 25 th International Symposium on Automation and Robotics in Construction, Vilnius Gediminas Technical University, Lithuania, June 26-29, pp-541-548.