Selection of Rapid Prototyping Process Using ...

International Journal of Information Science and System, 2014, 3(1): 15-22 International Journal of Information Science and System

ISSN: 2168-5754

Journal homepage: www.ModernScientificPress.com/Journals/IJINFOSCI.aspx

Florida, USA

Article

Selection of Rapid Prototyping Process Using Combined AHP and TOPSIS Methodology Mahmood Shahrabi 1,*, Mehrdad Javadi 2 1

PhD Student of Industrial Engineering / Abadan Oil Refining Company, Abadan, Iran 2

Assistant Professor, Islamic Azad University, South Tehran Branch

* Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.:00986312223040 Article history: Received 22 August 2014, Received in revised form 4 September 2014, Accepted 16 September 2014, Published 20 September 2014.

Abstract: The key to success in design and production companies is timely updating of their products. In contemporary competitive market, the need to produce new products and replacing them with existing ones is deeply felt. Rapid prototyping is the first and most important step in this regard. However, proper selection of a rapid prototyping technology is difficult even for experienced users. Therefore, in this paper, a combined methodology for identification, comparison and selection of rapid prototyping is provided. Rapid prototyping is a relatively new technology in which a prototype is directly made from its 3D file in layered manner. Application of this method in designing the engineering in different industries such as automotive, aerospace, medicine and especially oil, gas, petro-chemistry and refineries can be regarded as one of the designing steps for production of new products. A numerical example for better understanding of methodology is provided. Keywords: Rapid Prototyping (RP), TOPSIS, AHP.

Copyright © 2014 by Modern Scientific Press Company, Florida, USA

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1. Introduction Rapid prototyping makes it possible for the engineers to acquire a 3D model of the desired work piece in a quick and inexpensive manner. By using rapid prototyping technology, the physical sample can be observed and examined after designing. Due to the fact that each design seeks a better quality, such a sample can be used to refine the design and to evaluate the favorable product characteristics. In general, rapid prototyping methods use the following algorithm: Firstly, the 3D model is drawn using the available modeling software, then other software divides the model into layers. The linear movement path of each layer is provided from its Slice file. This file includes X, Y coordinates of each layer. Z coordinate is introduced to the system based on specified layer thickness. Finally, a physical 3D model is made based on the type of applied method. 1.1. Difference between Rapid Prototyping Machines and Computer Numerical Control (CNC) Machines Rapid prototyping and CNC machines use the so-called incremental method and subtractive method respectively. This means that in a CNC machine, a material block is given to the system and the desired work piece is cut based on the file provided for the system. In case of the rapid prototyping machine, liquid or powder material is poured on the production tray and is solidified through different methods. Thus, the intended piece is made in a layered or so-called incremental manner. There are a lot of rapid prototyping technologies in the market in which new developments of materials production and techniques occur. However, selection of a proper rapid prototyping technology is difficult even for experienced users, because many rapid prototyping systems are widely used over the world and selecting the best of them depends on many features. In addition, each system has its own strengths and weaknesses, applications and limitations. So, appointing a proper technology depends on different criteria such as elongation, heat deflection temperature, strength, roughness, build time, cost, material properties, type of material, surface finish, accuracy, speed, variety, reliability, flexibility, etc.[1-6]. The most common technologies of rapid prototyping include SLA, SLS, FDM, 3DP and LOM each of which has its own strengths and weaknesses. Fig. 1 provides their categorization [7].


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Fig. 1: Classification of Rapid Prototyping Techniques

2. Methodology 2.1. Analytical Hierarchy Process (AHP) Method AHP method, suggested based on analysis of human brain in complicated problems, uses paired comparison to apply the following three principles. i.

Establishing a hierarchical structure for the problem

ii.

Establishing preferences through paired comparisons (weight measurement)

iii.

Establishing logical harmony through measurements The utilized definitions are provided in table 1. The medial value (2, 4, 6, and 8) can be used

for preferences. One of the strengths of AHP method is calculating the incompatibility of decisions defined in the following manner: Definition: If A (aij) is a m×m matrix, such a matrix is compatible if aij = aik .akj. Due to the fact that judgments depend on understanding, provided information and mental conditions of individuals, incompatibilities usually exist in judgments. Copyright © 2014 by Modern Scientific Press Company, Florida, USA

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Table 1. Definition of Judgment Matrix Level of Significance

Numerical Value

Equally important

1

Moderately more important

3

Strongly more important

5

Very Strongly more important

7

Extremely more important

9

Using the special vector, a natural measurement of compatibility index (CI) of existing information in a matrix (such as A) is calculated through the following equation: (1)

CI= Saaty showed that

(the highest value of special vector) for a reversible matrix, is always

higher than/ equal to matrix aspect (m) and this value would equal 'm' for a matrix with complete compatibility[1]. Thus,

is a proper measurement of the degree of incompatibility in a matrix.

Saaty also compared CI index with RI index so that RI for different values of m is provided by generation of random matrices A and measurement of CI average for them. [8] Compatibility rate (CR) is calculated in table 2 using equation (2) given the exact value of RI:

Table 2: Index of Accidental Incompatibility m

1

RI

0.0

2 0.0

3 0.58

4 0.9

5 1.12

CR=

6 1.24

7 1.32

8 1.41

9 1.45

10 1.49

(2)

So, if CR ≥ 0.1, compatibility of the matrix is confirmed [8]. 2.2. Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) Method TOPSIS method was suggested by Hwang and Yoon in 1981[2]. This method, is one of the multi-index decision-making methods which has many applications. In this method, m choices are evaluated using n indexes. This method is based on the concept that the selected choice should have the least difference with the ideal positive solution (the best possible case V+j) and the most possible Copyright © 2014 by Modern Scientific Press Company, Florida, USA

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difference with ideal negative position (the worst possible case V-j). It is assumed that propriety of each index will consistently increase or decrease. Problem solution by this method demands six steps: i.

Quantification and removal of scale of decision matrix (N): for removing the scale, norm scale removal method is applied.

ii.

Provision of harmonious non-scaled matrix (V): non-scaled matrix(N) is multiplied by diagonal matrix of weights(Wn*n) namely: V=N*Wn*n

iii.

(3)

Provision of an ideally positive solution and an ideally negative solution: the ideally positive solution (+Vj) and ideally negative solution are defined in the following manner:

Vj+ = {V vertex of the best values of each matrix index} Vj- = {V vertex of the worst values of each matrix index} The “best values” for positive indexes, are the highest values while for negative indexes, it is the lowest values. The “worst values” for positive indexes are the least ones while for negative indexes, they are the lowest values. iv.

Definition of difference of each choice with negative and positive ideals: Euclidean distance of each choice from a positive ideal(dj+) and difference of each choice from a negative ideal (dj-) is defined from the following equations:

v.

i = 1, 2,…, m

(4)

i = 1, 2,…, m

(5)

Definition of relative closeness (CLi+) of a choice to the ideal solution: CLi*=

vi.

(6)

Rating of choices: each choice for which CL is higher is better.

2.3. Numerical Instance A case study of comparison among the three systems of rapid prototyping was done. Selection of a rapid prototyping process depends on many factors. Based on collected data of the questionnaires distributed among different user groups such as service rooms, industry users, six factors of accuracy, roughness, tension strength, and elongation, cost and build time were identified as evaluation criteria for selection of rapid prototyping system. The weight of judgment matrix is shown in table 2 by using the provided definition. Its hierarchical structure is also shown in figure 2. In the present case study, a Copyright © 2014 by Modern Scientific Press Company, Florida, USA

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combined AHP-TOPSIS method is uses. AHP technique is used for definition of scales while TOPSIS technique is used for ranking of the three rapid prototyping techniques of SLA, SLS and LOM. The results of these calculations are provided in tables 3-6.

Fig. 2: The Hierarchical structure

Table 3. Priorities of criteria and sub-criteria Criteria

Objective

Subjective

Priorities of criteria

0.55

0.45

Sub criteria

Local priorities of sub criteria

Elongation

0.15

Global priorities of sub criteria 0.08

Strength Roughness

0.25

0.14

0.27

0.15

Accuracy

0.33

0.18

Build Time

0.70

0.32

Cost

0.30

0.14


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Table 4. Preference degree of the alternatives Local preference degree of the alternatives Sub criteria

SLA 0.54

SLS 0.28

LOM 0.18

Strength Roughness

0.63

0.20

0.14

0.51

0.15

0.31

Accuracy

0.48

0.26

0.19

Build Time

0.61

0.33

0.19

Cost

0.49

0.16

0.26

Elongation

Table 5. Positive ideal solution A+ and negative ideal solution AA+

0.03

0.20

0.12

0.14

0.05

0.02

A-

0.31

0.05

0.03

0.01

0.10

0.21

Table 6. di+, di- values and relative closeness for each alternative Alternatives

di+

di-

CL*

Rank

SLA

0.28

0.23

0.45

3

SLS

0.15

0.31

0.67

1

LOM

0.11

0.19

0.63

2

3. Conclusions Competition in international market has significantly increased. Nowadays, providing the products in the market before the competitors is vital. A new technology is needed for reduction of the time needed to introduce products to the market along with improvement of energy, time and cost. Therefore, rapid prototyping technology is very promising. In this method, there is no limitation regarding geometrical shape and the prototype is made without need for any mold or tool and with very high precision and accuracy. In this regard, selection of technology is very important. In the present study, AHP and TOPSIS methods were used to define SLS technology as the preferred and intended one. For more researches, the findings of the present study can be compared with other multi-scale decision-making methods such as VIKOR, ELECTERE, PROMETHEE and FUZZY.


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References [1] Masood, S.H.; Soo, A.et al., A rule based expert system for rapid prototyping system selection, Robotics and Computer Integrated Manufacturing, 18(3-4) (2002): 267-274. [2] H.S.Byun; K.H.Lee. A decision support system for the selection of a rapid prototyping process using the modified TOPSIS method, Int J Adv Manuf Technol, 26(11) (2005):1338-1347. [3] R. Venkata Rao; K.K. Padmanabhan. Rapid prototyping process selection using graph theory and matrix approach, journal of materials processing technology, 194(1) (2007): 81-88. [4] Behnam Vahdani, S. Meysam Mousavi, Reza Tavakkoli Moghaddam. Group decision making based on novel fuzzy modified TOPSIS method, Applied mathematical modelling, 35(9)(2011): 4257-4269. [5] Akshay Kumar, Supratik Dey, Amitava Ray, B.B.Pradhan. An Integrated management support methodology for the selection of rapid prototyping technologies, International conference on modeling optimization and computing, procedia engineering, 38(1)(2012): 3552-3559. [6] Vikram Shende, prafulla kulkarni. Decision support system for rapid prototyping process selection, International journal of scientific and research publications, 4(1)(2014): 1-6 [7] Deepa yagink. Fused Deposition Modeling A Rapid Prototyping technique for Product Cycle Time Reduction cost effectively in Aerospace Applications, Journal of Mechanical and Civil Engineering, (2014): 62-68. [8] Saaty, T.L., Multi criteria Decision Making: The Analytic Hierarchy Process, McGraw-Hill, New York, (1995). [9] Hwang, C. L. and Yoon, K., Multiple Attribute Decision Making Methods and Applications: A State of the Art Survey, Springer-Verlag, New York (1981).
