Fuzzy Axiomatic Design for Solving the Facility Layout Problem of a ...

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International Journal of Operations and Logistics Management Volume 5, Issue 3 Pages: 145-153 September 2016

e-ISSN: 2309-8023 p-ISSN: 2310-4945

Fuzzy Axiomatic Design for Solving the Facility Layout Problem of a Furniture Company Caner Erden*1, Furkan Yener2, İbrahim Çil3, and Feyza Çerezci4 1. Sakarya University, Department of Industrial Engineering, Sakarya, Turkey, ([email protected]) 2. Sakarya University, Department of Industrial Engineering, Sakarya, Turkey, ([email protected]) 3. Sakarya University, Department of Industrial Engineering, Sakarya, Turkey, ([email protected]) 4. Sakarya University, Department of Computer Engineering, Sakarya, Turkey, ([email protected])

In this study, we deal with fuzzy variables to develop a methodology for optimizing layout problem under uncertainty using the principles of axiomatic design. Axiomatic design provides a brief framework to decision-making in the manufacturing process. We use axiomatic design principles to solve facility layout problem of a furniture company by using practical information taken from company official. Some taken information which are maintenance, visual control, quality (Judoka), flexibility, volatility about layout problem is not numerical. Therefore, it is necessary to use fuzzy principles in order to get better results. To optimize facility layout can improve operations and process of the company which provides better lead time and more customer satisfactions. As a result of the study, it is recommended to the wooden company to decide U type facility layout system for its production system. Keywords: Fuzzy Axiomatic Design, Facility Layout Problem, Lean manufacturing INTRODUCTION Today, globalization process has huge momentum in the world. Corporate groups want to improve their competitive power for these reasons. They focus on their decision process efficiency. They mustn't abuse their power to stop new ideas having a chance of success. Contrarily, new approaches and techniques should implement to decision design process. Systematic creative design tools and strategies available to designers which are Soviet-

originated Theory of Inventive problem Solving, TRIZ as its foundation, the proposed design method also encompasses elements of, amongst others, QFD Design for X, Value Engineering, Axiomatic Design and Robust Design(Kim & Cochran, 2000). Mann (2002) examines the broad range of methods, describes the ongoing process of integrating these methods and reviews. As an engineering design theory, Axiomatic design (AD)

*Corresponding author: Caner Erden Sakarya University, Department of Industrial Engineering, Sakarya, Turkey, E-Mail [email protected].

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Fuzzy axiomatic design for solving the facility layout problem of a furniture company

provides a brief framework to decision-making in the manufacturing process. There are tidy of papers in literature about axiomatic design since 25 years. When the literature are examined, huge amount of study in different sectors would be seen. Kulak, Cebi, & Kahraman, (2010) made a brief literature review with examining 63 different papers about axiomatic design. Principals of axiomatic design developed by Nam P. Suh who is a mechanical engineering professor at MIT(Suh, 1990). Suh published quite a lot papers early 90s (Albano & Suh, 1992a; Harutunian, Nordlund, Tate, & Suh, 1996; Suh, 1995, 1995, 1998; Suh, Cochran, & Lima, 1998; Suh & Do, 2000). In addition, A Flexible manufacturing system (FMS) is a completely incorporated assembling and manufacturing framework comprising of computer numerically controlled (CNC) machines, associated by a computerized material handling system, all under the control of a central computer should be design properly(Kulak & Kahraman, 2005b). Babic (1999) presented philosophy for deciding the proper FMS configuration at the design stage to FMS planners. Kulak, Durmusoglu, & Tufekci, (2005) built a framework and a road map for cellular manufacturing design. They installed a feedback mechanism to learn improvements in cellular design. With the evaluation in preselected performance criteria and resulting performance improvements are provided with axiomatic design. There are different applications of Fuzzy Axiomatic design in different areas. For instance, Kahraman, Kaya, & Cebi, (2009) focused on renewable energy alternatives with axiomatic design and AHP. In this paper, they built their approach on two methodologies. The main approach depends on the AHP which permits the assessment scores from specialists to be linguistic expressions, crisp, or fuzzy numbers, while the other depends on AD standards under fuzziness which assesses the options under the useful necessities acquired from specialists. Celik et al. (2009) investigated a systematic evaluation model on docking facilities of shipyards to provide a decision aid for technical ship managers and to perform this responsibility in an efficient manner.Kulak & Kahraman, (2005a) aimed to improve decision processes between shipyard companies. Celik et al. (2009) examined a

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hybrid approach with fuzzy axiomatic design and fuzzy TOPSIS on ensuring Turkish container ports with incomplete information. Kahraman & Çebı, (2009) dealt with the deficiency of axiomatic design and they provided a new approach with adding three important tools to fuzzy axiomatic design. These were hierarchy, crisp and rank. They applied new approach of fuzzy axiomatic design to teaching assistant selection problem. Hirani & Suh, (2005) presented an approach to describe the ideal design strategy for enhancing working qualities of liquid film consistently stacked diary direction with axiomatic design and genetic algorithm. GonçalvesCoelho & Mourao (2007) showed how AD allows for perceiving the relationships between each product and the related manufacturing processes. The remainder of this paper is organized as follows. In this section, an overview of the relevant literature is given about axiomatic design. Section 2 informs about axiomatic design. Section 3 provides a problem statement and deals with characteristics and definition of the problem as a case study. In addition, results of a numerical investigation are presented in this section. Finally, conclusions are presented in Section 4. METHODOLOGY Axiomatic Design Axiomatic design(AD) is developed by Nam Pyo Suh in the 1990s which is used to design products, systems and process (Suh, 1990) (Suh, 2001). In brief description, axiomatic design is an answer of “what will we achieve” and “how can we achieve” questions. Before design process, it is needed to understand customer demands which is defined as functional requirements(FRs). FRs are related with the customer demands and requirements. Other definition of a design is design parameters(DPs). DPs are generated as the physical domain to maintain the FRs. DPs can be used as the process variables (PVs) for some process design studies. These design parameters are illustrated in Fig 1 (Suh, 1990). FIGURE 1 HERE

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Since firms are under pressure to minimize manufacturing costs and process time, they try to use axiomatic design for practical reasons even the objective of axiomatic design is to setup a scientific background for design process and improve design activities. Axiomatic design makes human more creative and productive. It has advantages to reduce unnecessary process, minimize the iterative procedure and help designer to decide best plans among those proposed. There are 8 steps for a good axiomatic design which are listed as: 1. Consider customer and their needs, 2. Describe FRs and DPs which are explained earlier, 3. Construct the design matrix, 4. Determine the coupling source, 5. Find a way to get rid of the coupling sources, 6. Describe FRs and DPs again for new situation, 7. Decompose the FRs and DPs hierarchy, 8. Use the newest design process. There are two design axioms to design products and decide best alternative those proposed which are independent axiom and the information axiom. These axioms are explained as follows (Suh, 1990). Axiom 1 (the independence axiom) makes FRs remain independent of each other. Axiom 2 (the Information axiom) minimizes the information content of the design. Axiom 1. Once an arrangement of FRs has been figured and conceivable arrangements of DPs have been combined, the two outline axioms are connected to assess the proposed plans. The use of the Independence Axiom will be depicted regarding the configuration network. Axiom 1 is used to accept design during planning process (Gebala & Suh, 1992; Suh, 1995). The mathematical relationship between FRs and DPs can be represented by equation 1. {FR} = [A] {DP} {FR} : Vector of functional requirements {DP} : Vector of design parameters [A]: Matrix that determines design An element of [A] matrix is given by equation 2.

Aij 

FR i DPj

Axiom 2 (the information axiom) is the probability of successfully achieving FRs or DPs. It is different for process and product design (Albano, Connor, & Suh, 1993; Albano & Suh, 1992b; Wallace & Suh, 1993). Information index(I) is defined as in equation 3.

1 Ii  log 2    pi 

Ii : Information index p i : The probability of achieving the functional requirement FRs. Pi can be calculated as equation 4.

 system area  pi  log 2    common area  System area is defined as the area stays under system ranges and generally it equals to 1. While there are a lot of FRs to satisfy, logarithmic function is chosen. Total information index values equal to 1 since it is a probability function. The best information index has the least information content. Equation 4 illustrates that as follows:

I min

 n     min  Ii   i  1  

A Numerical Application of Fuzzy Ad In this study, we deal with fuzzy variables to determine which layout is better for a shop producing wood products. A fuzzy axiomatic design is developed to solve the problem of choosing best layout problem under uncertainty. Firstly, criteria are specified by consulting with shop manager. The definitions which will be used as criteria for the models are given in this section. Work In Progress(WIP) is goods finishing incompletely and waiting for completion. Flow Time defines the finishing time of a specific work or works. Number of worker means that the number of the workers that are requires for a design.

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Maintenance is the process of making goods and machines more qualified and healthier. It is a part of health management system for machines and goods. Visual Control is a control process using visual signals unlike using written instructions. It allows a quick recognition of the things. Quality (Judoka) term is created by Toyota Production Experts and described as “automation with human touch.”. Flexibility can be used with adaptation term together. It is the design that have high adaptation level and change itself quickly. Volatility is the variation of price and speciation’s of goods over time. Throughput is the movement of inputs and outputs through a production process. By considering these factors we are going to specify the best decision for the shop. We prefer fuzzy sets because there are some fuzzy statements. Fuzzy statements were obtained from shop manager who know the shop best. Shop manager determined range of the design as shown in table. TABLE 1 HERE According to Table 1, the work in progress variable is required to be maximum 110 by the company managers. Above the numbers of 110 value company thinks it will lose their productivity ratio. Managers decide the flow time to be in a range of 0,5 and 1,6 because of flow time needs to be in a range to work properly inside the workshop. The company has number of workers in a range of 5-8 that’s why number of worker has to be in a range of 5-8. Next step is to determine maintenance range. Maintenance range has fuzzy processes and it is hard to specify the exact numbers for the maintenance specification. Company manager can not specify certain numbers about the maintenance. Hence, fuzzy numbers are used for the solution of this problem. Maintenance needs to be in a fuzzy triangle number as 5, 8, 14. As same as maintenance specification, it is also hard to determine visual control range exactly. That’s why again fuzzy numbers are used to describe the design range of the visual control. Its fuzzy triangle number is 3, 5, 14; fuzzy triangle number of Quality(Judoka) is 7, 14, 14; fuzzy triangle number of flexibility, volatility are 5, 14, 14 and 4, 8, 14 with the same order. Throughput number is the same with the other specifications such as work in progress, flow time and number of workers.

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The system ranges of the criteria obtained from lean production experts are given in the Table 2. For the range of a criteria can be string or numeric. The numerical values are considered as the easy numbers to deal with in the process of axiomatic design. But the string values need to be classified with the fuzzy triangle numbers. Table 2 shows there are some adjectives which are; Bad, Moderately, Good, Very Good, Perfect to describe the criteria. Those adjectives are also the fuzzy sets for this study. That’s why, there are 5 fuzzy sets described as the adjectives of the criteria. The fuzzy processes will be applied for 5 criteria shown in the Table 2. TABLE 2 HERE After specified the system range table, it is time to generate fuzzy triangle numbers. The range of fuzzy number is between 0-14. The integer number in the range of 0-14 refers a set on the fuzzy system. For instance, fuzzy number of 4 refers to mediocre adjective of the criteria, 14 value is the best value of the fuzzy system and 0 is the worst value of the system. FIGURE 2 & 3 HERE Using equation 3 and equation 7, information contents can be calculated. For instance, we calculate Straight Line for Work In Progress.

 115  80  I ws  log    0, 22  110  80  Maintenance, visual control, quality, flexibility and volatility criteria have string values and its probabilities will be calculated using fuzzy triangle numbers. For example, maintenance value for straight line is “bad” and the design range of it is 5, 8, 14 triangle fuzzy number. The ABC triangle is the common triangle between design and system triangles. The calculate the area of the ABC area, the following formula is used;

 theareaofthecommontriangle  I MS  log 2   theareaofthedesign   FIGURE 4 HERE TABLE 3 HERE

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The sum of the information index gives final and meaningful results of the axiomatic design obtained from the information index Table 3. According to the Table 3, due to the information index of axiomatic design the lowest information index is the best solution for the decision maker. If the information index number is infinitive than the solution with this index number is going to be eliminated from the system at the beginning. That’s why, straight line is eliminated from the system because it has the infinitive value for the information index. In other words, straight line layout does not cover the requirements of the system. U type has the lowest value of the sum li. Serpentine layout has higher li value than U type. That’s why U-Type is better than the other layouts for the company. CONCLUSIONS In this study, facility layout problem is solved by using axiomatic design principles. Axiomatic design needs the parameters which are important for the users and the alternative situations for those parameters to calculate information index value. The total information index value is the final result of axiomatic design process. That gives a clue for the right decision taken by managers or decision makers. A workshop producing wooden products is chosen to obtain data, the production manager of the company decided the requirements of the workshop and those requirements are taken as the principles of the design which gave the important decisions for facility layout problem of the company. It is very useful for the company to make right decision for facility layout problem. This problem for the company regards the decision making process with the multiple criteria is based on the scientific and systematic basics. Due to the positive sides of axiomatic design such as it can be worked with fuzzy numbers and uncertain values, fuzzy axiomatic design is chosen to apply for the facility problem of a wooden company. The parameters obtained from company managers and the experts contain some uncertain information’s. Therefore, traditional decision making methods are not useful for this situation. Parameters are including numerical and also string values which makes the study harder. To work with

string and uncertain values, fuzzy sets principles are applied for solving problems of uncertainty. Information indexes are calculated for the parameters by re-defining the design range and system range. As a result of the study, it is recommended to the wooden company to decide U type facility layout system for its production system. For the future work, the number of parameters can be increased and the components of the axiomatic design can be detailed. Also, other fuzzy numbers like triangle number can be used to get better results from managers and experts. REFERENCES Albano, L. D., Connor, J. J., & Suh, N. P. (1993). A framework for performance-based design. Research in Engineering Design, 5(2), 105–118. Albano, L. D., & Suh, N. P. (1992a). Axiomatic approach to structural design. Research in Engineering Design, 4(3), 171–183. Albano, L. D., & Suh, N. P. (1992b). Axiomatic approach to structural design. Research in Engineering Design, 4(3), 171–183. Babic, B. (1999). Axiomatic design of flexible manufacturing systems. International Journal of Production Research, 37(5), 1159–1173. Celik, M., Cebi, S., Kahraman, C., & Er, I. D. (2009). Application of axiomatic design and TOPSIS methodologies under fuzzy environment for proposing competitive strategies on Turkish container ports in maritime transportation network. Expert Systems with Applications, 36(3), 4541–4557. Celik, M., Kahraman, C., Cebi, S., & Er, I. D. (2009). Fuzzy axiomatic design-based performance evaluation model for docking facilities in shipbuilding industry: The case of Turkish shipyards. Expert Systems with Applications, 36(1), 599–615. Gebala, D. A., & Suh, N. P. (1992). An application of axiomatic design. Research in Engineering Design, 3(3), 149–162.

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Gonçalves-Coelho, A. M., & Mourao, A. J. (2007). Axiomatic design as support for decisionmaking in a design for manufacturing context: A case study. International Journal of Production Economics, 109(1), 81–89. Harutunian, V., Nordlund, M., Tate, D., & Suh, N. P. (1996). Decision making and software tools for product development based on axiomatic design theory. CIRP AnnalsManufacturing Technology, 45(1), 135–139. Hirani, H., & Suh, N. P. (2005). Journal bearing design using multiobjective genetic algorithm and axiomatic design approaches. Tribology International, 38(5), 481–491. Kahraman, C., & Çebı, S. (2009). A new multiattribute decision making method: Hierarchical fuzzy axiomatic design. Expert Systems with Applications, 36(3), 4848–4861. Kahraman, C., Kaya, İ., & Cebi, S. (2009). A comparative analysis for multiattribute selection among renewable energy alternatives using fuzzy axiomatic design and fuzzy analytic hierarchy process. Energy, 34(10), 1603–1616. Kim, Y.-S., & Cochran, D. S. (2000). Reviewing TRIZ from the perspective of axiomatic design. Journal of Engineering Design, 11(1), 79–94. Kulak, O., Cebi, S., & Kahraman, C. (2010). Applications of axiomatic design principles: A literature review. Expert Systems with Applications, 37(9), 6705–6717. Kulak, O., Durmusoglu, M. B., & Tufekci, S. (2005). A complete cellular manufacturing system design methodology based on axiomatic design principles. Computers & Industrial Engineering, 48(4), 765–787. Kulak, O., & Kahraman, C. (2005a). Fuzzy multiattribute selection among transportation companies using axiomatic design and analytic hierarchy process. Information Sciences, 170(2), 191–210.

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design approach. International Journal of Production Economics, 95(3), 415–424. Mann, D. (2002). Hands on systematic innovation. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/sum mary?doi=10.1.1.514.3435 Suh, N. P. (1990). The principles of design (Vol. 990). Oxford University Press New York. Retrieved from http://www.maelabs.ucsd.edu/mae156/A _New/Resources/DesignProcess/Axiomatic_Design/Axiomatic_Tex t_Excerpts.pdf Suh, N. P. (1995). Axiomatic design of mechanical systems. Journal of Mechanical Design, 117(B), 2–10. Suh, N. P. (1995). Axiomatic design of mechanical systems. Journal of Mechanical Design, 117(B), 2–10. Suh, N. P. (1995). Designing-in of quality through axiomatic design. IEEE Transactions on Reliability, 44(2), 256–264. Suh, N. P. (1998). Axiomatic design theory for systems. Research in Engineering Design, 10(4), 189–209. Suh, N. P. (2001). Axiomatic Design: Advances and Applications (The Oxford Series on Advanced Manufacturing). Retrieved from http://www.citeulike.org/group/300/arti cle/225343 Suh, N. P., Cochran, D. S., & Lima, P. C. (1998). Manufacturing system design. CIRP AnnalsManufacturing Technology, 47(2), 627–639. Suh, N. P., & Do, S.-H. (2000). Axiomatic design of software systems. CIRP AnnalsManufacturing Technology, 49(1), 95–100. Wallace, D. R., & Suh, N. P. (1993). Informationbased design for environmental problem solving. CIRP Annals-Manufacturing Technology, 42(1), 175–180.

Kulak, O., & Kahraman, C. (2005b). Multi-attribute comparison of advanced manufacturing systems using fuzzy vs. crisp axiomatic

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APPENDIX

Table 1. Design Range of Variables Design Range max 110 between 0,5-1,6 5-8 5,8,14 3,5,14 7,14,14 5,14,14 4,8,14 at least 90

Work In Progress – WIP Flow Time Number of Worker Maintenance Visual Control Quality(Judoka ) Flexibility Volatility Throughput

Table 2. System Range Data for the workstation Work In Progress WIP

Flow Time

Straigh t line:

80-115

1-1,7

7-10

85-150

Bad

U Type

60-120

0,3-1

4-6

80-100

Perfect

Serpent ine

100-120

1,3-2,2

6-9

75-120

Good

Number of Throug Mainten Worker hput ance

Visual Control

Quality(J Flexib Volat udoka ) ility ility

Moderate ly Very Good

Bad

Bad

Bad

Very Good

Very Good

Very Good

Good

Good

Good

Good

Table 3. Results of different Facility Layouts

Ii’s

WIP

Flow Time

Number of Worker

Throughput

Maintenance

Visual Control

Quality (Judoka )

Flexibility

Volatility

Total

Straight line: U Type Serpentine

0,22 0,26 1,00

0,22 0,49 1,58

1,58 1,0 0,58

0,12 1,0 0,58

4,58 0,58 1,43

1,11 2,0 1,33

Inf. 0,0 3,43

10,0 1,0 1,14

5,00 1,67 1,08

Inf 9,0 12,1

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Figure 1. Concept of domain, mapping and spaces

Figure 2. Triangular fuzzy numbers of intangible criterias

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Figure 3. System's area, design's area, common area and probability density of FRs

Figure 4. Design's area, system's area and their common area

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