Comparison of OR and AI methods in discrete manufacturing using ...

Journal of Intelligent Manufacturing, 15, 517±526, 2004 # 2004 Kluwer Academic Publishers. Manufactured in The Netherlands.

Comparison of OR and AI methods in discrete manufacturing using fuzzy logic C E M A L E T T I N K U B AT, H A R U N TA SË K I N and B AY R A M T O P A L Department of Industrial Engineering, Sakarya University, 54040 EsentepeÐAdapazari, Turkey Email: [email protected], [email protected], [email protected]

S A F I Y E T U R G AY Faculty of Education, Izzet Baysal University, Bolu, Turkey E-mail: [email protected] Received February 2003 and accepted December 2003

Since 1950s the techniques of Operations Research (OR) and Optimization have been utilized to increase the ef®ciency of the production systems. With the widespread use of computers, it has even become easier to deal with industrial problems. However the complexity of the problems still reveals the dif®culty in providing solutions. The use of arti®cial intelligence (AI) seems to attract the attention of the researcher to overcome to the dif®culties. This has already been realized with several successful applications. In this study, the use of AI and OR techniques is compared using fuzzy logic. The progress of manufacturing systems, characteristics of production processes, system managements and system behavior are taken into account. The study is focussed on only discrete manufacturing. Keywords: Discrete manufacturing, operations research, arti®cal intelligent, classi®cation, fuzzy logic

1. Introduction The intelligent manufacturing systems will be the driving force in the manufacturing industry for the following decades. In order to understand and foresee trends in utilizing these systems the characteristics and methods of classical and modern manufacturing systems need to be investigated and compared. It is now obvious that the manufacturing systems should have the features of agility, intelligence, and rapid response for the sake of high-quality products. There has been several research on the application of AI technology to the manufacturing systems (Qiao and Zhu, 2000). In some of these studies, the effect of AI is discussed in terms of providing solutions to illde®ned problems. In this study, the effect of AI is

investigated with respect to optimization problems focussing only to discrete manufacturing. To establish a baseline for this study, the developments of methods, techniques and tools in discrete manufacturing is studied. And then characteristics of manufacturing systems are categorized. For each category, the required functions are listed. Around 2600 different papers are reviewed and a comparison of the utilization of techniques (OR and AI) is given. Section 2 brie¯y describes the problem solving approaches. A classi®cation of these techniques is given in Section 3. Section 4 provides the comparison of the utilization of these techniques. Fuzzy logic is applied to compare these techniques and the results are provided in Section 5 and Section 6 provides the conclusion.

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Fig. 1. OR Methods development by years.

2. Problem-solving approaches This study ®rst outlines the scienti®c and technological progress of problem solving techniques. Problems are becoming more complex and more illde®ned requiring more and more heuristic solutions. Figure 1 indicates the trends of Manufacturing Systems Modeling Techniques. There seems to be basic changes between the years 1940 and 2000 (KarayalcËin, 1979). It is obvious from Fig. 1 that the intelligent methods are becoming more dominant then ever before for solving the problems.

1C. Engineering Activities 1D. Advanced Manufacturing Techniques. (2) Techniques and methods 2A. Operations Research (OR) 2B. Statistics (ST) 2C. Optimization (OPT) 2D. Arti®cal Intelligence (AI). Each category is divided into sub-groups including different techniques. For example Manufacturing techniques are de®ned with respect to *

3. Classi®cation of problem-solving techniques In order to be able to make a reasonable comparison, problem solving approaches are classi®ed into 5 categories. Around 150,000 papers from 1176 journals are reviewed and 2583 papers were selected and used to de®ne the techniques and systems used in the categories given below (www.sciencedrect.com). The following techniques have been employed in the present study: (1) Discrete manufacturing (DM) 1A. Manufacturing Functions 1B. CIM Component

*

*

*

Manufacturing Functions with 16 different techniques including marketing, quality control, forecasting, scheduling, project planning, design etc. These techniques are coded as 1A in the following Figures. CIM Component with 32 techniques from automation of CIM to lean production and agile manufacturing. These techniques are coded as 1B in the following Figures. Engineering activities with 7 techniques from system handling to modeling. These techniques are coded as 1C in the following Figures. Advanced Manufacturing techniques with 22 approaches from customer driven production to Micro and Nano Scale Manufacturing. These techniques are coded as 1D in the following Figures.

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Comparison of OR and AI methods

Fig. 2. OR techniques applied to manufacturing functions (2A-1A).

Same analysis is done for the other categories and 25 different Operations Research Techniques (from Linear Programming to Queing System and Heuristic Approaches such as Simulation) were identi®ed and coded as 2A for the illustration purpose. Nineteen techniques of Statistics from random variables to Value analysis (coded as 2B) and 20 Optimization Techniques (from static optimization to Wavelet analysis) were identi®ed and coded as 2C. Similarly, 35 Arti®cial Intelligence techniques were reviewed and recognized to be used for manufacturing. They include a wide range of technologies from game playing and theorem proving to constraint based systems. AI techniques are coded as 2D for the illustration purpose in the ®gures given below. The full list of the systems and techniques are given in Appendix.

4. Comparing the technologies and manufacturing functions The comparison of OR, AI, OPT and Manufacturing Functions is provided in Figs 2±5. Figure 2 shows number of applications of OR Technologies to Manufacturing Functions. Note that Linear Programming, 0-1 Programming, Quadratik Programming

techniques have large application areas compared to other OR techniques. Similarly Fig. 3 shows the number of applications of AI Techniques used in Advanced Manufacturing Systems. It seems that Fuzzy Logic is playing a leading role following that Advanced Probability Distributions, Decision Theory and Simulation and Modeling took the attention of the manufacturing community more than the others. Figure 4 also indicates the application of AI and OR techniques together. Exponential Type Service Systems and Simulation seems to be more applied to the problems than others. As indicated in Fig. 5 Dynamic Optimization is a mostly used technique along with AI.

5. Using fuzzy logic to compare the different techniques and systems The aim of Fuzzy classi®cation is to evaluate the ef®ciency of the techniques with respect to the importance of manufacturing functions. Two different linguistic variable is de®ned as U ˆ Ef®cient and V ˆ Important. U indicates the ef®ciency of the techniques on the system and V shows the degree of importance of the systems. Membership functions of

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Fig. 3. AI techniques used in advanced manufacturing systems (2D-1D).

Fig. 4. Application of OR techniques along with AI (2A-2D).

these variables are given in Figs 6 and 7 (TasËkin and GoÈlecË, 1996). The relationship between U and V is de®ned using the heuristic method proposed by Sanches (1976). The heuristic method is adapted to the current problem in the following way.

Step 2. De®ne the relations …rij † for the mth OR technique applied on nth manufacturing function (or AI techniques) using the following equation

Step 1. De®ne the membership functions for linguistic variables U and V (see Figs 6 and 7).

where ui operator.

rij ˆ ui 1



1

a vj

is transpose of ui and a is the composition

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Comparison of OR and AI methods

Fig. 5. Application of optimization techniques along with AI techniques (2C-2D).

Fig. 6. Membership functions of variable U (ef®cient).

Step 3: Calculate the intersection of rij 's using the following equation mRi …zu ; zv † ˆ r^ij mA…r† …zu ; zv † ˆ min‰mA…r† …zu ; zv †Š; zu ;zv

i ˆ 1; 2; . . . ; m and Ri ˆ \i rij . Step 4. De®ne the ideal u values (very really) as  indicating the ideal ef®ciency of OR techniques on Manufacturing functions.

Fig. 7. Membership functions of variable V (important).

Step 5. Solve the following equation for each Manufacturing function or technique vj

1



ˆ R j a u

1

The membership values for vj 1 is de®ned as below to indicate the ef®ciency of OR or AI techniques on Manufacturing functions.

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Table 1. Membership function values of techniques and manufacturing functions v1

u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11 u12 u13 u14 u15 u16 u17

v2

v3

v4

v5

v6

OR Tech.

Man. Func.

OR Tech.

Adv. Man.

OR Tech.

OPT Tech.

OR Tech.

AI Tech.

OPT Tech.

AI Tech.

AI Tech.

OPT Tech.

2A1 2A18 2A25 2A15 2A19 2A9 2A22 2A14 2A16 2A11 2A12 2A2 2A20 2A28 2A4 2A7

1 3 3 3 4 4 4 4 4 5 5 5 5 5 5 5

2A16 2A13 2A15 2A28 2A33 2A11 2A2 2A29 2A14 2A23 2A17 2A30 2A25 2A10 2A35 2A8

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

2A25 2A11 2A12 2A18 2A28

1 4 4 4 5

2A25 2A16 2A18 2A12 2A19 2A10 2A11 2A6 2A8 2A14 2A15 2A54

1 1 1 1 1 2 2 2 2 2 2 2

2C3 2C1 2C15 2C14 2C16 2C4 2C17 2C2 2C5

1 1 2 2 2 3 3 3 3

2D15 2D16 D10 2D14 2D12 2D23 2D21 2D3 2D13 2D30 2D33 2D17 2D18 2D22 2D24 2D28 2D7

2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3

For U 1-Very Really, 2-Very, 3-Upper Medium, 4-Lower Medium, 5-Very Little Ef®cient, and for V 1-Very Very Important, 2-Very Important, 3-Important, 4-Little Important, 5-Unimportant.



^

1 mA…v† ˆ ‰mA…R† …zu ; zv † a mA…u1 † …zu †Š

The membership values found in Step 5 can be compared with v (ideal ef®ciency is given as v ˆ very very important) and Hamming distance can be calculated as Dj ˆ …1=k†

X

6. Discussion with an example The heuristic algorithm de®ned above is applied to various combination of OR and Manufacturing functions such as * * *

jmA…v† …zv †

mA…v † …zv †j;

j ˆ 1; 2; . . . ; n where k ˆ zv is the number of elements of problem space; mA…v† …zv † ˆ For j is the techniques membership function at Step 5; mA…v † …zv † is the Membership functions of v which is de®ned above. The ef®ciency and importance of the techniques on manufacturing functions are de®ned according to the Hamming distance. Where the minimum distance is the most Ef®cient and Important.

* * *

OR-Manufacturing Functions, OR-Advance Manufacturing Functions, OR-OPT, OR-AI, OPT-AI, AI-OPT.

The heuristic algorithm de®ned above is used for OR-AI combination and detail explanations in each step is given below. Step 1. Membership values of U and V is shown in Table 1. Note that membership values are labeled from 1 to 5 in order to be able to ®t the all combinations into one table. Steps 2±5 is performed for OR-AI combination only.

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Step 2. Each OR technique evaluated against AI techniques and relation matrix is produced. For example for OR technique 2A25 the membership value u1 ˆ very really (1) for AI technique v4 ˆ very very Important (1). The relation matrix r14 is given as 2

r14

3 0 6 0 7 6 7 6 0 7 6 7 6 0 7 6 7 6 0 7 6 7 7 ˆ6 6 0 7 a ‰0 6 0 7 6 7 6 0:01 7 6 7 6 0:05 7 6 7 4 0:92 5 1



0 0

0

0 0

0

r14

1 61 6 61 6 61 6 61 ˆ6 61 6 60 6 60 6 40 0

1 1 1 1 1 1 0 0 0 0

1 61 6 61 6 61 6 61 R4 ˆ 6 61 6 60 6 60 6 40 0

1 1 1 1 1 1 0 0 0 0

Relative Hamming distance

Membership values of v

OR-AI AI-OPT OPT-AI OR-Adv. Manf. Func. OR-Man. Func OR-OPT

0.02000 0.03000 0.07091 0.13636

Very very important Important Very important Very important

0.18363 0.53647

Very very important Very important



mA…v1 † …zv † ˆ R4 a u

1 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0:02 1 1 0 0:02 0:20 1 0 0:02 0:20 0:98

1 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0:02 1 1 0:02 0:20 1 0:02 0:20 0:93

3

1 17 7 17 7 17 7 17 7 17 7 17 7 17 7 15 1

3 1 17 7 17 7 17 7 17 7 17 7 17 7 17 7 15 1

Step 4. De®ne the ideal membership of u …u ˆ very really†, from the Fig. 6, as: mA…u † …zu † ˆ ‰ 0 0

0

0 0

0

0 0:02 0:20 0:98 1 Š

Step 5. Solve the following equation

1



by replacing u 1 with mA…u † …zu † in v4 1 ˆ R4 a u 1 which indicates the relationship of AI and OR. This produces

Similarly all relationship matrices …r24 ; . . . ; r124 † can be de®ned. Step 3. Calculate Rj which is the intersection of relationships de®ned in Step 2 …r14 ; r24 ; . . . ; r124 †. In this case R4 is the intersection of the relationship of OR and AI is given as: 2

Combinations

0:02 0:20 0:98 1 Š

that produces a matrix of size 11 6 11. 2

Table 2. Ordered values of relative Hamming distances

mA…v1  † …zv † ˆ ‰ 0

0 0

0

0 0

0

0:01 0:05 0:92 1 Š

Step 6. Calculate Hamming distance between v (very very important) as given in Fig. 7 with the membership values calculated in Step 5. In the example above, the Hamming distance is found to be D4 ˆ 0:020000. This indicates the importance of AI on OR. The same analysis can be found for the other combinations and the results are provided in Table 2. Table 2 shows that the minimum distance is in between the OR and AI techniques that OR techniques are ``very really'' ef®cient in AI and AI is ``very very important'' for OR. Similarly, AI and OPT has also second minimum distance. This indicates that AI is ``ef®cient'' in OPT and OPT is important for AI. However OPT is not as much ef®cient in AI. Furthermore Table 2 indicates that OR is ef®cient in manufacturing and advanced manufacturing functions. OR is less ef®cient in OPT and OPT is not as much important in OR.

7. Conclusion In this study a relationship and comparison of OR, OPT, AI and their utilization in manufacturing function have been investigated by reviewing in around 2600 papers. Fuzzy classi®ers are used to compare their use and effect of these tecniques on each other.

524 Appendix: Classi®cation of manufacturing systems and techniques (OR, OPT, AI) Manufacturing Functions are grouped in 1A: 1. Market Research, 2. Long-Range Forecasting, 3. Capital Equipment and Facility Planning, 4. Customer Order Servicing, 5. Engineering and Design, 6. Manufacturing Process Planning, 7. Marketing, 8. Production Order Scheduling and Manufacturing Control, 9. Purchasing and Receiving, 10. Inventory Management, 11. Quality Control, 12. Maintenance, 13. Accounting, 14. Forecasting, 15. Project Planning, 16. Sequencing and Scheduling (Rambold et al., 1993; Dietrich, 1991). CIM Component functions are grouped in 1B: 1. Automation of CIM, 2. Industrial Control Systems, 3. Sensors, Actuators, and Other, Control System Components, 4. Numerical Control, 5. Industrial Robotics, 6. Discrete Control Usable Programmable Logic Controllers and Personel Computers, 7. Material Handling, 8. Material Transport Systems, 9. Storage Systems, 10. Automatic Data Capture, 11. Just in Time Manufacturing (JIT), 12. Single Station Manufacturing Cells, 13. Group Technology and Cellular Manufacturing, 14. Flexible Manufacturing Systems, 15. Manual Assembly Lines, 16. Transfer Lines and Similar Automated Manufacturing Systems, 17. Automated Assembly Systems, 18. Automated Material Handling Storage Systems, 19. Enterprise Integration CIM and Future Trends, 20. Introduction to Quality Assurance, 21. Inspection Principles and Practices, 22. Inspection Technologies, 23. Computer Control of Manufacturing, 24. Computer Graphics and Transformations, 25. Geometric Modelling, 26. Computer Aided Process Planning, 27. Product Design and CAD/CAM in the Production System, 28. Process Planning and Concurrent Engineering, 29. Production Planning and Control Systems, 30. Lean Production and Agile Manufacturing, 31. Reengineering, Kanban (Singh, 1996). Engineering Activities are grouped in 1C: 1. System Planning, 2. Product Design, 3. Process Planning, 4. Production Planning, 5. Execution Planning, 6. Shop Floor Supervision, 7. Modelling (Matos et al., 1995). Advanced Manufacturing Techniques are grouped in 1D: 1. CDP (Customer Driven Production), 2. BR

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(Business Reengineering), 3. EFM (Environment Friendly Manufacturing), 4. MAMS (Multi-Agent Manufacturing System), 5. VM (Virtual Manufacturing), 6. HMS (Holonic Manufacturing System), 7. BMS (Biological Manufacturing System), 8. LCE (Life Cycle Engineering), 9. GM (Green Manufacturing), 10. CM (Collaborative Manufacturing), 11. RM (Remote Manufacturing), 12. OAMS (Open Architecture Manufacturing System), 13. IMS (Intelligent Manufacturing System), 14. FE (Fractal Enterprise), 15. P 3 IS (Pre-Planned Product Improvement System), 16. SOPS (Self-Organized Production System), 17. RMS (Recon®gurable Manufacturing, Systems), 18. GM (Global Manufacturing), 19. NGMS (Next Generation Manufacturing System), 20. ECommerce, 21. Internet Technology in Manufacturing, 22. Micro and Nano Scale Manufacturing (Qiao, Zhu., 1999). Operations Research methods and techniques are grouped in 2A: 1. Optimization problems. Linear programs, 2. Linear Programming: Basic Concepts, 3. Linear Programming: The Simplex and Dual Simplex Methods, 4. Linear Programming: Duality ad Sensigtivity Analysis, 5. Linear Programming: Extensions, 6. Integer Programming: Branch-andBound Algorithms, 7. Integer Programming: Cut Algorithms, 8. Integer Programming: The Transportation Algorithm, 9. Integer Programming: Scheduling, 10. Nonlinear Programming: SingleVariable Optimization, 11. Nonlinear Programming: Multivariable Optmization without constraints, 12. Nonlinear Programming: Multivariable Optimization with constraints, 13. Network Analysis, 14. Project Planning Using PERT/CPM, 15. Inventory Models, 16. Forecasting, 17. Game Theory, 18. Decision Theory, 19. Dynamic Programming, 20. Finite Markov Chains, 21. Markovian Birth-Death Processes, 22. Queing Systems, 23. M/M/1 Systems, 24. Other Systems with Poisson-Type Input and Exponential-Type Service Times, 25. Simulation (Taha,1997; Hillier, Lieberman, 1995; Ravindran et al., 1987). Statistics methods and techniques are grouped in 2B: 1. Probability, 2. Random Variables, 3. Joint Distributions, 4. Expected Values, 5. The Normal Distribution, 6. Statistical Estimation, 7. Hypothesis Testing, 8. Regression and Correlation, 9. Time Series

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Analysis and Forecasting, 10. Inferences Using Two Samples, 11. Chi-Square Applications, 12. Analysis of Variance, 13. Further Probability Distributions and the Goodness-of-®t Test, 14. Nonparametric Statistics, 15. Decision Theory and Bayesian, Inference, 16. Data Mining, 17. Statistical Process Control, 18. Taguchi Method, 19. Value Analysis, 10. Inferences Using Two Samples, 11. Chi-Square Applications, 12. Analysis of Variance, 13. Further Probability Distributions and the Goodness-of-®t Test, 14. Nonparametric Statistics, 15. Decision Theory and Bayesian Inference, 16. Data Mining, 17. Statistical Process Control, 18. Taguchi Method, 19. Value Analysis (Ravindran and et al., 1987; Mendenhall, 1987; Fukunago, 1990; Freund et al., 1990; Wackerly et al., 1996). Optimization methods and techniques are grouped in 2C: 1. Static Optimization, 2. Dynamic Optimization, 3. Dynamical Optimization with Terminal Constraints, 4. Dynamic Optimizaion with Open Fianl Time, 5. Linear-Quadratic Terminal Controllers, 6. Linear-Quadratic Regulations, 7. Dynamic Programming, 8. Neighboring Optimal Control, 9. Inequality Constraints, 10. Singualar Optimal Control Problems, 11. Hybrid Optimization, 12. Fractal Theory, 13. Combinatorial Mathematics, 14. Petri Nets, 15. Tabu Search, 16. Stokastic Approach, 17. Chaos Theory, 18. Application of Virtual, Convex Polytype (Graph Theory), 19. Memetic Algorithms, 20. Wavelet Analysis (Bryson, 1999). Arti®cial Intelligence methods and techniques are grouped in 2D: 1. Game Playing, 2. Automated Reasoning and Theorem Proving, 3. Expert Systems, 4. Natural Language Understanding and Semantic Models, 5. Modeling Human Performance, 6. Planning and Robotics, 7. Machine Learning, 8. Graph Theory, 9. Recursion-Based Search, 10. Pattern-Direct Search, 11. The Blackboard Architecture for Problem Solving, 12. KnowledgeIntensive Problem Solving, 13. Languages and Programming Techniques for AI-Prolog-LISPObject Oriented Programming, 14. Genetic Algorithm, 15. Fuzzy Logic, 16. Neural Network, 17. Intelligent Agents, 18. Computer Visions, 19. Qualitative Reasoning, 20. Multiple Valued Logic, 21. Immune Networks, 22. Associative Memory, 23. Multi Agent Systems, 24. Simulated Annealing, 25.

Visual Inspection, 26. Logic Programming, 27. Robotics, 28. Software Engineering, 29. Information Systems, 30. Evaluating Algorithms, 31. Computer Animation, 32. Belief Networks, 33. Agent-Based, 34. Pattern Recognition, 35. Constraint-Based System, 36. Arti®cial Intelligence (Luger, 1999; Schutzer, 1987; Bobrow, 1994; Luger, Stubble®eld, 1998; Nilsson, 1998; Banenji, 1980; Winston, 1992; Rich, Knight, 1991).

References Banenji, R. B. (1980) Arti®cial Intelligence: A Theoritical Approach, North Holland, New York. Bobrow, D. G. (1994) Arti®cial Intelligence in Perspective, MIT Press, Cambridge, MA. Dietrich, B. L. (1991) A taxonomy of discrete manufacturing systems. Operations Research, 39(6), 886±902. Freund, J. E. and Walpole, R. E. (1987) Mathematical Statistics, Prentice-Hall, Englewood Cliffs, NJ. Fukunago, K. (1990) Introduction to Statistical Pattern Recognition, Academia Press, Boston. Hillier, F. S. and Lieberman, G. J. (1995) Introduction to Operations Research, McGraw Hill. KarayalcËin, I. An Invited Paper, 6A. Education in OR Evaluation Of Progress in Operations Research Education in Europe in The Last Decade And Some Proposals. EURO III±The Third European Congress on Operations Research, Amsterdam, Netherlands, 9±11 April, 1979. Luger, G. F. and Stubble®eld, W. A. (1998) Arti®cial Intelligence: Structures and Strategies for Complex Problem Solving, Harlow, England, Addison Wesley Longman, Reading, MA. Luger, G. F. (1999) Arti®cial Intelligence, Addison Wesley Longman, Inc. Matos, C. and Pita, H. (1995) Towards a taxonomy of CIM activities. International Journal of Computer Integrated Manufacturing, 8(3), 160±176. Mendenhall, W. (1987) Introduction to Probability and Statistics, Duxbury Press, Boston. Nilsson, N. J. (1998) Arti®cial Intelligence: A New Synthesis, Morgan Kaufmann Publishers, San Francisco, California. Qiao, B. and Zhu, J. (2000) Agent-based intelligent manufacturing systems for the 21st century. International Forum for Graduates and Young Researchers of EYPO, Hannover, The World Exposition in German. Rambold, Y., Nnaji, B. O. and Storr, A. (1993) Computer Integrated Manufacturing and Engineering, AddisonWesley Publishing Company.

526 Ravindran, A., Philips, D. T. and Solberg, J. J. (1987) Operations Research: Principles and Practice, Wiley, New York. Rich, E. and Knight, K. (1991) Arti®cial Intelligence, McGraw-Hill, New York. Sanches, E. (1976) Resolution of composite fuzzy relation equations. Information and Control, 20, 38±48. Schutzer, D. (1987) Arti®cial Intelligence: An ApplicationsOriented Approach, Van Nostrand Reinhold, New York, www.sciencedrect.com. Singh, N. (1996) System Approach to Computer-Integrated Design and Manufacturing, John Wiley and Sons Inc.

Kubat et al. Taha, A. H. (1997) Operations Research, Prentice Hall. Taskin, H. and Golec, A. (1996) Bir Imalat KurulusËunda Bulanik Maktikla Bilgisayar BuÈtuÈnlesËik Imalat Sistemlerinin DegÆerlendirilmesi. Proceeding of The First Turkish Symposium on Intelligent Manufacturing Systems, 30±31 May 1996, pp. 103±118. Wackerly, D., Mendenhall III, W. and Scheaffer, R. L. (1996) Mathematical Statistics with Applications, Duxbury Press, Belmont. Winston, P. H. (1992) Arti®cial Intelligence, AddisonWesley Pub. Co.