optimization of reconfigurable flow lines applying real

AMOC 2011

OPTIMIZATION OF RECONFIGURABLE FLOW LINES APPLYING REAL CODED GENETIC ALGORITHM Kapil Kumar Goyal Mechanical and Industrial Engineering Department Indian Institute of Technology Roorkee, Roorkee, India-247667 [email protected]

P. K. Jain Mechanical and Industrial Engineering Department Indian Institute of Technology Roorkee, Roorkee, India-247667 [email protected]

Madhu Jain Department of Mathematics

Indian Institute of Technology Roorkee, Roorkee, India-247667 [email protected]

ABSTRACT The last few decades have witnessed fierce competition and dynamic business environment caused by globalization of economies, fast pace of development in the process technology and the customer driven market. These modern challenges have paved the way for the new manufacturing paradigm known as Reconfigurable Manufacturing System (RMS) which justifies the need of hour by combining the high throughput of dedicated manufacturing system with the flexibility of flexible manufacturing systems. At the heart of RMS lies the Reconfigurable Machine Tools which are capable of performing multiple operations in its existing configuration and can further be reconfigured into more configuration by keeping its base modules and just adding/removing or adjusting the auxiliary modules. In such circumstances there are many feasible machine configurations available for performing an operation on the part. The parts are processed in multiple stages as per the requirements of the operation sequence. Therefore selecting machines for different production stages becomes the combinatorial problem. In the present research work reconfigurable flow lines have been considered which allow paralleling of identical machines. Real coded genetic algorithm has been applied to optimise the flow line configuration in the presence of reconfigurable machine tools. A numerical problem has been taken to illustrate the developed methodology of flow line optimization applying real coded genetic algorithm. A few near best configurations are also listed, so as to facilitate the reconfiguration process for handling the production requirements of multiple time periods.

KEYWORDS: Reconfigurable Manufacturing Systems (RMS), Reconfigurable Machine Tool (RMT), Machine selection, Genetic algorithm.

1. INTRODUCTION The inability of existing/conventional manufacturing systems to cope up with the present manufacturing environment has paved the way for a new class of manufacturing system to respond rapidly and cost-effectively to the ever changing products and process technologies as well as increasingly fluctuating and uncertain demands. The dedicated manufacturing systems (DMS) are designed to produce very large quantities of just one product and they are cost effective as long as they operate at full capacity. But the present scenario is of increasingly fluctuating and uncertain demands, which the DMS is unable to handle cost effectively. Furthermore with the globalization, the product life is becoming shorter and the customers are demanding the personalized products but the DMS is unable to produce even products which are similar and of the same product family. These realities make DMSs uneconomical, and in fact they are vanishing from the manufacturing industries.

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Capacity (Parts per unit time)

The cellular manufacturing systems are designed around a fixed set of part families. These systems are structurally inflexible and redesigning of cells or changing shop floor layout is very expensive (Abdi and Labib, 2003). Thus handling the variations in the product design and fluctuations in the demand is very uneconomical and difficult. The flexible manufacturing systems (FMS) are flexible and scalable systems, which support product variety. These systems are rather complex as they are constructed with all possible functionality built-in despite of the fact that in many cases not all of it is required. The higher level of complexity requires highly skilled manpower to be employed. As a result, the capital costs and the acquisition risk are very high. Although FMSs focus on flexibility, still they face obsolescence, as their hardware and software are predetermined and fixed. This means that they are not adequately responsive to change, as their capabilities in terms of upgrading, addons and customization, are limited. Moreover, FMSs are built for low or medium volume productivity, so they cannot handle the large market fluctuations efficiently. Considering the limitations of existing manufacturing systems in terms of adjusting the capacity and functionality economically and rapidly, has paved the way for a new manufacturing paradigm. Moreover the existing systems are facing a threat of obsolescence due to the fast pace of development in the enabling technologies and the ever changing needs of the customers. Therefore, there is an acute need of a manufacturing system, which is responsive to the market requirements and can easily be upgraded. The responsiveness of the system is the ability of a system to adjust its functionality and capacity rapidly with respect to ever changing product mix and volume. The answer to all these requirements was proposed by Koren (1999) in terms of Reconfigurable Manufacturing Systems. The reconfigurable manufacturing system is designed at the outset to offer the exact functionality and capacity, exactly when it is needed. As shown in Figure 1 (Mehrabi at al., 2000). RMS is having positive attributes of both the DMS and FMS.

Dedicated Manufacturing System Reconfigurable Manufacturing System Flexible Manufacturing System

Functionality (Product variety) Figure 1: Schematic diagram for the comparison of Dynamically Adaptable RMS with DMS and FMS. An RMS is designed to “reconfigure,” within the scope of its lifetime, so that it can be easily upgraded in response to the market changes. The upgrading of the system may be in terms of either capacity (volume of parts that can be produced) or functionality (number of different types of parts that can be produced). Reconfiguration allows an RMS to achieve throughput approaching that of a DMS but allows it to produce the whole range of products in the family of parts. Thus the goal of RMS is to provide exactly the capacity and of spindles. Short conversion times between processing of different batches or between two members of a part family within the same day plays a crucial role in the efficiency of RMS. Figure 2 depicts the configuration of RMTs from the standard module library, in

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which two machine configurations (i.e. and ) of machine one are assembled by just varying ) the auxiliary modules, while the machine two is shown in its single configuration (i.e. Liles and Huff (1990) have defined an RMS as the system capable of tailoring the configuration of manufacturing system to meet the production demand placed on it dynamically. The concept of ‘modular manufacturing’ defined by Tsukune et al. (1993) is also similar to the Reconfigurable Manufacturing System. Later in 1996 the Engineering Research Center for Reconfigurable Manufacturing Systems (ERC-RMS) was established at the University of Michigan, Ann Arbor to develop and implement reconfigurable manufacturing systems. Koren et al. (1999) defined RMS as: “An RMS is designed at the outset for rapid change in its structure, as well as in hardware and software components, in order to quickly adjust the production capacity and functionality within a part family in response to sudden unpredictable market changes as well as introduction of new products or new process technology”. In the conventional manufacturing systems (DMS, FMS, CMS) the operation sequence required for

RMT Configurations

Auxiliary Modules

Basic Modules

Figure 2: Reconfigurable machine configurations in RMS. manufacturing a part is generated after knowing the operational capabilities of the available machine tools but in RMS the process is reverse first of all the operation sequence of parts is generated based on which the RMS configuration is designed. According to Urbani et al. (2001) the reconfigurability is the ability of a system to adapt to expected or unexpected demand changes through the changes in the system or system component's structure guaranteeing the efficient use of functionalities. Pattanaik et al. (2007) have solved the cellular layout problem with reconfigurable machines. Maier-Speredelozzi et al. (2003) presented the system convertibility as the capability of a system to adjust production functionality and presented the system convertibility measures based on the assessment of convertibility of the system configuration, machines and material handling equipments. Gumasta et al. (2011) have suggested reconfigurability of the RMS on system level. Son et al. (2001) and Youssef and ElMaraghy (2007) have modeled a multiple demand period configuration generation by first recording the k best configurations for all the demand periods based on cost as single performance criterion by applying Genetic Algorithm (GA) and in later stage selected the configurations based on configuration similarity and reconfiguration smoothness. Spicer and Carlo (2007) have attempted the multiple periods RMS modeling by considering the cost and reconfiguration. In nutshell the design of RMS configuration is a very crucial issue on which the performance and reconfigurability of the system is highly dependent. In the present work an attempt has been made to apply the real coded genetic algorithm for the optimal design of single part flow line in a reconfigurable manufacturing environment.

2. MATHEMATICAL MODEL FOR RMS OPTIMIZATION 1291

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In a reconfigurable manufacturing system, the machines are capable of performing variety of operations in its existing configurations and the reconfigurable machine tools (RMT) can further be reconfigured into other configurations. The different configurations thus can further enhance the functionality and can perform number of operations. In such a scenario the availability of large number of machines to perform a single operation, makes it a combinatorial complex problem to assign the RMTs to various operations in an operation sequence. The authors have developed a real coded genetic algorithm approach to handle the single part flow lines in the reconfigurable manufacturing environment. To model the developed approach following notations have been used:

mcij

machine i (1< i < I) in its jth (1< j < J i ) configuration

nij

number of machines required to satisfy the demand when machine i with jth configuration is selected demand rate a set of feasible alternative machine configurations to perform kth (1< k < K) operation {(i 1 , jFk }. Here each feasible alternative f (1< f < F k ) is defined as j 1 ), (i 2 , j 2 ),….(i f , j f )……. (iFk , )

D FS k

(i f ,j f ), where i f specifies the feasible machine and j f specifies the feasible machine configuration

CM i j

cost of machine i with jth configuration (i.e.

mcij )

Pi ,jk

production rate of machine i with jth configuration for performing kth operation

δ i ,jk

1 if operation k can be performed with machine i having its jth configuration, otherwise 0

C p,q

cost of assigning pth machine with qth configuration from the feasible alternative machine configurations to perform an operation at specified demand rate

Cost is the important performance parameter driving the selection of machine configuration for a particular operation. In the present scenario the manufacturers are facing stiff competition due to globalization and volatile markets. Thus meeting the customer demands economically is most important. The cost (C p,q ) of a feasible alternative machine configurations for performing kth operation on the specified demand rate is calculated using the equations (1) and (2). The cost is a non beneficial attribute and is to be minimized. (1) (2) Where, C p,q represents the cost of pth machine with qth configuration to perform kth operation on the specified demand rate n p,q

is the number of machines required for selected machine configuration

D

is the demand rate of the product is the cost of machine p with qth configuration is the production rate of pth machine in its qth configuration for performing operation

number k The ratio

is rounded off to the higher integer as number of machines can’t be a fraction.

3. IMPLEMENTATION OF REAL CODED CHROMOSOMES 1292

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Genetic algorithms are very efficient stochastic search algorithms that try to emulate natural evolution. They mimic the evolutionary process by implementing a survival of the fittest strategy. The GA approach was originally introduced by Holland J.H. (1975) and has been applied successfully to solve a wide range of optimization problems including combinatorial problems. An important feature of GA is that it searches several paths simultaneously starting with an initial population. Each individual element in the population is called a chromosome. Each chromosome can represent a feasible solution containing a sequence/string of binary numbers known as genes. During an evolution process, the current population is replaced by a new generation of chromosomes. The new population may contain both parent chromosomes and newly generated chromosomes called offsprings. Operators like crossover, mutation etc. are used to generate the offspring chromosomes. The crossover operation is a process of merging two parent chromosomes and formation of one or two new chromosomes. Mutation refers to a process of modifying the structure of a selected chromosome by arbitrarily changing one or more genes. A fitness function representing the objective function is used to evaluate the chromosomes. The chromosomes with high fitness among the parents and offspring will be selected for the next generation. This process repeats until the satisfaction of the stopping criteria that can be either a limited number of generations are reached or no further improvement in solutions. A major shortcoming of binary GAs is that they face difficulties when applied to problems having large search space and seeking high precision. In binary GAs string length must be selected in advance to get a desired degree of precision in the final solution. Another important drawback in binary coded GA is the ‘‘Hamming-Cliff’’ problem i.e. a large number of bits are to be altered to change an integer to its adjacent value which causes reduction in the efficiency of binary GA. The real-encoding of chromosomes is used to overcome these difficulties related to binary encoding of continuous parameter optimization problems (Wright 1991, Michalewicz 1992). The basic GA with real coded chromosomes has been implemented in Youssef et al. (2006), to handle the discrete and discontinuous variable domain size in the RMS modeling. The real coded genetic algorithm is implemented in the present study for obtaining the optimal configuration along with the k near best configurations to help in further reconfiguration cycle optimization.

4. OBJECTIVE FUNCTION, SOLUTION MAPPING

CONSTRAINT

HANDLING

AND

The number of decision variables involved in the present study is twice (one for the machine type and other for the machine configuration.) the number of stages and all the variables in the solution vector are discrete and discontinuous. The basic principle of evolutionary algorithms is to create an initial population of solutions by choosing the variables randomly. But in the present case feasible solutions are rather sparse which will lead to infeasible population. Further the crossover and mutation of the chromosomes will give rise to the infeasibility. Therefore to handle the problems mentioned above, a real coded chromosome is proposed along with the constraint handling through decoding of chromosomes using the feasible alternative machine configurations generated beforehand. The length of chromosome is equal to the number of stages and on each stage an operation has to be performed according to the operation sequence. A set of feasible alternative machine configurations FS k for each operation is already recorded as shown in Figure 3. Now each stage is to be assigned with a feasible machine configuration which is mapped in the present study through the real coded chromosomes. As shown in Figure 1, the first production stage (S-1) gene value is taken 0.6539 and operation 4 is to be performed. From Table 1 the feasible alternative machine configurations FS 4 can , }. Thus there are four feasible alternative machine configurations be read as { capable of performing operation 4. Now the gene value has to be multiplied by the number of feasible alternative machine configurations (F k ) available to perform the operation, which in this case is four and the final value is to be rounded off to the higher integer. The final value represents the order of the selected machine configuration alternative from the already recorded feasible alternatives. In the Figure 4, the third option is selected from the set of feasible alternative machine configurations which is fourth machine in its third configuration. The decoding of real variables ensures that for any random value of the gene a feasible machine configuration is always assigned to each production stage. The crossover

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Figure 3: Feasible solution recording for the single part flow line configuration. Figure 4: Solution mapping through real coded chromosome

and mutation is not going to affect the feasibility of the solution due to the mapping schema adopted in the present study. All the feasible alternatives are having equal probability of selection and the search space is also restricted to the feasible region only. The present study proposes the assignment of machines to all the operations allocated on production stages from the feasible alternative machine configurations based on the objective Function: S

Minimize F1 =                     (3) ∑C ps ,qs s =1

Here equation (3) represent the fitness function i.e. cost of the configuration selected for the single product flow line. The subscripts p s and q s represent the feasible alternative machine p with its configuration q assigned at the sth stage. The real-encoding of solution is proposed to map the discrete and discontinuous search space. A set of feasible alternative machine configurations FS k for each

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Table 1: Reconfigurable machine tools capabilities and cost

RMT Production rate in parts/hour for performing various Operation operations (k) → j mci ↓ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 mc11

-

-

- 14 -

mc12

-

-

-

3 1

-

- 20 -

mc

mc12

14 -

-

- 15 -

- 12 -

-

- 20 -

- 15 -

-

-

- 8 -

-

- 18 -

-

-

-

-

-

-

-

-

-

- 25 -

-

-

-

-

-

-

- 15 -

-

-

-

- 12 -

mc22

- 15 -

-

-

-

-

-

-

-

-

mc23

-

- 25 -

-

-

- 18 -

mc24

- 20 -

- 20 - 18 -

1 3

- 12 -

-

mc

mc32

30 -

mc14 mc42

mc

-

-

-

- 26 -

-

- 24 -

1140

-

-

-

-

1350

- 10 -

-

-

780

-

-

-

-

- 22 -

-

-

- 30 -

-

-

-

-

- 18 - 25 -

-

- 16 -

-

- 22 -

- 15 -

-

- 24 - 20 -

-

-

mc53

-

-

- 24 -

-

- 30 -

- 25 -

-

-

-

-

- 22 14 -

-

-

1825

-

-

- 20 -

-

1350

-

-

910

-

-

20 -

-

-

mc52

mc54

1215

-

-

-

-

- 20

- 20 - 35 - 15 -

25 -

-

1025

-

- 30 -

- 15 -

-

-

-

-

955

-

- 24 -

- 25 -

-

-

-

- 10 -

-

-

- 16 -

-

- 24 -

-

16 -

750

-

-

- 15 -

-

-

-

-

-

- 14 - 15 -

- 25 -

-

-

mc43 1 5

-

-

-

Cost of RMT (in 103 $)

-

- 25 -

- 28 -

- 24 -

-

- 26

- 20 -

- 18 -

- 18 -

-

-

-

-

-

-

- 18 -

-

-

- 20 - 16 -

-

-

1500 1400

-

900

- 20

1175

-

-

1230

- 18 -

1175

-

Table 2: Top 10 configurations recorded through the real coded genetic algorithm Solutions Machine assigned/No. of machines

Chromosomes #

Fitness value ]

S-1

S-2

S-3

S-4

S-5

S-1

S-2

S-3

S-4

S-5

Cost in 103 of USD (F1)

1

0.6539

0.6577

0.1610

0.4324

0.5051

43/2

42/2

22/4

23/3

42/2

15860

2

0.1652

0.6207

0.0773

0.3385

0.5806

11/4

42/2

22/4

23/3

42/2

16060

3

0.6077

0.6201

0.6482

0.2687

0.4620

43/2

42/2

31/5

23/3

42/2

16120

4

0.5978

0.6207

0.0773

0.0894

0.5806

43/2

42/2

22/4

11/5

42/2

16190

5

0.5553

0.1276

0.1588

0.3558

0.4182

43/2

23/3

22/4

23/3

42/2

16280

6

0.7461

0.6625

0.2417

0.2599

0.9620

43/2

42/2

22/4

23/3

54/3

16385

7

0.0596

0.6820

0.0424

0.0714

0.5216

11/4

42/2

22/4

11/5

42/2

16390

8

0.6539

0.6577

0.8772

0.4324

0.5051

43/2

42/2

43/3

23/3

42/2

16420

9

0.5447

0.6473

0.5439

0.2101

0.5225

43/2

42/2

31/5

11/5

42/2

16450

10

0.5822

0.5407

0.1610

0.4324

0.5051

43/2

32/2

22/4

23/3

42/2

16510

operation is already recorded as shown in Figure 3.As shown in Figure 4, now each stage is to be assigned with a feasible machine configuration which is mapped in the present study through the real coded solution.

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5. NUMERICAL ILLUSTRATION For illustrating the developed approach of optimal machine configuration assignment, a set of RMTs having the operational capabilities and cost as given in Table 1 are considered. The optimal machine assignment for a single part flow line allowing paralleling of similar machines for a single fixed demand period is illustrated. As shown in Figure 3, the operation sequence of the product to be produced is assumed to be 4→17→2→8→1 with a demand rate of 50. The number of stages is also assumed to be five. The k near best solutions are obtained in this case 10 near optimal solutions are obtained and listed in the Table 2. A number of trials were conducted to optimize the parameters involved in the real coded genetic algorithm implementation to the present problem. The final values of the parameters used in the experiment are, population size = 50, number of generations = 100, crossover probability = 0.9 and mutation probability = 0.1. In the present algorithm the tournament selection has been implemented, with tournament size of two along with the single point crossover.

6. CONCLUSION AND FUTURE SCOPE In the present study a novel approach has been proposed to design the configuration of single part flow line in reconfigurable manufacturing system. The search space has been reduced to the feasible region making it very efficient to find the optimal solution. The real coded chromosomes are used for the constraint handling and solution mapping. The k near best solutions are recorded which can further be considered for optimization of the reconfiguration cycle consisting of multiple time horizon. Considering the ranking of the solutions the decision manager may choose a suitable candidate among the top ranking solutions to justify the objectives defined by the management along with the present market scenario. In future authors plan to study RMS for the multiple periods planning horizon.

REFERENCES 1. Abdi, M. R. and Labib, A. W., 2003. A design strategy for reconfigurable manufacturing systems (RMSs) using analytical hierarchical process (AHP): a case study, International Journal of Production Research, Vol. 41, No. 10, pp. 2273-2299. 2. Gumasta, K., Gupta, S. K., Benyoucef, L. and Tiwari, M. K., 2011. Developing a reconfigurability index using multi-attribute utility theory, International Journal of Production Research, Vol. 49, No. 6, pp. 1669-1683. 3. Holland, J. H., 1975. Adaptation in natural and artificial systems, University of Michigan Press, Ann Arbor, USA. 4. Koren, Y., Hiesel, U., Jovane, F., Moriwaki, T., Pritschow, G., Ulsoy, G. and Van-Brussel, H., 1999. Reconfigurable manufacturing systems, Annals of the CIRP, Vol. 48, No. 2, pp. 527-540. 5. Liles, D. H. and Huff, B. L., 1990. A computer based computer scheduling architecture suitable for driving a reconfigurable manufacturing system, Computer and Industrial Engineering, Vol. 19, No. 1-4, pp. 1-5. 6. Maier-Speredelozzi, V., Koren, Y. and Hu, S. J., 2003. Convertibility measures for manufacturing systems, Annals of the CIRP, Vol. 52, pp. 367-370. 7. Mehrabi, M. G., Ulsoy, A. G. and Koren, Y., 2000. Reconfigurable manufacturing systems: Key to future manufacturing, Journal of Intelligent Manufacturing, Vol. 11, No. 4, pp. 403-419. 8. Michalewicz, Z., 1992. Genetic algorithms + data structures = evolution programs, New York: SpringerVerlag. 9. Pattanaik, L. N., Jain, P. K. and Mehta, N. K., 2007. Cell formation in the presence of reconfigurable machines, International Journal of Advanced Manufacturing Technology, Vol. 34, pp. 335-345. 10. Son, S. Y., Olsen, T. L. and Derek, Y., 2001. An approach to scalability and line balancing for RMS, Integrated Manufacturing Systems, Vol. 12, No. 7, pp. 500-511. 11. Spicer, P. and Carlo, H. J., 2007. Integrating reconfiguration cost into the design of multi-period scalable reconfigurable manufacturing systems, Transactions of the ASME, Vol. 129, pp. 202-210. 12. Tsukune, H., Tsukamoto, M., Matsushita, T., Tomita, F., Okada, K., Ogasawara, T., Takase, K. and Tuba, T., 1993. Modular manufacturing, Journal of intelligent manufacturing. Vol. 4, pp. 163-181.

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13. Urbani, A., Molinari-Tosatti, L., Pedrazzoli, P., Fassi, I. and Boer, C. R., 2001. Flexibility and reconfigurability: An analytical approach and some examples, CIRP 1st International Conference on Reconfigurable Manufacturing Systems, Ann Arbor, MI. 14. Wright, A. H., 1991. Genetic algorithms for real parameter optimization, In: G.J.E. Rawlins, ed. Foundations of Genetic Algorithms I. San Mateo: Morgan Kaufmann, 205-218. 15. Youssef, Ayman M. A. and ElMaraghy, H. A., 2006. Modelling and optimization of multiple-aspect RMS configurations, International Journal of Production Research, Vol. 44, No. 22, pp. 4929-4958. 16. Youssef, A. M. A. and ElMaraghy, H. A., 2007. Optimal configuration selection for reconfigurable manufacturing systems, International Journal of Flexible Manufacturing Systems, Vol. 19, pp. 67-106.

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