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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 10, October 2013)

Dynamic Scheduling of Flexible Manufacturing System Using Scatter Search Algorithm M. Krishnan1, T. Karthikeyan2, T. R. Chinnusamy3, A. Murugesan4 1,3

Department of Mechanical Engineering, K.S. Rangasamy College of Technology, Tiruchengode - 637 215, Tamil Nadu, India. 2 Arulmurugan College of Engineering, Karvazhi road, Thennilai - 639 206, Tamil Nadu, India. 4 Department of Mechatronics Engineering, K.S. Rangasamy College of Technology, Tiruchengode - 637 215, Tamil Nadu, India. Asadzadeh and Zamanifar (2011) discussed the Flexible Job-Shop Scheduling Problem (FJSP) is one of the most popular manufacturing optimization models in practice and is NP-hard, for this case; deterministic methods of search are inefficient generally. The n x m classical FJSP involves n jobs and m machines. Each job is to be processed on each machine in a pre-defined sequence and each machine processing only one job at a time. In practice, the shopfloor setup typically consists of multiple copies of the most critical machines so that bottlenecks due to long operations or busy machines can be reduced. Therefore, an operation may be processed on more than one machine having the same function. This leads to a more complex problem known as the FJSP. The extension involves two decisions; assignment of an operation to an appropriate machine and sequencing the operations on each machine. In addition, for complex manufacturing systems, a job can typically visit a machine more than once (known as recirculation). These three features of the FJSP significantly increase the complexity of finding optimal solutions.

Abstract—Flexible manufacturing system (FMS) scheduling is one of the most trusted and complicated task in machine scheduling. It is strongly Non polynomial complete combinatorial problem. FMS is agile and flexible which is well suited for simultaneous production of a wide variety of product mix in low volumes. Meta-heuristic approaches such as genetic algorithm, simulated annealing etc. are widely applied for the static scheduling problems. Now-a-day's manufacturing systems operate in dynamic environments where usually inevitable unpredictable realtime events may cause a change in the planed previously feasible schedule and may turn infeasible when it is released to the shop floor. In this paper, a meta-heuristic approach called Scatter-Search (SS) is applied for scheduling optimization of flexible manufacturing systems by considering the objective, i.e., minimizing the makespan with the machine breakdown. It provides a wide exploration of the search space through intensification and diversification and also with unifying principle for joining solutions and they exploit adaptive memory principle to avoid generating or incorporating duplicate solutions at various stages of the problem. The comparative study of this approach is presented with static scheduling.

II. REVIEW OF LITERATURE

Keywords—Dynamic scheduling; Flexible manufacturing system; Scatter search algorithm.

Scheduling of FMS is an ongoing research topic. The high investment and the high potential of FMS because of its adaptive nature, attracts many researcher. The performance of a Flexible manufacturing system (FMS) is highly depends on the selection of the right scheduling policy. Hence, there are many approaches and procedures have been developed for scheduling FMS and still the research is going on. All these algorithms aim to find an optimal solution or a near optimal solution efficiently. Saravanan and Noorul Haq (2007, 2008) explored the potential of scatter search for FMS scheduling problems. Vijay Kumar et al. (2011) proposed a heuristic based genetic algorithm for generating optimized production plans in flexible manufacturing systems.

I. INTRODUCTION Customer demand and requirements of any product changes are very rapid in the present market scenario. It is very important that, the manufacturing system is to accommodate these changes as quickly as possible to compete in the market. This advancement induces habitually a conflict for a manufacturing system because as the variety increases the productivity decreases. So the FMS is a good combination between variety and productivity. Solving a scheduling problem is to determine a sequence of operations in every job so that the make span is minimized or the utilization of machines is maximized while satisfying the manufacturing objectives. 329

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 10, October 2013) The Key-point objective was the reduction of machine idle time obtained by an optimized evolutionary strategy needed to reach the optimal schedule in complex manufacturing systems. Udhayakumar and Kumanan (2010, 2012) proposed particle swarm optimization for scheduling problem and highlighted the importance of integration between production schedule and MHS schedule in FMS. The Giffler and Thompson algorithm with different priority dispatching rules was developed to minimize the makespan in the FMS production schedule. Pickardt and Branke (2012) surveyed dispatching rules that explicitly take into account setup times in their decision making. He and Sun (2013) proposed job shop scheduling problem with machine breakdown was considered in improving robust and stable performance of rescheduling with a single strategy. The computational results proved the effectiveness of the new strategies and new algorithms compared with other strategies. The problem of real-world scheduling systems is of great importance for the successful implementation with real time events. Very few work carried out in this dynamic scheduling of flexible manufacturing system and is the order of the day.

Step 2 : Use the improvement method to create one or more enhanced trail solutions Step 3 : With these initial solutions update the reference set (Refset) Step 4 : Combination method 4.1. Generate subsets of Refset 4.2. Combine these subsets and obtain new solutions 4.3. Use the improvement method to create a more enhanced trail solution 4.4. Continue to maintain and update the reference set until Refset is stable (no new solutions are included) Step 5 : If iterations (steps 1-4) elapse without improvement stop, or else returns to step 1. B. Numerical Illustration Step 1: Assume seed solution and use the diversification generator Glover F [7] suggested a method for generating diversified solutions as follows, P = (1, 2 ...n). Subsequence P (h: s); Where, s is a positive integer between 1 and h, to be P(h: s) = (s; s + h; s + 2h . . . s + rh), r is the largest nonnegative integer such that s + rh ≤ n, permutation P (h), for h ≤ n, to be P(h)=(P(h: h); P(h: h – 1). . .P(h: 1)): Suppose, P is given by P =(1,2,3,4,5,6,7,8,9). If we choose h=4, then P(4:4)= (4, 8), P(4:3)= ( 3, 7), P(4:2)= (2, 6), P(4:1)= (1, 5, 9), therefore P(4)= (4,8,3,7,2,6,1,5,9) In general, for the goal of generating a diverse set of permutations, preferable values for ‘h’ range from 1 to n/2 [Saravanan and Noorul Haq, 2008].

III. SCATTER SEARCH ALGORITHM Glover (1977) introduces Scatter Search as a heuristic for solving integer programming problems. As like Genetic Algorithm(GA), SS is also belongs to evolutionary computation family from the point of view that they build, maintain and evolve a population of solutions for the purpose of generating new trail solutions. In SS, the initial population is created with good solutions. Then a reference set (Refset) is generated from initial population of solutions. It uses Refset to combine its solutions and construct other solutions. Size of the Refset in SS is relatively small when compared to the population size of other evolutionary algorithms. In other algorithms like GA, reproduction based on probabilistic selection of parents where as in SS, it is based on deterministic selection of reference solutions. For combining, SS operates unifying principles based on strategic designs, where other approaches use randomization methods like cross over and mutation.

Step 2: Improvement method Use the improvement method for the all diverse set solutions and produce more enhanced solutions. For example:

4

8

3

7

2

6

1

5

9

The sequence is divided into two by taking half the number of jobs on both sides. If the number of jobs is not an even number, one more than half the number of jobs is taken in the left side. The jobs on the right side of the sequence have to get inserted on the left side.

A. Steps in Scatter Search algorithm The basic steps involved in the Scatter Search are explained in the Fig. 1 and are listed below, Step 1: Use the diversification generator to generate diverse trail solutions from the seed solutions(s) 330

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 10, October 2013) Step 3: Reference set update method Build and maintain a reference set consisting of 50% of superior solution and 50% of inferior solution, where the total number of solutions in the reference set is equal to number of machines (where the value of reference set is typically small, e.g., no more than 20).

Start

Seed solution preparation

Step 4: Subset generation method and Solution combination method Creating the new solutions by the forming the subset as follows, Subset Type = 1: All two-element subsets. Subset Type = 2: Three-element subsets derived from the two-element subsets by augmenting each two-element subset to include the best solution not in this subset. Subset Type= 3: Four-element subsets derived from the three-element subsets by augmenting each three-element subset to include the best solutions not in this subset. Subset Type = 4: The subsets consisting of the best i elements, for i=5 to no. of solutions in the Ref set. By combining the subset generated in step 4 described by the following example.

Generate a set of diverse solutions by diversification method

Transform solutions into improved solutions by improvement method

Build and maintain a reference set and Update the reference set

Produces subset of solutions subset generation method

Generate new solution Combination method

Example: Two Element subset : (1, 2) Yes

Solution 1 : 4 8 3 7 2 6 1 5 9

If any improved solution

Solution 2 : 3 5 6 2 1 4 9 7 8 Combining the above two solution, the new solution is 4 3 8 5 6 7 2 1 9, Similarly, combining all the subset and update the Ref set. If any improvement in step 4, the improved solution will proceed with insertion heuristics to find the new solution i.e. move to step 2.

Yes If stopping criteria reached

Step 5: If no improvement, check the stopping criteria and stop else go to step 1.

No

TABLE 1. CONFIGURATION OF FMS

Layout type U-loop

End Fig 1. Steps In Scatter Search Algorithm

No. of Machines

No. of parts

Load /unload Stations

No. of AGV

6

6

1 Each

1

To assess the performance of proposed method, simulation is carried out through the software and the solution quality is compared with and without breakdown the Scatter Search algorithm.

331

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 10, October 2013) To validate the model a benchmark instance for the job shop scheduling problem which is available from the OR library web site [Mattfeld D.C., and Vaessens] FT06 is selected. The parameter values for the scatter search algorithms as follows: Number of Iteration :10 Arrival Pattern :Poisson’s Number of Host :1 Total Operation Time :480 min.(8 Hours shift) Breakdown :10min. for every 10min. of working (while assuming with breakdown) and it follows Gamma distribution.

V. CONCLUSION The flexible manufacturing system scheduling problem is an important and complicated problem in machine scheduling. In this paper, scatter search algorithm is proposed. Use of software simulation the results of scatter search algorithm is compared both without and with machine breakdown for the benchmark problem. In future this work may be extended to all cases in the OR library with multi objective. REFERENCES [1] [2]

IV. RESULS AND DISCUSSION [3]

The table 2 shows the simulation result of FMS with and without breakdown for varying values of inter arrival time. When arrival time increases the makespan also increases for one shift operation (480min.) and it reaches to 8 min. then the make span is not reached at one shift due to the delay in parts arrival. While comparing with the results obtained with breakdown, due to the machine breakdown the delay of getting make span in all cases of inter arrival time as shown in table 2 and fig. 2.

[4]

[5]

[6]

TABLE 2. COMPARATIVE RESULTS OF MAKE SPAN FOR VARIOUS INTERVAL ARRIVAL TIME

Inter Arrival Time (Min.)

Make span - Without Breakdown (Min.)

Make span - With Breakdown (Min.)

1

230

244

2

267

287

3

304

305

4 5 6 7

341 378 415 452

342 379 416 456

[7]

[8]

[9]

460 440 420

Make Span (Units)

400 380

360 340 320

300

Without Breakdown

280

With Breakdown

260 240 220

1

2

3

4

5

6

7

Inter Arrrival Time (Units)

Fig 2. Performance Of Scatter Search Algorithm

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Christoph, W., Pickardt and Jurgen Branke. 2012. Setup-oriented dispatching rules – a survey. Int. J. Pro. Res. 50, 5823-5842. Leila Asadzadeh and Kamran Zamanifar. 2011. Design and implementation of a multi-agent system for the job shop scheduling problem”, Int. J. Comp. Sci. Sec. 5, 287-297. Saravanan, M.,and Noorul Haq, A. 2008. Evaluation of scattersearch approach for scheduling optimization of flexible manufacturing systems. Int. J. Adv. Manuf. Tech. 38, 978–986. Saravanan, M., Noorul Haq, A., and Vivekraj, A.R. 2007. Performance evaluation of the scatter search method for permutation flowshop sequencing problems. Int. J. Adv. Manuf. Tech. 37, 12001208. Udhayakumar P., and Kumanan, S. 2012. Integrated scheduling of flexible manufacturing system using evolutionary algorithms. Int. J. Adv. Manuf. Tech. 61, 621-635. Udhayakumar, P., and Kumaran, S. 2010. Sequencing and scheduling of job and tool in a flexible manufacturing system using ant colony optimization algorithm. Int. J. Adv. Manuf. Tech. 50, 1075–1084. Vijay Kumar M., Murthy, A. N. N., and Chandrasekhara K. 2011. Dynamic scheduling of flexible manufacturing system using heuristic approach, Opsearch. 48, 1-19. Wei He, and Di-hua Sun. 2013. Scheduling flexible job shop problem subject to machine breakdown with route changing and right-shift strategies. Int. J. Adv. Manuf. Tech. 66, 501-514. Mattfeld D.C., and Vaessens, R. J. M. Job shop scheduling benchmarks. Available: OR Library online, http://mscmga.ms.ic.ac.uk