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)

329

Dynamic Scheduling of Flexible Manufacturing System Using

Scatter Search Algorithm M. Krishnan

1, T. Karthikeyan

2, T. R. Chinnusamy

3, A. Murugesan

4

1,3Department of Mechanical Engineering, K.S. Rangasamy College of Technology,

Tiruchengode - 637 215, Tamil Nadu, India. 2Arulmurugan College of Engineering, Karvazhi road, Thennilai - 639 206, Tamil Nadu, India.

4Department of Mechatronics Engineering, K.S. Rangasamy College of Technology,

Tiruchengode - 637 215, Tamil Nadu, India.

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 real-

time 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.

Keywords—Dynamic scheduling; Flexible manufacturing

system; Scatter search algorithm.

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.

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 shop-

floor 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.

II. REVIEW OF LITERATURE

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.

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)

330

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.

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.

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)

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].

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.

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Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 10, October 2013)

331

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).

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.

Example: Two Element subset : (1, 2)

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

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.

Step 5: If no improvement, check the stopping criteria and

stop else go to step 1.

TABLE 1.

CONFIGURATION OF FMS

Layout

type

No. of

Machines

No. of

parts

Load

/unload

Stations

No. of

AGV

U-loop 6 6 1 Each 1

Fig 1. Steps In Scatter Search Algorithm

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.

Transform solutions into improved solutions by

improvement method

Build and maintain a reference set and Update

the reference set

Generate new solution Combination method

Yes

If any improved

solution

Produces subset of solutions subset generation

method

Start

Seed solution preparation

Generate a set of diverse solutions by

diversification method

No

End

If stopping

criteria reached

Yes

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Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 10, October 2013)

332

220

240

260

280

300

320

340

360

380

400

420

440

460

1 2 3 4 5 6 7

Ma

ke

Sp

an (

Un

its)

Inter Arrrival Time (Units)

Without Breakdown

With Breakdown

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.

IV. RESULS AND DISCUSSION

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.

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

4 341 342

5 378 379

6 415 416

7 452 456

Fig 2. Performance Of Scatter Search Algorithm

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.

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[4] Saravanan, M., Noorul Haq, A., and Vivekraj, A.R. 2007.

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1208.

[5] Udhayakumar P., and Kumanan, S. 2012. Integrated scheduling of

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[7] Vijay Kumar M., Murthy, A. N. N., and Chandrasekhara K. 2011. Dynamic scheduling of flexible manufacturing system using

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http://mscmga.ms.ic.ac.uk