1. DYNAMIC FACILITY LAYOUT : GENETIC ALGORITHM BASED MODEL
King Saud University College of Engineering Department of Industrial Engineering
DYNAMIC FACILITY LAYOUT : GENETIC ALGORITHM BASED MODEL By
HASSAN ALI AL-BAHARNAH

2. Main component are: Introduction Review of the Relevant Literature
Solution Methodology
Comparison among mothedologies.
Conclusion

3. Introduction:
The Facility Layout Problem is concerned with how to arrange block areas within the facility.
The dynamic plant layout problem (DPLP) extends the static plant layout problem (SPLP) by considering the changes in material-handling flow over multiple periods and the costs of rearranging the layout.
This solution not gives an optimal but near to optimal solution based on genetic algorithms.

4. Review of the Relevant Literature:
The Facility layout problem has been treated by a large number of researches, but all or most of those researchers concerned with the static one. In this project, I try to introduce a general review for this problem and to deal with the dynamic nature of this problem.

5. SOLUTION METHODOLOGY Step 1 : Given
Genetic algorithm can solve the dynamic layout problem without utilizing the dynamic programming:
Step 1 : Given
NP, the number of periods.
NN, number of department.
NFIX, number of deportment that have fixed location.
SI, the fixed and variable rearrangement cost vector.
X and Y, the initial centeroid vector for all department.
JF, the weight matrix for each period.

6. SOLUTION METHODOLOGY step 2: Step 3:
Calculate the first evaluation for first period as NP times.
Step 3:
Apply the first procedures on the first period considering the first modified evaluation and the given layout as shown below:

7. FLOW DATA AND SHIFTING COSTTO
FROM F TO
FROM F TO
FROM F TO
FROM F

8. Initial layout (parent)TO
FROM F
Si = ( )
Facility layout Representation on genetic :
Initial layout (parent) 1 2 5 6 4 3
Coded layout
Chromosome 1 2 3 4 5 6

9. Period Layout Zij
(1,3,5,6,4,2) 12,822
(1,4,2,5,3,6) 14,853
(1,5,3,2,4,6) 13,172
(1,6,4,2,5,3) 13,032
(3,2,6,4,1,5) 12,819
66,698
Total cost when the best layout in period t is used
Layout Rank in period Total cost
(1,3,5,6,4,2) ,610
(1,4,2,5,3,6) ,137
(1,5,3,2,4,6) ,416
(1,6,4,2,5,3) ,336
(3,2,6,4,1,5) ,510

10. Optimal solution for the numerical example
Period
( 2 , 4 , 6 , 1 , 3 , 5 )
( 2 , 4 , 6 , 1 , 3 , 5 )
( 2 , 4 , 6 , 1 , 5 , 3 )
( 2 , 6 , 4 , 1 , 5 , 3 )
( 2 , 1 , 4 , 6 , 5 , 3 )
Layout

11. Read NN,JF( i ,j), X(i),Y(i)
Randomly initialize a population of layout solution.
yes
Is any bit-string
Duplicate? No
Is the pop size reached? No
yes
Population of individual strings (coded-layout solution)
Evaluate the fitness value of the population string.
Preserve the best-fit individual (minimum-rating layout)
Select individual string for new population based on Roulette-wheel.
Implement genetic operator:
Crossover- Mutation- Inversion No
Is the termination criteria reached?
yes
Obtain the minimal-rating
layout solution.
End

12. 1.Single position crossover
Before crossover
After crossover 1 2 3 4 5 6
Parent1:
Child1: 4 3 1 4 5 6
Parent2:
Child2: 1 2 3 6 2 5
Before repair
After repair
Child1: 4 3 1 4 5 6
Child1: 2 3 1 4 5 6
Child2: 1 2 3 6 2 5
Child2: 1 4 3 6 2 5

13. 2.Mutation: Old chromosome Random Number New Chromosome 1 0 1 0

14. 3. Inversion: Before Inversion After Inversion 1 2 3 4 5 6 Parent1:
Offspring: 3 2 1 4 5 6

15. SOLUTION METHODOLOGY Step 4:
Execute GENETIC ALGORITHM again considering the find facility layout of Step 3 as initial layout for the second period as well as the second modified period evaluation.
Step 5:
Step 4 will be repeated till the program reached the last period .
The find layout of each period will be considered as a near optimal solution resulted from that algorithm. Finally, the total cost as a result of material handling cost for each period as well as the rearrangement cost between periods, if any, is computed.

16. COMPARISON AMONG PRESENT
Number of time periods
Model
No. of
Depts. 16 12 8 4
1599
1582
1628
1591
1265
1200
1223
1192
833
800
802
788
379
389
386
376
Proposed (GA)
Urban
Random
Ballou 6
3187
3851
4104
3715
2573
2884
3093
2789
1779
1933
2063
1864
892
944
1028
911
Table :Comparison of the Accuracy of the Heuristic
for Various problem size

17. Standard
Deviation
Mean
Data
Model
Proposed (GA)
Urban
Random
Table :Mean results and standard deviation for 24 combinations tested problems

18. Table :Level of significanceP
Model
0.0054
Proposed (GA) vs. Ubran
0.0024
Proposed (GA) vs. Random
0.1292
Proposed (GA) vs. Ballou
0.0032
Ubran vs. Random
0.0098
Ubran vs. Ballou
0.0168
Random vs. Ballou
Table :Level of significance

19. Conclusion :
we can say that the first proposed genetic algorithm is superior over other three models because it gives a significant saving in costs, in all combinations of tested problems, especially in large problems.
In this project, we made the comparisons based on the costs only, neglecting the execution time factor because of the difference in the language of programming and type of computer used in running.