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 421000919

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

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.

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.

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.

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:

FLOW DATA AND SHIFTING COST TO 1 2 3 4 5 6 FROM 1 0 63 605 551 116 136 2 63 0 635 941 50 191 F1 3 104 71 0 569 136 55 4 65 193 622 0 70 90 5 162 174 607 591 0 179 6 156 13 667 611 175 0 TO 1 2 3 4 5 6 FROM 1 0 175 804 904 56 176 2 63 0 743 936 45 177 F2 3 168 85 0 918 138 134 4 51 94 962 0 173 39 5 97 104 730 643 0 144 6 95 115 938 597 24 0 TO 1 2 3 4 5 6 FROM 1 0 90 77 553 769 139 2 168 0 114 653 525 185 F3 3 32 35 0 664 898 87 4 27 166 42 0 960 179 5 185 65 44 926 0 104 6 72 128 173 634 687 0 TO 1 2 3 4 5 6 FROM 1 0 112 15 199 665 649 2 153 0 116 173 912 671 F4 3 10 28 0 182 855 542 4 29 69 15 0 552 751 5 198 71 42 24 0 758 6 62 109 170 90 973 0

Initial layout (parent) TO 1 2 3 4 5 6 FROM 1 0 663 23 128 11 50 2 820 0 5 98 141 66 F5 3 822 650 0 137 78 91 4 826 570 149 0 93 151 5 915 515 53 35 0 177 6 614 729 178 10 99 0 1 2 3 4 5 6 Si = ( 887 964 213 367 289 477 ) Facility layout Representation on genetic : Initial layout (parent) 1 2 5 6 4 3 Coded layout Chromosome 1 2 3 4 5 6

Period Layout Zij 1 (1,3,5,6,4,2) 12,822 2 (1,4,2,5,3,6) 14,853 3 (1,5,3,2,4,6) 13,172 4 (1,6,4,2,5,3) 13,032 5 (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 2 3 4 5 (1,3,5,6,4,2) 1 25 381 629 705 76,610 (1,4,2,5,3,6) 21 1 181 553 413 74,137 (1,5,3,2,4,6) 197 329 1 245 469 74,416 (1,6,4,2,5,3) 673 625 305 1 593 78,336 (3,2,6,4,1,5) 629 469 609 501 1 78,510

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

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

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

2.Mutation: Old chromosome Random Number New Chromosome 1 0 1 0 1 0 1 0 0.801 0.1 0.27 0.37 1 0 1 0 0 1 1 0 0.76 0.47 0.89 0.001 0 0 1 1

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

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.

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

Standard Deviation Mean Data Model 24507.84 17345.29 Proposed (GA) 26710.8 19222.58 Urban 31472.26 22429.29 Random Table :Mean results and standard deviation for 24 combinations tested problems

Table :Level of significance P 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

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.