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  • 1. How Limited Resources Affect Schedule Float 3 6 9 9 4 13 C I 3 0 9 9 0 13 0 3 3 3 R 3 R A 0 0 3 3 2 5 5 3 8 18 0 18 13 2 15 15 3 18 3 R D E J K F IN IS H0 0 0 8 5 10 10 5 13 13 0 15 15 0 18 18 0 18 ST AR T 4 R 2 R 4 R 5 R 0 R0 0 0 5 3 8 0 R F 10 5 13 1 R ES D EF 0 5 5 5 4 9 9 5 14 A ctivity B G H LS F LF 4 4 9 9 4 13 13 4 18 R e sou rc e s 2 R 3 R 2 RSpring 2008, Resources Leveling & Allocation 1King Saud University Dr. Khalid Al-Gahtani
  • 2. A 3 3 3 C 3 3 3 3 3 3 I 3 3 3 3 J 4 4 K 5 5 5 B 2 2 2 2 2 G 3 3 3 3 H 2 2 2 2 2 D 4 4 E 2 2 2 F 1 1 1 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 R 5 5 5 7 7 9 9 9 6 5 5 5 5 6 4 5 5 5 R 5 10 15 24 33 42 51 60 66 76 76 81 86 92 96 101 106 111 10 9 8 7 6 5 4 3Spring 2008, 2 Resources Leveling & Allocation 2King Saud University 1 Dr. Khalid Al-Gahtani
  • 3. A 3 3 3 C 3 3 3 3 3 3 I 3 3 3 3 J 4 4 K 5 5 5 B 2 2 2 2 2 G 3 3 3 3 H 2 2 2 2 2 D 4 4 E 2 2 2 F 1 1 1 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 R 3 3 3 3 5 5 5 5 9 10 9 9 9 6 6 7 7 7 R 3 6 9 12 17 22 27 32 41 51 60 69 78 84 90 97 104 111 10 9 8 7 6 5 4 3Spring 2008, 2 Resources Leveling & Allocation 3King Saud University 1 Dr. Khalid Al-Gahtani
  • 4. Spring 2008, Resources Leveling & Allocation 4King Saud University Dr. Khalid Al-Gahtani
  • 5. 111 to tal units A vg. da ily requ ire m e nt = = 6.2 units/da y 18 days S uppo se the ana lyzed reso urce is ava ila b le at a m a xim u m le ve l o f 7 units/da y. 126 units are requ ired fo r 18 days 6 .2 C ritic a lit y inde x = = 0.88 < 1 ok 7 .0 S uppo se the ana lyzed reso urce is ava ila b le at a m a xim u m le ve l o f 6 unit s/da y. 6 .2 C ritic a lit y inde x = = 1.03 > 1 6 .0 W here 108 units are requ ired fo r 18 days < 111 units, lea ving so m e w o rk unfin ished and thus requ iring a n exte nsio n o f the pro ject be yo nd 18 da ys.Spring 2008, Resources Leveling & Allocation 5King Saud University Dr. Khalid Al-Gahtani
  • 6. Spring 2008, Resources Leveling & Allocation 6King Saud University Dr. Khalid Al-Gahtani
  • 7. A nalys is o f L ine I: 1,000,000 cu. yds.A vg. daily requ irem ent = = 5000 cu.yds./day 200 days< 6000 cu.yds./day pro ject w ill be o n tim e m isleading resu ltA na lys is o f L ine II: 1,000,000 cu. yds.A vg. da ily requ ire m e nt = = 8333 cu.yds./da y (185 - 65) days 8333 C ritic a lity inde x = = 1.39 > 1 pro ject w ill de la y 6000Spring 2008, Resources Leveling & Allocation 7King Saud University Dr. Khalid Al-Gahtani
  • 8. L2 L1L o w er bo und estim ate o f avg. da ily requ ire m e nt = reso urce units/da y T2 T1 Spring 2008, Resources Leveling & Allocation 8 King Saud University Dr. Khalid Al-Gahtani
  • 9. Spring 2008, Resources Leveling & Allocation 9King Saud University Dr. Khalid Al-Gahtani
  • 10. OVERVIEW OF BASIC SCHEDULING PROCEDURES• Scheduling procedures for dealing with resource constraints can be roughly divided into 2 major groups, according to the problem addressed: – (1) resource leveling, and – (2) fixed-limits resource scheduling (resource allocation).Spring 2008, Resources Leveling & Allocation 10King Saud University Dr. Khalid Al-Gahtani
  • 11. Resource Leveling vs. Allocation• I. Resource Leveling. – Using resources in the most efficient manner possible when the project duration is fixed.• II. Resource Allocation – Scheduling a project with unlimited resources and a flexible duration.Spring 2008, Resources Leveling & Allocation 11King Saud University Dr. Khalid Al-Gahtani
  • 12. Resource Leveling Algorithm:S tep 1 . L ist the p ro ject activ it ies in o rd er o f p reced enc e b y arrang in g the arro w head o r no d e nu m b ers in a sce nd in g o rd er. W he n u sin g act iv it y -o n-arro w fo rm at and tw o o r m o re activ it ies ha ve the sa m e head nu m b er, list the m so that the arro w tail n u m b er s are a lso in asce nd in g o rd er.S tep 2 . Starting w ith the la st activ it y (the o ne at the bo tto m o f the d iag ra m ), sc hed u le it p er io d b y p er io d to g ive the lo w es t su m o f sq u ares o f reso u rce re q u ire m e nts fo r each tim e u n it. If m o re than o ne sc hed u le g iv es the sa m e to tal su m o f sq u ares, then sc hed u le the activ it y as late as po ssib le to g et as m u ch slack a s p o ssib le in a ll p reced ing act iv it ies.S tep 3 . H o ld in g the la st activ it y fix ed , rep eat Step 2 o n the ne xt to the la st activ it y in the netw o rk, tak ing ad v a ntag e o f a n y slack that m a y h ave bee n m ad e a va ila b le to it b y the resch ed u lin g in S tep 2 .S tep 4 . C o ntinu e S tep 3 u ntil the first activ it y in the list has b ee n co nsid ered ; th is co m p letes the first resched u lin g c yc le.S tep Spring 2008,u t ad d it io na l re sc hed u lin g c yc les b y & AllocationS tep s 2 thro u g h 4 u ntil no 12 5 . C arry o Resources Leveling rep eating King Saud University n in the to tal su m o Khalidares o f reso u rce req u ire m e nts is p o ssib le, fu rther red u ctio Dr. f sq u Al-Gahtani
  • 13. p reced ing act iv it ies.S tep 3 . H o ld in g the la st activ it y fix ed , rep eat Step 2 o n the ne xt to the la st activ it y in the Resource Leveling Algorithm: netw o rk, tak ing ad v a ntag e o f a n y slack that m a y h ave bee n m ad e a va ila b le to it b y the resch ed u lin g in S tep 2 .S tep 4 . C o ntinu e S tep 3 u ntil the first activ it y in the list has b ee n co nsid ered ; th is co m p letes the first resched u lin g c yc le.S tep 5 . C arry o u t ad d it io na l re sc hed u lin g c yc les b y rep eating S tep s 2 thro u g h 4 u ntil no fu rther red u ctio n in the to tal su m o f sq u ares o f reso u rce req u ire m e nts is p o ssib le, no ting that o n ly m o ve m e nt o f an act iv it y to the rig ht (sched u le later) is p er m issib le u nd er th is sc he m e.S tep 6 . If th is reso u rce is p articu lar ly cr it ica l, rep eat Step s 1 thro u g h 5 o n a d iffere nt o rd ering o f the activ it ies, w h ic h, o f co u rse, m u st still list the activ it ies in o rd er o f p reced en ce.S tep 7 . C ho o se the best sched u le o f tho se o btained in S tep s 5 and 6 .S tep 8 . M ak e fin a l ad ju st m e nts to the sched u le c ho se n in S tep 7, tak ing into acco u nt facto rs no t co nsid ered in the b asic sc hed u lin g p ro ced u re. Spring 2008, Resources Leveling & Allocation 13 King Saud University Dr. Khalid Al-Gahtani
  • 14. A 3 3 3 C 3 3 3 3 3 3 I 3 3 3 3 J 4 4 K 5 5 5 B 2 2 2 2 2 G 3 3 3 3 H 2 2 2 2 2 D 4 4 E 2 2 2 F 1 1 1 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 R 5 5 5 7 7 6 6 6 6 6 6 6 5 6 6 7 7 5 679 2 R 25 50 75 124 173 209 245 281 317 353 389 425 450 486 522 571 620 645 8 779 7 6 5 4 3Spring 2008, 2 Resources Leveling & Allocation 14King Saud University 1 Dr. Khalid Al-Gahtani
  • 15. Parallel vs. Serial methods• Serial methods – Activities CAN NOT be interrupted.• Parallel methods – It is more widely used. – Activities CAN be interrupted.Spring 2008, Resources Leveling & Allocation 15King Saud University Dr. Khalid Al-Gahtani
  • 16. Spring 2008, Resources Leveling & Allocation 16King Saud University Dr. Khalid Al-Gahtani
  • 17. Multiple Resources Allocation• Select the most CRITICAL resources, and then allocate all the critical resources in the same time.• For simplicity, only one resource at a time will be considered in this course with no interruption for an activity (Serial method).Spring 2008, Resources Leveling & Allocation 17King Saud University Dr. Khalid Al-Gahtani
  • 18. Example of Resource Allocation (Serial Method) 3 6 9 9 4 13 C I 3 0 9 9 0 13 0 3 3 3 R 3 R A 0 0 3 3 2 5 5 3 8 18 0 18 13 2 15 15 3 18 3 R D E J K FIN ISH0 0 0 8 5 10 10 5 13 13 0 15 15 0 18 18 0 18 ST A R T 4 R 2 R 4 R 5 R 0 R0 0 0 5 3 8 0 R F 10 5 13 1 R ES D EF 0 5 5 5 4 9 9 5 14 A ctivity B G H LS F LF 4 4 9 9 4 13 13 4 18 R e sou rc e s 2 R 3 R 2 RSpring 2008, Resources Leveling & Allocation 18King Saud University Dr. Khalid Al-Gahtani
  • 19. A C C C D D D D D D I I J J J J K K K K 1EAS B D D D G G I I I I E E H H H G G G I I F F A C D D D D D D I I H J K K K 2O SS B D G I E F A 3 3 3 B 2 2 2 2 2 C 3 3 3 3 3 3 G 3 3 3 3 D 4 4 I 3 3 3 3 E 2 2 2 F 1 1 1 H 2 2 2 2 2 J 2 2 K 5 5 5D ay 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 3UR 6 6 6 6 6 6 6 6 6 6 66 6 6 6 6 6 6 6 6 6 6 3 3 3 4 4 3 3 3 3 2 23 3 3 3 4 4 4 4 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 2 2 0 0 0 Spring 2008, 4 Resources Leveling & Allocation 19AR 5 5 5 5 5 6 6 6 6 4 4 6 6 6 5 4 4 2 2 5 5 5 King Saud University Dr. Khalid Al-Gahtani
  • 20. Example of Resource Allocation (Parallel Method) 3 6 9 9 4 13 C I 3 0 9 9 0 13 0 3 3 4 R 3 R A 0 0 3 3 2 5 5 3 8 18 0 18 13 2 15 15 3 18 3 R D E J K F IN IS H0 0 0 8 5 10 10 5 13 13 0 15 15 0 18 18 0 18 ST AR T 3 R 2 R 4 R 4 R 0 R0 0 0 5 3 8 0 R F 10 5 13 1 R ES D EF 0 5 5 5 4 9 9 5 14 A ctivity B G H LS F LF 4 4 9 9 4 13 13 4 18 R e sou rc e s 3 R 3 R 2 R Spring 2008, Resources Leveling & Allocation 20 King Saud University Dr. Khalid Al-Gahtani
  • 21. A A A C C C C C C B B I I I I E E E J J H H H 1 EAS B B B B B B B B B D D G G G G F F F H H K K K C C D D D D D D I I E E E E J J K D D G I I I I I G G F F F F H H G G G G G G G E F A A A C C C C C C B B I I I I E E E J J H H H 2 O SS B B B B B D D D D D D G G G G F F F H H K K K D D G G G G I I E E E E F F F F A 3 3 3 B 3 3 3 3 3 C 4 4 4 4 4 4 D 3 3 I 3 3 3 3 G 3 3 3 3 E 2 2 2 F 1 1 1 J 2 2 H 2 2 2 2 2 K 4 4 4 D ay 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 3 UR 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 3 3 3 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 2 2 4 4 4Spring 2008, 0 0 4 0 Resources Leveling &0Allocation 3 0 0 0 0 0 3 3 0 0 0 0 0 21KingRSaud 6 6 6 A University 4 4 4 4 4 Dr. Khalid Al-Gahtani 6 4 6 6 6 6 6 3 3 3 6 6 6 6 6

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