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 H
0 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 R
0 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 R
Spring 2008, Resources Leveling & Allocation 1
King 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
3
Spring 2008, 2 Resources Leveling & Allocation 2
King 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
3
Spring 2008, 2
Resources Leveling & Allocation 3
King Saud University
1 Dr. Khalid Al-Gahtani

4. Spring 2008, Resources Leveling & Allocation 4
King 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 5
King Saud University Dr. Khalid Al-Gahtani

6. Spring 2008, Resources Leveling & Allocation 6
King 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 lt
A 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
6000
Spring 2008, Resources Leveling & Allocation 7
King Saud University Dr. Khalid Al-Gahtani

8. L2 L1
L o w er bo und estim ate o f avg. da ily requ ire m e nt = reso urce units/da y
T2 T1
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9. Spring 2008, Resources Leveling & Allocation 9
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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 10
King 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 11
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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
3
Spring 2008,
2
Resources Leveling & Allocation 14
King Saud University
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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 15
King Saud University Dr. Khalid Al-Gahtani

16. Spring 2008, Resources Leveling & Allocation 16
King 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 17
King 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 ISH
0 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 R
0 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 R
Spring 2008, Resources Leveling & Allocation 18
King 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
1
EAS 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
2
O 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 5
D ay 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22
3
UR 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 19
AR 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 H
0 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 R
0 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 4
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4
0 Resources Leveling &0Allocation 3
0 0 0 0 0 3 3 0 0 0 0 0 21
KingRSaud 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