CPM prob-6

Activity	Predecessor	Duration (in days)
A	-	4
B	-	7
C	-	6
D	AB	5
E	AB	7
F	CDE	6
G	CDE	5

AB

A & B starts from  1st node; They start from same nodes, and they are not repeated, therefore dummy is required from either A to B or B to A

To analyses CDE we need to break this into three pair of CD, DE & CE

CD

DE

CE

NWD diagram

CPM prob-5

Activity	Predecessor	Duration (in days)
A	-	6
B	-	4
C	-	7
D	ABC	5
E	ABC	6
F	D	9
G	E	4
H	FG	8
I	FG	6
J	H	7

FG

F starts from D & G starts from E;They start from different nodes, and there is no repetition of either F or G,therefore heads of F&G should be merged.

To analyses ABC we need to break this into three pair of AB, BC & AC

AB

A & B starts from  1st node; They start from same nodes, and they are not repeated, therefore dummy is required from either A to B or B to A

BC

B & C starts from  1st node; They start from same nodes, and they are not repeated, therefore dummy is required from either B to C or C to B

AC

A & C starts from  1st node; They start from same nodes, and they are not repeated, therefore dummy is required from either A to C or C to A

Each pair need dummy, take nay one letter say B, draw DY from A to B & C to B

 

NWD diagram

CPM

Critical path	Duration (in days)
1-3-5-7-8-9	4-5-9-8-7           =33
1-2-3-6-7-8-9	6-0+6+4+8+7      =31
1-4-3-5-7-8-9	7+1+5+9+8+7      =36
1-2-3-5-7-8-9	6+0+5+9+8+7      =35
1-2-3-6-7-9	6+0+6+4+6         =22
1-2-3-5-7-9	6+0+5+9+6=26    =26

CPM prob-7

From the following project draw the NMD. Identify the critical path.     Find out the project duration & associated cost. Calculate the total float for each activity.

NWD diagram

Critical path;

Critical path	Duration (in days)
1-2-4-5-6-7-8	3+7+0+6+4+10    =30
1-2-3-5-6-7-8	3+3+5+6+4+10    =31
1-2-5-6-7-8	3+9+6+4+10       =32 - Critical path
1-2-5-6-8	3+9+6+13           =31
1-2-4-5-6-8-	3+7+0+6+13       =29
1-2-3-5-6-8	3+3+5+6+13       =30

 

Project duration	32 days
cost	32*9=288
Normal cost	704
Total cost	992

 

 

Activity	Duration	EST	EFT	LST	LFT	TF
1-2	3	0	3	0	3	0
2-3	3	3	6	4	7	1
2-4	7	3	10	5	12	2
2-5	9	3	12	3	12	0
3-5	5	6	11	7	12	1
4-5	0	10	10	12	12	2
5-6	6	12	18	12	18	0
6-7	4	18	22	18	22	0
6-8	13	18	31	19	32	1
7-8	10	22	32	22	32	0

CPM prob-4

From the following data construct a NWD

Activity	Predecessor	Duration (in days)
A	-	5
B	A	9
C	A	7
D	BC	4
E	A	8
F	DE	14
G	C	12
H	FG	6
I	H	8

Solution

Let us analysis the various nodes.

BC

B & C starts from A; They start from same nodes, and C is repeated, therefore dummy is required from either C to B.

DE

D starts from BC & E starts from A;They start from different nodes, and there is no repetition of E or D,therefore heads of D&E should be merged

FG

F starts from DE & G starts from C;They start from different nodes, and there is no repetition of F or G,therefore heads of F&G should be merged.

NWD diagram

 

Critical path

Path	Duration

Table calculating various matrix

Activity	Duration	EST	EFT	LST	LFT	TF
A (1-2)
B (2-3)
C (2-4)
D (3-5)
E (2-5)
F (5-6)
G (4-6)
H (6-7)
I (7-8)

CPM prob-3

1. From the following data construct a NWD
2. Identify the critivcal path & project completions time
3. Construct a critical schedule
4. If activity A is delayed by 2 days, find out whether project completion time is affected or not.

Activity	Predecessor	Duration (in days)
A	-	3
B	-	1
C	A	4
D	B	4
E	B	5
F	D	2
G	E	3

NWD diagram

 

Critical path

Path	Duration
A-C	3+4     =7
B-D-F	1+4+2  =7
B-E-G	1+5+3  =9 - Critical path

Table calculating various matrix

Activity	Duration	EST	EFT	LST	LFT	TF
A (1-2)
B (1-3)
C (2-4)
D (3-4)
E (3-5)
F (4-6)
G (5-6)

CPM prob-2

From the following data calculate NWD. Identify the critical path & its duration. Calculate EST, EFT, LST, LFT & TF for each activity.

NWD Diagram

 

Path	Duration
1-2-4-9-10	4+1+5+7               =17
1-3-5-7-8-10	1+6+8+2+5         =22 -Critical Path
1-3-4-9-10	1+1+5+7               =14
1-3-5-6-8-10	1+6+4+1+5            =17

Table showing EST, EFT etc

Activity	Duration	EST	EFT	LST	LFT	TF
1-2	4	0	4	5	9	5
1-3	1	0	1	0	1	0
2-4	1	4	5	9	10	5
3-4	1	1	2	9	10	8
3-5	6	1	7	1	7	0
4-9	5	5	10	10	15	5
5-6	4	7	11	12	16	5
5-7	8	7	15	7	15	0
6-8	1	11	12	16	17	5
7-8	2	15	17	15	17	0
9-10	7	10	17	15	22	5
8-10	5	17	22	17	22	0

CPM prob-1

From the following data calculate NWD. Identify the critical path & its duration. Calculate EST, EFT, LST, LFT & TF for each activity.

NWD Diagram

 

Path	Duration
1-2-5-6	6+7+5                =18
1-3-6	5+6                   =11
1-2-3-6	6+8+6               =20
1-2-3-4-5-6	6+8+5+4+5        =28 -Critical Path
1-2-4-5-6	6+4+4+5           =19
1-3-4-5-6	5+5+4+5           =19

Table showing EST, EFT etc

Activity	Duration	EST	EFT	LST	LFT	TF
1-2	6	0	6	0	6	0
1-3	5	0	5	9	14	9
2-3	8	6	14	6	14	0
2-4	4	6	10	15	19	9
2-5	7	6	13	16	23	10
3-4	5	14	19	14	19	0
3-6	6	14	20	22	28	8
4-5	4	19	23	19	23	0
5-6	5	23	28	23	28	0