Question

1. Describe the project network to build a house from the data below. Calculate the time and critical path.

Activity	Description	Predecessor	Time (Days)
A	Clear the location	-	1
B	Bring the tool to the location	-	2
C	Conducting excavations	A	1
D	Pour the foundation	C	2
E	Plumbing installation from outside	B, C	6
F	Create a home frame	D	10
G	Installation of electric wire	F	3
H	Install the floor	G	1
I	Installing the roof	F	1
J	Installation of plumbing from inside	E, H	5
K	Installing the roof	I	2
L	Installation of the outer wall layers	F, J	1
M	Installing windows and outside doors	F	2
N	Build a wall	L, M	4
O	Isolate the walls and ceiling	G, J	2
P	Close the walls and ceiling	O	2
Q	Isolate the roof	I, P	1
R	Finish the interior	P	7
S	Finish the exterior	I, N	7
T	Build a garden	S	3

Answer 1

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Solution:

Activity	Immediate Predecessors	Duration
A	-	1
B	-	2
C	A	1
D	C	2
E	B,C	6
F	D	10
G	F	3
H	G	1
I	F	1
J	E,H	5
K	I	2
L	F,J	1
M	F	2
N	L,M	4
O	G,J	2
P	O	2
Q	I,P	1
R	P	7
S	I,N	7
T	S	3

Edge and it's preceded and succeeded node

Edge	Node1 → Node2
A	1→2
B	1→3
C	2→4
E	3→8
d	4→3
D	4→5
F	5→6
G	6→7
I	6→9
L	6→11
M	6→12
H	7→8
O	7→14
J	8→10
d	9→13
d	9→16
K	9→18
d	10→6
d	10→7
d	11→12
N	12→13
S	13→17
P	14→15
d	15→16
R	15→18
Q	16→18
T	17→18

The network diagram for the project, along with activity time, is

Forward Pass Method
E1=0

E2=E1+t1,2 [t1,2=A=1]=0+1=1

E3=Max{Ei+ti,3}[i=1,4]

=Max{E1+t1,3;E4+t4,3}

=Max{0+2;2+0}

=Max{2;2}

=2

E4=E2+t2,4 [t2,4=C=1]=1+1=2

E5=E4+t4,5 [t4,5=D=2]=2+2=4

E6=Max{Ei+ti,6}[i=5,10]

=Max{E5+t5,6;E10+t10,6}

=Max{4+10;0+0}

=Max{14;0}

=14

E7=Max{Ei+ti,7}[i=6,10]

=Max{E6+t6,7;E10+t10,7}

=Max{14+3;0+0}

=Max{17;0}

=0

E8=Max{Ei+ti,8}[i=3,7]

=Max{E3+t3,8;E7+t7,8}

=Max{2+6;0+1}

=Max{8;1}

=8

E9=E6+t6,9 [t6,9=I=1]=14+1=0

E10=E8+t8,10 [t8,10=J=5]=8+5=0

E11=E6+t6,11 [t6,11=L=1]=14+1=0

E12=Max{Ei+ti,12}[i=6,11]

=Max{E6+t6,12;E11+t11,12}

=Max{14+2;0+0}

=Max{16;0}

=0

E13=Max{Ei+ti,13}[i=9,12]

=Max{E9+t9,13;E12+t12,13}

=Max{0+0;0+4}

=Max{0;4}

=0

E14=E7+t7,14 [t7,14=O=2]=0+2=0

E15=E14+t14,15 [t14,15=P=2]=0+2=0

E16=Max{Ei+ti,16}[i=9,15]

=Max{E9+t9,16;E15+t15,16}

=Max{0+0;0+0}

=Max{0;0}

=0

E17=E13+t13,17 [t13,17=S=7]=0+7=0

E18=Max{Ei+ti,18}[i=9,15,16,17]

=Max{E9+t9,18;E15+t15,18;E16+t16,18;E17+t17,18}

=Max{0+2;0+7;0+1;0+3}

=Max{2;7;1;3}

=0


Backward Pass Method
L18=E18=0

L17=L18-t17,18 [t17,18=T=3]=0-3=-3

L16=L18-t16,18 [t16,18=Q=1]=0-1=-1

L15=Min{Lj-t15,j}[j=18,16]

=Min{L18-t15,18;L16-t15,16}

=Min{0-7;-1-0}

=Min{-7;-1}

=-7

L14=L15-t14,15 [t14,15=P=2]=-7-2=-9

L13=L17-t13,17 [t13,17=S=7]=-3-7=-10

L12=L13-t12,13 [t12,13=N=4]=-10-4=-14

L11=L12-t11,12 [t11,12=d=0]=-14-0=-14

L10=Min{Lj-t10,j}[j=7,6]

=Min{L7-t10,7;L6-t10,6}

=Min{-11-0;-16-0}

=Min{-11;-16}

=-16

L9=Min{Lj-t9,j}[j=18,16,13]

=Min{L18-t9,18;L16-t9,16;L13-t9,13}

=Min{0-2;-1-0;-10-0}

=Min{-2;-1;-10}

=-10

L8=L10-t8,10 [t8,10=J=5]=-16-5=-5

L7=Min{Lj-t7,j}[j=14,8]

=Min{L14-t7,14;L8-t7,8}

=Min{-9-2;-5-1}

=Min{-11;-6}

=-11

L6=Min{Lj-t6,j}[j=12,11,9,7]

=Min{L12-t6,12;L11-t6,11;L9-t6,9;L7-t6,7}

=Min{-14-2;-14-1;-10-1;-11-3}

=Min{-16;-15;-11;-14}

=-16

L5=L6-t5,6 [t5,6=F=10]=-16-10=-26

L4=Min{Lj-t4,j}[j=5,3]

=Min{L5-t4,5;L3-t4,3}

=Min{-26-2;-11-0}

=Min{-28;-11}

=-28

L3=L8-t3,8 [t3,8=E=6]=-5-6=-11

L2=L4-t2,4 [t2,4=C=1]=-28-1=-29

L1=Min{Lj-t1,j}[j=3,2]

=Min{L3-t1,3;L2-t1,2}

=Min{-11-2;-29-1}

=Min{-13;-30}

=-30

No critical path found

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