Answer to Question #274249 in Operations Research for Prathibha Rose

Question

Consider a project consisting of nine jobs (A, B, C,….,I) with the following precedence

relations and time estimates.

Job Predecessor Time (Days)

A -- 15

B -- 10

C A,B 10

D AB 10

E B 5

F DE 5

G CF 20

H DE 10

I GH 15

a. Draw the project network for this problem designating the jobs by arcs and event by nodes. b.

Determine the earliest completion time of the project, and identify the critical path.

c. Determine a project schedule listing the earliest and latest starting times of each job. Also identify

the critical job.

Answer 1

a)

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

b)

Forward Pass Method:

E1=0

E2=Max{Ei+ti,2}[i=13,]

=Max{E1+t1,2;E3+t3,2}

=Max{0+15;10+0}

=Max{15;10}

=15

E3=E1+t1,3 [t1,3=B=10]=0+10=10

E4=Max{Ei+ti,4}[i=23,]

=Max{E2+t2,4;E3+t3,4}

=Max{15+10;10+5}

=Max{25;15}

=25

E5=Max{Ei+ti,5}[i=24,]

=Max{E2+t2,5;E4+t4,5}

=Max{15+10;25+5}

=Max{25;30}

=30

E6=Max{Ei+ti,6}[i=45,]

=Max{E4+t4,6;E5+t5,6}

=Max{25+10;30+20}

=Max{35;50}

=50

E7=E6+t6,7 [t6,7=I=15]=50+15=65

Backward Pass Method:

L7=E7=65

L6=L7-t6,7 [t6,7=I=15]=65-15=50

L5=L6-t5,6 [t5,6=G=20]=50-20=30

L4=Min{Lj-t4,j}[j=65,]

=Min{L6-t4,6;L5-t4,5}

=Min{50-10;30-5}

=Min{40;25}

=25

L3=Min{Lj-t3,j}[j=42,]

=Min{L4-t3,4;L2-t3,2}

=Min{25-5;15-0}

=Min{20;15}

=15

L2=Min{Lj-t2,j}[j=54,]

=Min{L5-t2,5;L4-t2,4}

=Min{30-10;25-10}

=Min{20;15}

=15

L1=Min{Lj-t1,j}[j=32,]

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

=Min{15-10;15-15}

=Min{5;0}

=0

The critical path has been done by double lines by joining all those events where E-values and

L-values are equal.

The critical path of the project is : 1-2-4-5-6-7 and critical activities are A,D,F,G,I

The total project time is 65

c)