A project manager is faced with the following activities and times associated wi

Question

A project manager is faced with the following activities and times associated with a building construction. Each activity can be crashed at most by 2 weeks. The cost associated with each week time reduction is given below. Activity Immediate Predecessor Normal Time (weeks) Crash Cost 1st week Crash Cost 2nd week A - 6 $5,000 $9,000 B - 5 $3,000 $8,000 C A 4 $10,000 $9,000 D B 3 $4,000 $8,000 E C,D 2 $10,000 $14,000 F C,D 3 $12,000 $15,000 G F 4 $14,000 $18,000 What is the earliest completion time for the project? What is the latest completion time for the project? What is the minimum cost to reduce the project time by 3 weeks? Which activities need to be reduced? What is(are) the critical path(s) after the time reduction?

Explanation / Answer

Activity

Immediate Predecessor

Normal time

Crash cost per wk($)

Crash cost /2 wks($)

A

-

6

5000

9000

B

-

5

3000

8000

C

A

4

10000

9000

D

B

3

4000

8000

E

C,D

2

10000

14000

F

E

3

12000

15000

G

F

4

14000

18000

The calculation of ES, LS EF and LF is done based forward and backward pass.

Based on the above calculation the earliest project completion time is 15 weeks.

Latest project completion time is 19 weeks.

At present the critical path is that path where the slack is zero. Slack = ES –LS or LF –EF.

Here the critical path is A –C – E – F –G

As given each activity can be crashed for at most by 2 weeks.

Therefore one will select only those activities to crash which are lying on CP and the slope per wk is minimum.

So , we will select activity A for 2 weeks crash and activity C for one week crash because project manager wants to reduce it by 3 weeks.

That’s why Cost involved will be for activity A              $ 9000 (given crash cost per 2 weeks)

                                                                For activity C              $ 10,000 (given crash cost per 2 weeks)

Total cost will be $ 19, 000 to reduce the project duration by 3 weeks

Activity

Immediate Predecessor

Normal time

Crash cost per wk($)

Crash cost /2 wks($)

A

-

6

5000

9000

B

-

5

3000

8000

C

A

4

10000

9000

D

B

3

4000

8000

E

C,D

2

10000

14000

F

E

3

12000

15000

G

F

4

14000

18000

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