Question

Given the information below: (Use normal time to calculate original path)

a) Which activity(s) should be crashed and what is the cost to reduce the project completion time from 22 to 21 days?

b) Which activity(s) should be crashed and what is the cost to reduce the project completion time from 21 to 20 days?

c) Which activity(s) should be crashed and what is the cost to reduce the project completion time from 20 to19 days?

d) What is the total cost to reduce the project from the original normal completion time to 19 days?

Activity	Immediate Predecessors	Normal time	Crash time	Normal cost	Crash cost
A	-	5	3	$3,000	$3,600
B	-	6	4	$3,500	$4,300
C	A	7	5	$3,300	$4,000
D	B	5	4	$2,200	$2,400
E	B	3	2	$1,700	$2,200
F	D,E	5	3	$2,200	$3,600
G	C,D	7	6	$1,900	$2,550
H	F,G	3	2	$1,200	$1,750

Answer 1

Crash cost per week for each activity is, (Crash Cost - Normal Cost) / (Normal time - Crash time)

For A, ($3600 - $3500) / (5-4) = $100

For B, ($4300 - $3500) / (6 - 4) = $400

For C, ($3900 - $3300) / (4 -2) = $300

For D, ($2900 - $2200) / (5 -4) = $700

For E, ($2200 - $1700) / (3 -2) = $500

For F, ($3600 - $2000) / (7 -5) = $800

For G, ($2550 - $1900) / (3-2) = $650

For H, ($1750 - $1200) / (4 -3) = $550

The path from the graph for project execution is,

A, C, G, H ( Total normal time = 5 + 4 + 3 + 4 = 16 days)

A, D, F, H ( Total normal time = 5 + 5 + 7 + 4 = 21 days)

B, D , F , H ( Total normal time = 6 + 5 + 7 + 4 = 22 days)

B, E, F, H ( Total normal time = 6 + 3 + 7 + 4 = 20 days)

So, the critical path is B, D , F , H with total normal time = 22 days

(a)

1. To reduce the project completion time from 22 to 21 days.

2. We need to reduce the time for any of the activity B, D , F , H.

3. Among B, D, F, H, the minimum Crash cost per week is for B ($400)

4. So activity B should be crashed and the total cost = $400

(b)

1. When Activity B is crashed, there are two critical paths - A, D, F, H and B, D , F , H with project completion time of 21 days.

2. To reduce the project completion time from 21 to 20 days, we need to crash atleast activity from both the critical paths.

3. Among A, D, F, H, the minimum Crash cost per week is for A ($100)

4. Among B, D, F, H, the minimum Crash cost per week is for B ($400) [Activity B can be crashed for one more day. (Difference between Normal and Crash time for B is 2 , so, B can be crashed for 2 days).]

So activity A and B should be crashed and the total cost = $100 + $400 = $500

(c)

1. When Activity A and B is crashed, there are three critical paths - A, D, F, H ; B, D , F , H and B, E, F, H with project completion time of 20 days.

2. To reduce the project completion time from 20 to 19 days, we need to crash at least one activity from all three critical paths.

3. Among A, D, F, H, the minimum Crash cost per week is for A ($100), but A has already been crashed and cannot be crashed for more than 1 day. (Difference between Normal and Crash time for A is 1)

4. After A, the next minimum Crash cost per week is for H ($550)

5. If H is crashed, then it will also apply for other critical paths , B, D , F , H and B, E, F, H

6. So activity H should be crashed and the total cost = $550

(d)

1. To reduce the project cost from 22 to 19 days, activity A and H should be crashed for 1 day and activity B should be crashed for 2 days.

2. Total project cost to reduce the project completion time (22 days) to 19 days = $400 + $500 + $550 = $1450

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