Question

The following CPM network has estimates of the normal time in weeks listed for the activities:

Activity	Immediate Pred	Weeks
A	-	7
B	A	2
C	A	4
D	B, C	5
E	B, C	2
F	D, E	4
G	F	5

Activity	Normal Time	Crash Time	Normal Cost	Crash Cost
A	7	6	$7,000	$8,000
B	2	1	5,000	7,000
C	4	3	9,000	10,200
D	5	4	3,000	4,500
E	2	1	2,000	3,000
F	4	2	4,000	7,000
G	5	4	5,000	8,000

1. Please identify the critical path.
2. What is the length of time to complete the project?
3. Which activities have slack, and how much?
4. Based on the table of normal and crash times and costs, which activities would you shorten to cut two weeks off the expected completion time? Does this change the critical path—if so, what is(are) the new path(s).

USE AN EXCEL FILE

Answer 1

Given

activity	required time	cost	time available for crashing= normal duration-crashed duration	cost of crashing per period= (crashing cost-normal cost)/periods available for crashing
normal duration	crashed duration	normal cost	crashing cost
A	7	6	7,000	8,000	1	$1,000
B	2	1	5,000	7,000	1	$2,000
C	4	3	9,000	10,200	1	$1,200
D	5	4	3,000	4,500	1	$1,500
E	2	1	2,000	3,000	1	$1,000
F	4	2	4,000	7,000	2	$1,500
G	5	4	5,000	8,000	1	$3,000

paths

PATH	normal duration
ABDFG	28
ABEFG	20
ACDFG	25
ACEFG	22

a. Critical path is the longest path: ABDFG

b. duration: 28

c:

	Steps for crashing a project
1	select the critical path and find the process with the least cost of crashing per week
2	If there are multiple critical paths, look for processes that are common, common processes may have low effective cost as common process crashes more than 1 path at once
3	you can only crash an activity depending on the time available for crashing. If an activity is only crashed that much time, choose another activity
4	add the cost of crashing later

Crashing

PATH	normal duration	crash A by 1 periods	crash D by 1 period
ABDFG	28	27	26
ABEFG	20	19	19
ACDFG	25	24	24
ACEFG	22	21	21

No it does not change the critical path.