Question

A construction project has indirect costs totaling $40,000 per week. Major activities of the project, their expected time, and crashing costs per week are:

			Crashing costs ($000)
Activity	Expected time (week)	Predecessor	First week	Second week	Third week
A	5	-	18	22	-
B	4	-	12	24	26
C	3	-	10	15	25
D	8	A	24	25	25
E	12	B	-	-	-
F	12	C	8	13	-
G	6	B	3	10	12
H	7	D	30	30	35
I	4	H	15	20	-
J	5	E	40	40	40
K	9	G	2	7	10
L	9	F	5	12	-
M	8	L	14	15	-
N	1	K,M	26	-	-
P	11	I,J	30	33	36

What would be your recommended lowest cost duration for this project? Show your work. For each step specify what activity is crashed and show why.

Answer 1

SOLUTION:

Network Diagram:

Possible Paths:

Start-A-D-H-I-P-End = 35 weeks .... Critical Path

Start-B-E-J-P-End = 32 weeks

Start-B-G-K-N-End = 20 weeks

Start-C-F-L-M-N-End = 33 weeks

The critical path is Start-A-D-H-I-P-End with duration 35 weeks.

Total Indirect Cost = 35 * 40000 = $1,400,000

Crashing:

Below table shows the activities to be crashed weekwise, and the total resulting project cost.

- Activity with lowest crash cost shoud be considered for crashing. In case of multiple critical paths, activities with lowest cost on each of these critical path should be crashed.

	1	2	3	4
Crashed Activity	I	A	I,L	A,F,B
Crashing Cost	15000	18000	25000	42000
Total Crashing Cost	15000	33000	58000	100000
Indirect cost/week	40000	40000	40000	40000
Critical Path	A-D-H-I-P	A-D-H-I-P C-F-L-M-N	A-D-H-I-P C-F-L-M-N	A-D-H-I-P B-E-J-P C-F-L-M-N
TPT	34	33	32	31
Total Project Cost (TPT * Indirect cost/week + Total Crashing Cost)	1375000	1353000	1338000	1340000

From the above table, we observe post the 3rd crashing, the total project cost is increasing.

Thus, the lowest cost duration is 32 weeks, and the resulting project cost is $1338000