Question

1. The project manager of a task force planning the construction of a domed stadium had hoped to be able to complete construction prior to the next season. After reviewing construction duration estimates, it now appears that a certain amount of crashing will be needed to ensure project completion before the season opener. Given the following information, determine a minimum-cost crashing schedule that will shave five weeks off the project length.

Activity	Precedes	Normal Duration (Weeks)	CRASHING COSTS First Week	CRASHING COSTS Second Week
A	----	12	15000	$20000
B	A	14	10000	10000
C	----	10	5000	5000
D	CC	17	20000	21000
E	CC	18	16000	18000
F	CC	12	12000	15000
G	D	15	24000	24000
H	E	8	-----	------
I	F	7	30000	----
J	I	12	25000	25000
K	B	9	10000	10000
M	G	3	----	----
N	H	11	40000	-------
P	H, J	8	20000	20000

Assumptions:

1. There is no minimum crash duration.
2. Crashing cost varies by activity and by week i.e. Cash cost for 1^st week, Crash cost for 2^nd week.
3. Activities without a crash cost cannot be crashed.
4. No penalties and no incentives given.

Answer 1

Different paths and their duration is as below=

A-B-K=12+14+9=35

C-E-H-P=10+18+8+8=44

C-D-G-M=10+17+15+3=45

C-E-H-N=10+18+8+11=47

C-F-I-J-P=10+12+7+12+8=49

The below mentioned table has the details of crashing activities=

First of all we will crash activity C as it has least crashing cost

Path	0	1	2	3	4	5
A-B-K	35
C-E-H-P	44	43
C-D-G-M	45	44
C-E-H-N	47	46
C-F-I-J-P	49	478
Crashed activity		C

When it comes to second week, even then we will crash activity C due to least second week crash cost

Path	0	1	2	3	4	5
A-B-K	35
C-E-H-P	44	43	42
C-D-G-M	45	44	43
C-E-H-N	47	46	45
C-F-I-J-P	49	48	47
Crashed activity		C	C

Now in the remaining activities, F has the second least first week crashing cost so we will not crash Activity F

Path	0	1	2	3	4	5
A-B-K	35
C-E-H-P	44	43	42	41
C-D-G-M	45	44	43	42
C-E-H-N	47	46	45	44
C-F-I-J-P	49	48	47	46
Crashed activity		C	C	F

Again we will crash Activity f due to least second week crash cost after C activity

Path	0	1	2	3	4	5
A-B-K	35
C-E-H-P	44	43	42	42	42
C-D-G-M	45	44	43	43
C-E-H-N	47	46	45	45	45
C-F-I-J-P	49	48	47	46	45
Crashed activity		C	C	F	F

Final Table will be

Path	0	1	2	3	4	5
A-B-K	35
C-E-H-P	44	43	42	42	42	40
C-D-G-M	45	44	43	43
C-E-H-N	47	46	45	45	45	44
C-F-I-J-P	49	48	47	46	45	44
Crashed activity		C	C	F	F	E,P

Total cost of crashing=   5000+5000+12000+15000+3600=$73000