Question

Assume the network and data that follow:

ACTIVITY	NORMAL TIME (WEEKS)	NORMAL COST			CRASH TIME (WEEKS)	CRASH COST			IMMEDIATE PREDECESSORS
A	3	$	60		2	$	80		—
B	5		70		4		110		A
C	9		50		6		80		A
D	7		100		6		130		A
E	8		90		6		100		B
F	5		30		3		50		D
G	6		110		5		190		C, E, F

b. Indicate the critical path when normal activity times are used.

	A-B-E-G
	A-C-F-G
	A-D-E-G
	A-D-F-G

c. Compute the minimum total direct cost for each project duration based on the cost associated with each activity. Consider durations of 17, 18, 19, 20, 21, and 22 weeks. (Leave no cells blank - be certain to enter "0" wherever required.

	ABEG
Length of path	ACG
	ADFG
Activity crashed		Choose: E, E&F, Non, G, B&F, A	(Click to select)	(Click to select)	(Click to select)	(Click to select)	(Click to select)
Crash cost
Cum. crash cost
Total direct cost

d-1. If the indirect costs for each project duration are $400 (22 weeks), $350 (21 weeks), $300 (20 weeks), $250 (19 weeks), $200 (18 weeks), and $150 (17 weeks), what is the total project cost for each duration?+

Duration	Total Costs
22	$
21
20
19
18
17

d-2. Indicate the minimum total project cost duration.

	17 weeks
	13 weeks
	18 or 19 weeks
	14 or 15 weeks

Answer 1

b. The critical path is ABEG with a duration of 22 days

c. Cost of crashing per week

Crash cost - Normal cost / normal time - crash time

For activity A, crashing cost per week = 80-60/3-2 =20

similarly

Activity	Crash cost per week
A	20
B	40
C	10
D	30
E	5
F	10
G	80

Lengths of path

ABEG -22

ACG -18

ADFG -21

Without crashing, i.e. 22 days duration, the cost is 510.

Steps in crashing

(a) Crashing the activity that has least crash cost i.e. E for 1 week at 5. The duration is now 21 days and total cost is 510+5 =515. Now there are two critical paths viz ABEG and ADFG.

(b) The next activities to be crashed are E and F at a combined cost of 15. Duration is now 20 days. The critical paths remain the same and the total cost is 515+15 =530

(c) Next activity to be crashed is A which has crash cost of 20 per day. The duration decreases to 19. THe cost is 530+20 =550. Criticl path remain the same.

(d) Next activities to be crashed are B and F. The cost of crashing is 40+10 =50. The total cost of project is 550+50 =600. Duration is now 18 days, and there are 3 critical paths.

(e) Now, G is the only activity that can be crashed a day at a cost of 80. The duration is now 17 days and cost is 600+80 =680

d1

Total duration	Total cost ( incl. crashing)	Indirect cost	Grand total
22	510	400	910
21	515	350	865
20	530	300	830
19	550	250	800
18	600	200	800
17	680	150	830

d2 - The minimum cost pertains to 18 o 19 weeks. The cost is 800.