Question

The Advanced Tech Company has a project to design an integrated information database for a major bank. Data for the project are given in Table 1 below. Indirect project costs amount to $300 per day. The company will incur a $150 per day penalty for each day the project lasts beyond day 14. (a) What is the shortest time duration for this project regardless of cost? 

 (b) What is the total cost and time of the minimum-cost schedule?

Answer 1

ANSWER (a)

Project duration is 23 days i.e. shortest time duration for this project regardless of cost

Project	Activity time	Predessor	ES	EF	LS	LF	Slack (LS-ES)
A	6	-	0	6	0	6	0
B	4	-	0	4	2	6	2
C	3	A,B	6	9	6	9	0
D	2	B	4	6	7	9	3
E	6	C,D	9	15	9	15	0
F	2	E	15	17	21	23	6
G	4	E	15	19	15	19	0
H	4	G	19	23	19	23	0
		Project	23

Critical Path is A-C-E-G-H = 6+3+6+4+4 = 23

ANSWER (b)

Project	Normal time	Crash time	Normal cost	crash cost	Crash cost/pd	Crash by	Crashing cost
A	6	5	1000	1200	200	1	200
B	4	2	800	2000	600	0	0
C	3	2	600	900	300	1	300
D	2	1	1500	2000	500	0	0
E	6	4	900	1200	150	2	300
F	2	1	1300	1400	100	0	0
G	4	4	900	900	0	0	0
H	4	2	500	900	200	2	400
Totals			7500				1200

We can crash only Critical path activities to shorten project duration.

So Max crash time is 6 days for $1200.

So Minimum Project duration = 23-6 = 17 days

So Penalty is payable for 17-14 = 3 days

So minimum cost = Project cost + Crash cost + Indirect cost + penalty

= 7500 + 1200 + 300*17 + 3*150

= 14,250

Critical path has Not changed & remains A-C-E-G-H

Critical path length is now 5+2+4+4+2 = 17