Question

Activity	Immediate Predecessor(s)	Normal Time (wks)	Crash Time (wks)	Normal Cost ($)	Crash Cost ($)
A	—	4	1	5,000	8,000
B	—	5	3	8,000	10,000
C	A	1	1	4,000	4,000
D	B	6	3	6,000	12,000
E	B, C	7	6	4,000	7,000
F	D	7	6	4,000	7,000

1. You are the manager of a project to improve a billing process at your firm. Table 3 contains the data you will need to conduct a cost analysis of the project. Indirect costs are $1,600 per week, and penalty costs are $1,200 per week after week 12.
   1. What is the minimum-cost schedule for this project?
   2. What is the difference in total project costs between the earliest completion time of the project using “normal” times and the minimum-cost schedule you derived in part (a)? minimum- cost schedule derived in part A was = 15 weeks.

Answer 1

a.

Activity	Predecessor	Normal time	Crash time	Normal cost	Crash cost	Cost/ week
A	-	4	1	5000	8000	1000
B	-	5	3	8000	10000	1000
C	A	1	1	4000	4000	NA
D	B	6	3	6000	12000	2000
E	B,C	7	6	4000	7000	3000
F	D	7	6	4000	7000	3000

Cost/week of crashing = (Crash cost-normal cost)/(normal time-crash time)

The network diagram is drawn as shown:

The paths with times are given below:

Paths	Time
A-C-E	12
B-D-F	18
B-E	12

hence path B-D-F taking 18 weeks is the critical path

Cost for normal project time = normal total cost of 31000

plus 1600 per week indirect costs + 1200 per week penalty post week 12

Here project is taking 18 weeks; Hence 6 weeks penalty

So total costs = 31000 + 1600X18 + 6X1200 = 67000

For the minimum cost schedule let us work at reducing the time

For the critical path B-D-F, B has the lowest cost of 1000
hence crashing B by 2 units results in project time going to 16
Additional cost of 2000 is incurred and there is a saving of 1600X2 = 3200 in indirect cost
and penalty saving of 1200X2 = 2400

Hence net cost saving = 3200+2400-2000 = 3600

Next let us reduce the next activity i.e. D by 3 week costing 6000
Hence project duration becomes 13 weeks

And there is a saving of 3X1600 + 3X1200 - 6000 = 2400

Now if we reduce activity F by one week it will cost us 3000 whereas benefit will only be 1600+1200 = 2800. Hence we cannot reduce cost further

So minimum cost = 67000 - 3600 - 2400 = 61000

b. Difference = 67000 - 61000 = 6000