Question

# Activity Immediate Predecessor(s) Normal Time (wks) Crash Time (wks) Normal Cost (\$) Crash Cost (\$) A...

 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.

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