Toy City Case Study

Question 1

We have the total project duration of 313 hours with cost of $19,350.

If I were Bert, I would have a accommodated John’s vacation request. We could see in the below network diagram, Audit of Receivables (Activity 8) is not a critical activity that the early start is not equal to late start an d the early finish is not equal to the late finish.

There is a slack time of 175 hours, so it is possible to give John a vacation if he promises to come back before the 247th hour of the project which is the latest start time of audit of liquid asset. As a week involve 40 audit hours, the maximum time for John’s off is 175/40 = 4.375 weeks.

We have the Critical Path: Activity 1-2-3-4-5-9-11-17-20-22.

Table 1

[pic 1]

As shown in below schedule, John could work 10 hours daily from Jan 16 to Feb 13 and get his vacation as requested. If John is only responsible for auditing receivables, he can extend his vacation till Feb 12.

Table 2

[pic 2]

Question 2

Part One

As it is assumed that the activities were processed exactly on schedule for the first 106 duration hours, the desired project completion time of the remaining part should be 313 - 106 - 60 = 147hours. Therefore, the desired project completion time of the whole project is 147 + 106 = 253 hours. Yet, the required duration is actually 320 - 60 = 260 hours, and the time we need to crash is 313 - 260 = 53 hours.

Table 3

[pic 3]

Identify 1st activity to crash:

The Total Costs is $19,350 with 313 hours. Looking at the critical paths of Activity 5-9-11-17-20-22, and the crashable activities are 9, 11 and 20 with limits of 36, 45 and 5 respectively. The best option would be lowest Crash cost of Activity 11 is $18.67, and from[table Q1] Slack Time of Activity 14 is 40, thus we Crash Task 11 by 40 hours. The Total Costs is $19,350 with 313 hours.

Identify 2nd activity to crash:

The Total Costs is $20,097 with 273 hours now. Again, taking look at the critical paths of Activity 5-9-11-17-20-22, this time we could either crash task 9 by 13 hours, or crash Activity 11 and 15 simultaneously with the total cost of $58.67, clearly Activity 9 is the best option.

Now, the the Total Costs is $20,655 with 260 hours, achieved the goal.

Part Two

We could have further $70 hourly cost reduction:

• Reduce Activity 9 by 23 hours at cost of $42.91/day,

• Reduce Activity 11 and 15 by 5 hours at a cost of $58.67/day,

Thus, at most 23+5 = 28 hours to be reduced.

Question 3

According to the schedule, Early Start of both Activity of 11 and 14 185, thus after 189 duration hours:

• Activity 11 is 4 hours in progress, 4/53 = 7.55% done,

• Activity 14 is 4 hours in progress, 4/25 = 16% done,