A project has 8 activities. The project completion time must be shortened by 2 d

Question

A project has 8 activities. The project completion time must be shortened by 2 days. Activity A. 29 days, IP: none: $55 per day: 3 days Activity B, 33 days, IP: none: $47 per day: 3 days Activity C, 40 days. IP: none: $59 per day; 3 days Activity D, 25 days. IP: A; $41 per day; 3 days Activity E. 38 days. IP: B; $54 per day; 3 days Activity F. 29 days. IP: C; $44 per day; 3 days Activity G. 36 days. IP: D; $30 per day; 1 day Activity K. 20 days. IP: E. F; $86 per day; 1 day The above information signifies that activity D has a duration of 25 days, has activity A as its immediate predecessor. Furthermore, its crashing cost is $41 per day and it can be crashed for a maximum of 3 days The minimum cost to crash the project by 2 days is $

Explanation / Answer

Let us put all the given data in the tabular format as mentioned below;

$86

Step 1

Now we have to draw the network diagram to before we go to the solution. Network representation is the important step in solving Project Management problems using network analysis. It represents a relation among activities and various paths present in the project.

The network diagram using AoA method (Activity on Arrow);

Step 2

EST - Earliest Start Time

EFT - Earliest Finish Time

LST - Latest Start Time

LFT - Latest Finish Time

Step 3

List down the various paths present in the network and find out the critical path(s) with durations;

Normal Project duration is the duration of the critical path;

Total Duration = 91 months (addition of activity time of all the activities on critical path)

Step 4

Crashing the project by 2 days meaning reducing the project duration by 2 days, we have to reduce the project duration of activities on critical path.

Now here, the difference between duration of critical path and next non-critical path is only 1 day. However, reducing the duration of critical path by 2 days will reduce the overall project duration by only 1 day with new critical path Start - B - E - H - End and the total duration of 90 days.

Therefore, we will crash the project in two stages by crashing activities on 2 paths one at a time.

First, crashing the activity on critical path Start - B - E - H - End by 2 days;

To minimize the cost select the activity with lower crashing cost, among activities B, E & H crashing cost of activity B is lowest, hence crashing activity B by 2 days.

Incremental Project Cost = Crashing cost per day of activity B x no. of crash days

Incremental Project Cost = $47 x 2 days

Incremental Project Cost = $94

Now, the duration of path Start - B- E - H - End has reduced to 89 days and the new critical path is Start - A - D - G - End.

We have to reduce the duration of new critical path by 1 day by crashing one of the activity among A, D & G. Activity G incurs lowest crashing cost for 1 day. Hence crashing activity G by 1 day.

Incremental Project Cost = Crashing cost per day of activity G x no. of crash days

Incremental Project Cost = $30 x 1 day

Incremental Project Cost = $30

Step 5

Minimum project cost to reduce the project duration by 2 days is;

Total Cost = $94 + $30

Minimum Cost = $124

Activity IP Normal Time (Days) Max Crashing (Days) Crash Time (Days) Crashing Cost (per day) A - 29 3 26 $55 B - 33 3 30 $47 C - 40 3 37 $59 D A 25 3 22 $41 E B 38 3 35 $54 F C 29 3 26 $44 G D 36 1 35 $30 H E 20 1 19

$86

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