Question

Lecture Exercise #13 Project Crashing Time (weeks) Cost Activity Predecessori s) Normal Crash Normal Crash A None 3 2 1000 1600 B None 2 1 2000 2700 C None 1 1 300 300 D A 7 3 1300 1600 E B 6 3 850 1000 F с 2 1 4000 5000 D, E 2000 G 4 2 1500 What's the normal project completion time? Identify the critical path If you'd like to shorten the project by one week, which activity should you shorten? )

Answer 1

Based on the given data, we find the crash cost per week as shown below:

Activity Predecessor Crash cost per day 600 700 A B C D E F G Normal Time 3 2 1 7 6 2 4 Crash Time 2 1 1 3 3 1 2 Total Normal Cost 1000 2000 300 1300 850 4000 1500 10950 Crash Cost 1600 2700 300 1600 1000 5000 2000 A B С DE 75 50 1000 250

Based on the predecessor relationships and normal durations given, we prepare a project network diagram as shown below:

Legend EST ID EFT SLK LST DUR LFT 0 A 3 D 10 0 - wow 0 3 3 7 10 G 14 10 0 10 B 2 E 8 4 14 0 2 2 2 2 4 14 END 14 0 14 0 14 2 4 6 10 1 1 C 1 1 F 3 0 11 11 11 12 1 1 12 2 14

The above network diagram in form of formulas is shown below for better understanding and reference

A C D E G H K M N O 1 2 3 B Legend ID EFT EST SLK LST 4 DUR LFT А =A6+B8 D =E6+F8 5 60 7 =A8-A6 8 =C8-B8 =C6 =E8-E6 | =G8-F8 3 =E8 7 =110 9 =MAX(G6, G10) G =18+J10 =110-18 =K10-110 4 =M12 B =A10+B12 =C10 E =E10+F12 =E12-E10 =G12-F126 =110 =MAX(K8,614) END =M10+N12 =M12-M10 =O12-N12 o =010 =E12 10 O 11 =A12-A10 12 =C12-B12 13 14 O 15 =A16-A14 16 =C16-B16 1 C =A14+B16 =C14 F =E14+F16 =E16-E14 =G16-F16 2 =M12 =E16

The above project diagram is prepared as per the legend shown in the top-left corner.

EST = Early start time

LST = Late start time

EFT = Early finish time

LFT = Late finish time

SLK = Slack = LST - EST or Slack = LFT - EFT

The EST of an activity = EFT of previous activity

EFT of an activity = EST + Duration

Similarly, LFT & LST are calculated during the backward pass.

There are multiple paths in the diagram. However, path A-D-G is the longest path and has 0 slack. Hence, this is the critical path of the project.

To reduce project duration, we have to crash activities on critical path first.

As seen from above table, we start with crashing activities with minimum crash cost per day to have minimum cost impact.

As seen from the table on the top, if we want to crash the project by 1 week, we crash activity D since it has lowest crash cost per week and hence, least cost impact on the project.

We summarize the answers as shown below:

The project completion time = 30 weeks

Critical path = A-D-G

To shorten the project by 1 week, we crash activity D

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