Question

Below are the data for a Time-Cost CPM Scheduling model analysis. The time is in days and the costs include both direct and indirect costs. If you crash this project to reduce the total time by two days what is the total time of the project and total cost? Explain. (Note: Cut and paste your Precedence diagram.)

Activity	Immediate Predecessor	Normal Time	Crash Time	Normal Cost	Crash Cost
A	None	3	2	200	400
B	A	4	3	300	600
C	A	1	---	400	---
D	B and C	3	2	200	250
E	D	2	1	500	600
F	E	2	---	600	---
G	E	3	1	300	450
H	G	1	---	400	---

Answer 1

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

The formula for calculating crash cost per day is shown in the table.

Total Normal Cost of the project = $2900

Based on the predecessor relationship, we prepare project network diagram as shown below:

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

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 - 1

Similarly, LFT & LST are calculated during the backward pass. The activity END is only a dummy activity that is introduced for backward pass calculations only. It will not be considered for any other purpose.

There are multiple paths in the diagram:

A-B-D-E-F

A-B-D-E-G-H

A-C-D-E-F

A-C-D-E-G-H

Out of the above paths, path A-C-D-E-G-H is the longest path and has 0 slack. Hence, this is the critical path.

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

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

Step-1: We crash activity D as it has the lowest crash cost. We crash D by 1 day which is the maximum possible. Additional cost = No. of days crashed * crash cost per day = 1*50 = $50

Step-2: We crash activity G as it has the lowest crash cost. We crash G by 1 day which is required. Additional cost = No. of days crashed * crash cost per day = 1*75 = $75

Revised network diagram is shown below:

We have reduced the project duration from 16 days to 14 days.

Total cost for this crashing = Additional cost for Step-1 + Additional cost for Step-2 = 50 + 75 = $125

Total Project time = 14 days

Total Project cost = Total Normal cost + Additional cost = 2900 + 125 = $3125

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