Question

PM.62 The US government has recently contracted with Boeing to build its fleet of airborne tankers. The project has been laid out with durations (in weeks), predecessors, and costs included:

Activity	Normal Time (weeks)	Crashed Time (weeks)	Normal Cost	Crashed Cost	Predecessor(s)
A	2	1	$1,350	$1,950	-
B	7	5	$1,250	$2,610	-
C	5	4	$800	$1,300	B
D	3	2	$2,100	$3,000	A
E	4	3	$630	$1,150	B
F	2	1	$560	$1,350	E
G	8	6	$550	$740	C, D, F

What is the critical path of the project?

		A-D-G
		B-C-G
		B-E-F-G

If you wanted to shorten the overall duration of the project, which activity would you crash first?

		G
		B
		C
		E

What would be the weekly crashing cost of the activity you selected in the previous question? (Display your answer to two decimal places.)

   

Crash the project by 3 weeks. What is the total cost of crashing the project (just the additional cost, not total project cost)? (Display your answer to two decimal places.)

   

Answer 1

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

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

Based on the predecessor relationship, we prepare the 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

Similarly LFT & LST are calculated during backward pass.

There are multiple paths in the diagram:

A-D-G

B-C-G

B-E-F-G

Out of the above paths, path B-E-F-G 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 week to have a minimum cost impact.

Step-1: We crash activity G as it has the lowest crash cost. We crash G by 2 weeks which is the maximum possible. Additional cost = No. of weeks crashed * crash cost per week = 2*95 = $190

Step-2: Next, we crash activity E as it has the lowest crash cost. We crash E by 1 week which is the maximum possible. Additional cost = No. of weeks crashed * crash cost per week = 1*520 = $520

Revised network diagram is shown below:

As seen from above, we have reduced project duration to 18 weeks from 21 weeks. We have crashed it by 3 weeks as required.

Total additional cost = Additional cost in Step-1 + Additional cost in Step-2 = 190 + 520 = $710

Hence, we get answers as:

Question: What is the critical path of the project? Answer: B-E-F-G

Question: If you wanted to shorten the overall duration of the project, which activity would you crash first?

Answer: G

Question: What would be the weekly crashing cost of the activity you selected in the previous question?

Answer: $95.00

Question: Crash the project by 3 weeks. What is the total cost of crashing the project (just the additional cost, not total project cost)?

Answer: $710

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