Question

The following data were obtained from a project to build a pressure vessel:

Activity Duration Predecessors

Predecessors:

A is none

B is none

C is B

D is A & C

E is B

F is D, E, G

G is B

H is F

I is G

J is I

What is slack time (float) for

A6 weeks---B6 weeks---C5 weeks D4 weeks, E5 weeks F7 weeks, G4 weeks H8 weeks I5 weeks J3 weeks

Step 1: Construct a network diagram for the project.

Calculate completion time

Identity critical path

What is slack time (float) for A?

What is slack time (float) for D?

What is slack time (float) for E?

What is slack time (float) for G?

Answer 1

Based on the given data, we prepare a network diagram as shown below:

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

The above project diagram is prepared as per legend shown in 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. The activity END is only a dummy activity which is introduced for backward pass calculations only. It will not be considered for any other purpose.

There are multiple paths in the diagram. However, path B-C-D-F-H is the critical path.

As seen from the network diagram, the project completion time = 30 weeks

As seen from the network diagram and the legend,

Slack time for A = 5 weeks

Slack time for D = 0 weeks

Slack time for E = 4 weeks

Slack time for G = 5 weeks

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