# Project scheduling with AOA and AON to arrive at critical path

PROJECT MANAGEMENT

Please help me with the following questions.

Work breakdown structure

- Critical path

- AOA and AON networks

- Forward and backward passes

- Variability in activity times

https://brainmass.com/business/operations-research/project-scheduling-aoa-aon-arrive-critical-path-562669

#### Solution Preview

Please see attached for full solution with diagrams.

1) A list of activities, precedence relations, and optimistic, most likely, and pessimistic activity completion times for a project are as given below.

Activity Name Predecessor Activities Optimistic Most Likely Pessimistic

A - 4 5 6

B A 3 4 8

C B 1 2 3

D A, C 3 6 8

E D 7 8 9

F E 4 5 7

G C 3 4 5

H D, E, G, I 12 13 15

I C 1 2 4

J G, H 1 1 1

K F, H, J 1 6 7

a) Draw an AOA network diagram for this project.

(see attached file for diagram)

b) What is the expected completion time for each activity in the project?

The expected completion time for each activity is computed as

Expected completion time = (Optimistic time + 4*Most likely time + Pessimistic time)/6

Computation for activities A and B is demonstrated through formula use.

Activity Name Predecessor Activities Optimistic Most Likely Pessimistic Expected

A - 4 5 6 (4+4*5+6)/6

= 5

B A 3 4 8 (3+4*4+8)/6

= 4.5

C B 1 2 3 2

D A, C 3 6 8 5.834

E D 7 8 9 8

F E 4 5 7 5.167

G C 3 4 5 4

H D, E, G, I 12 13 15 13.167

I C 1 2 4 2.167

J G, H 1 1 1 1

K F, H, J 1 6 7 5.34

c) What is the variance associated with the expected completion time of each activity in the project?

Variance associated with the expected completion time is calculated as

Variance = (Pessimistic time - Optimistic time)^2/36

Calculation details for activities A and B is as shown below

Activity Name Predecessor ...

#### Solution Summary

This solution provides step by step calculation guide on how to arrive at project shedule and identify critical path. Diagrams and charts are included.