# OR-Notes

## J E Beasley

OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.

A full list of the topics available in OR-Notes can be found here.

#### Network analysis - uncertain completion times tutorial question

In a project there are 9 activities as below (all times in months):

```Activity   Optimistic    Most likely   Pessimistic    Immediate predecessor
time          time          time           activities
A           4             6            8              -
B           1             2            3              -
C           4             4            4              A
D           4             5            6              A
E           7             10           16             B
F           8             9            10             B
G           2             2            2              C
H           2             3            7              D,E,F
I           1             3            11             F```
• Draw the network diagram
• What is the expected project duration?
• What is the probability of completing the project in 18 months?

The project manager of Good Public Relations has gathered the data shown below for a new advertising campaign (all times in days).

```Activity    Optimistic    Most likely   Pessimistic    Immediate predecessor
time          time          time           activities
A           8             10            12             -
B           5             8             17             -
C           9             10            11             -
D           1             2             3              B
E           8             10            12             A,C
F           5             6             7              D,E
G           1             3             5              D,E
H           2             5             8              F,G
I           2             4             6              G
J           4             5             8              H
K           2             2             2              H```
• Draw the network diagram
• How long is the project likely to take - by which we mean what is the expected project duration ?
• What is the probability that the project will take more than 38 days?