# OR-Notes

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 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?
- What is the probability that the project will take more than 38 days?

Information concerning a certain project is given in the
table below. Indirect project costs amount to £250 per day. The company
will experience a £100 per day penalty for each day the project lasts
beyond day 14.
Activity Normal Normal Crash Crash Immediate
time cost time cost predecessor
(days) (£) (days) (£) activities

A 4 1000 3 1100 -
B 6 800 3 2000 -
C 3 600 2 800 A,B
D 2 1500 1 2000 B
E 5 700 3 1200 C,D
F 2 1300 1 1400 E
G 2 900 1 1200 E
H 4 100 2 900 G

- Draw the network diagram
- What is the project duration using only normal times?
- What completion date do you recommend in order to minimise total cost
(hint: you need to include the indirect cost per day and the penalty cost
as well as the direct cost of the project)?
- What activities need to be crashed, and by how much, to achieve the
date recommended?