# 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 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?