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?