Operations Management

NATIONAL UNIVERSITY OF SCIENCE AND TECHNOLOGY

FACULTY OF APPLIED SCIENCES

APPLIED MATHEMATICS DEPARTMENT

MSc. in OPERATIONS RESEARCH – Part I

SMA5172: Operations Management Assignment 2 – November 2012

Q1. The following is a table showing details of a project:

Activity Immediate Normal Crash
Predecessor Time(wks) Cost($) Time(wks) Cost($)

A – 10 20 7 30
B – 8 15 6 20
C B 5 8 4 14
D B 6 11 4 15
E B 8 9 5 15
F E 5 5 4 8
G A,D,C 12 3 8 4
Indirect cost is $400 per day.

Draw the network and identify the critical path.
Find out the total float associated with each activity.
Find the optimum duration and the associated minimum project cost. [25 marks]
Q2. The activities comprising a certain project have been identified as follows:

Activity Preceding Duration Cash Required to Complete
Activity (weeks) Activity ($’000s)

A – 10 30
B A 6 18
C A 3 12
D B,C 12 12
E C 4 8
F B 6 12
G D,F 2 6
H E 5 15
I E 4 16
J H,I 6 12
K G,J 2 6

Draw the network to represent the above. Indicate the critical path and determine the minimum duration of the project.
By how much the duration of activity I have to increase before it becomes critical?
What would be the effect, if any, on both the duration of the project and the critical path if activity D does not have to be preceded by activity B?
If all activities start at their earliest time and the necessary cash is used at a uniform rate throughout the duration of each activity, determine by means of a Gannt Chart the maximum amount of cash required in any one week.
If, due to cash flow problems, there is a limit of $7500 per week on outgoings, by how many weeks must the project be extended? [25 marks]

End of Assignment: 50 Marks