# 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 - cost/time tradeoff tutorial question

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?
• Which activity would you crash to reduce the project completion time by one day? Which activity would you crash to reduce the project completion time by a further day?
• Formulate the problem of crashing the project so as to find the completion time that minimises total cost as a single linear program (hint: you need to include the indirect cost per day and the penalty cost as well as the direct cost of the project).
• If activity B can now be crashed a further day, at an additional cost of £750, how does this affect your formulation?