# 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.

#### Decision trees tutorial question

Nova Ltd is considering whether to spend a further £30K to develop a new product. If the development program is successful two alternative sizes of plant are likely to be considered:

```Plant    Production capacity  Capital cost   Running cost
(tonnes)             (£K)           (£K per year)
Small    2,000                100            50
Large    5,000                200            100
```

The development program, which is thought to have a 70% chance of success, will take a year to complete. After completing that program it would take one year to build a small plant and two years to build a large plant. It is believed that one other major company in this field is developing a competing product and the marketing intelligence unit of Nova believe that there is a 25% chance that this company will have their product on the market 3 years from now, a 50% chance that they will have their product on the market 4 years from now and a 25% chance that it will take them 5 years to get their product onto the market.

The following estimates of Nova's possible selling price have been obtained from the marketing department:

```                     Small           Large
Output (per year)    2,000 tonnes    5,000 tonnes
Monopoly price       £50 per tonne   £30 per tonne
Competitive price    £30 per tonne   £25 per tonne
```

where the monopoly price applies whilst Nova is without competition and the competitive price applies once the competitor company have their product on the market.

• If the likely lifetime of the Nova product is 10 years (once released onto the market) what should Nova do?
• What is the "downside" of your suggested course of action?