# OR-Notes

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 class question

Company X is deciding whether it should invest £750,000 in a program
of *major* improvements for a particular product which, with or without
these major improvements, will remain in production for just one more year.
Company Y produces an almost identical product which is in direct competition
with X's and it is predicted that there is a 50/50 chance (irrespective
of any action X takes) that Y will institute similar major improvements
to its own product.

If X improves and Y does not then for X the probabilities are 0.6, 0.3
and 0.1 of sales improving by 15%, 10% and 5% respectively.

If X and Y both improve then the total market will increase and X would
expect its sales to rise by 8%.

If neither X nor Y improve then the present demand is expected to continue
and this for X is 500,000 units a year.

If X doesn't improve and Y does then the probabilities are 0.8, 0.1
and 0.1 of X's sales falling by 15%, 10% and 5% respectively.

If X decides not to invest £750,000 in the program of major improvements
it has the option, in the event that Y does carry out major improvements,
of instituting either a normal program of minor improvements or a crash
program of minor improvements (*instead* of the program of major improvements).

A crash program could be instituted very quickly but would cost 50%
more than the normal program. The normal program is certain of success,
the crash program however has a 10% chance of failure and the sales if
the crash program fails would be the same as if X had done nothing in response
to Y's major improvements. If, however, X is successful with its crash
program it could expect to attain a 7% increase in sales. The normal program
would attain a 5% increase in sales.

The contribution to profit of each unit sold by X is £40. The
cost of the normal program of minor improvements for X is estimated to
be £400,000.

What should X do and what is the expected monetary value of your suggested
course of action? What is the downside of your suggested course of action
(i.e. how much will X lose if the worst happens).