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 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).