# 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.

#### Markov processes tutorial question

Research done by the Gulf Oil Corporation produced the following matrix of probabilities that a person with one form of central heating would switch to another within a year.

```                      Will switch to
Oil   Gas Electric
Currently has   Oil | .825 .175 0    |
Gas | .060 .919 .021 |
Electric | .049 0    .951 |
```

If the current (year one) market share is

Oil 26%, Gas 60% and Electric 14% then:

• What is the long-run prediction for the market, as calculated using the algebraic method.

In two years time a rival company is believed to be going to introduce cheaper oil for domestic heating. It is estimated that this will change the probabilities for switching to:

```                      Will switch to
Oil  Gas  Electric
Currently has   Oil | .930 .070 0       |
Gas | .070 .910 .020    |
Electric | .090 .020 .890    |
```
• What is the long term prediction for the market under this condition.
• What will be the market shares for oil, gas and electric in three years time (i.e. in year 4).