Question

V. Nimania plc builds water treatment facilities throughout the world. One contract it has concerns an installation in an area
prone to outbreaks of a dangerous disease. The company has to decide whether or not to vaccinate the employees who will be working there. Vaccination will cost £200,000, which will be deducted from the profit it makes from the venture. The company expects a profit of £1.2m from the contract but if there is an outbreak of the disease and the workforce has not been vaccinated, delays will result in the profit being reduced to £0.5m. If the workforce has been vaccinated and there is an outbreak of the disease, the work will progress as planned but disruption to infrastructure will result in their profit being reduced by £0.2m. Advise the company using:

(a) the maximax decision rule

(b) the maximin decision rule

(c) the minimax regret decision rule

(d) the equal likelihood decision rule

Answer 1

a) Under the maximax decision rule the company would choose the alternative where it maximizes the maximum payoff. In this case the company would not get its employees vaccinated so that it is able to earn the maximum profit of 1.2m assuming that there will be no disease outbreak.

b) Under the maximin decision rule the company would choose an alternative that would maximize its minimum payoff. In this case if the company does not provide the vaccination and outbreak happens then the minimum payoff is 0.5m. If the company provides vaccination and there is an outbreak then the payoff is 1.2-0.2-0.2 = 0.8m

The maximum payoff is thus 0.8m for the employees getting vaccinated.

c) Under the minimax regret decision rule the company would minimize the maximum return. In this case the maximum the company could earn without vaccination will be 1.2m. However in case vaccination is given then the company would earn 1.2 - 0.2 = 1m. By the minimax rule the company would decide to vaccinate the employees.

d) Under the equal likelohood decision rule it is assumed that both events will occur with equal probabilities. So we have for no vaccination case the expected payoff as:

1.2 * 0.5 + 0.5 *0.5 = 0.85m

In case vaccination is given to the employees the payoff is:

1*0.5 + 0.8*0.5 = 0.9m

We will choose the strategy that provides a larger expected payoff which in this case is providing vaccination to th eemployees.