In: Operations Management
Suppose that a car-rental agency offers insurance for a week
that costs $100. A minor fender bender will cost $3,500, whereas a
major accident might cost $16,000 in repairs. Without the
insurance, you would be personally liable for any damages. What
should you do? Clearly, there are two decision alternatives: take
the insurance, or do not take the insurance. The uncertain
consequences, or events that might occur, are that you would not be
involved in an accident, that you would be involved in a fender
bender, or that you would be involved in a major accident. Develop
a payoff table for this situation. What decision should you make
using each of the following strategies?
a) aggressive strategy
b) conservative strategy
c) opportunity-loss strategy
(a)
Aggressive strategy (Maximax)
Take maximum possible payoff for each alternative. Then select the alternative which shows the maximum of payoff out of these maxima.
Payoff matrix | States of nature | Max | ||
Alternatives | No accident | Minor accident | Major accident | payoff |
Take insurance | -100 | -100 | -100 | -100 |
Don't take insurance | 0 | -3,500 | -16,000 | 0 |
Note that the payoffs have been written as negative of costs.
So, based on the aggressive strategy, the best decision is to not to buy the insurance.
(b)
Conservative strategy (Maximin)
Take minimum possible payoff for each alternative. Then select the alternative which shows the maximum of payoff out of these minima.
Payoff matrix | States of nature | Min | ||
Alternatives | No accident | Minor accident | Major accident | payoff |
Take insurance | -100 | -100 | -100 | -100 |
Don't take insurance | 0 | -3,500 | -16,000 | -16,000 |
So, based on the conservative strategy, the best decision is to buy the insurance.
(c)
Opportunity-loss strategy (Minimax Regret)
First, develop the regret matrix by subtracting each payoff from the corresponding column maxima.
Regret matrix | States of nature | ||
Alternatives | No accident | Minor accident | Major accident |
Take insurance | 100 | 0 | 0 |
Don't take insurance | 0 | 3,400 | 15,900 |
Then take maximum possible regrets for each alternative and select the alternative which shows the minimum of regrets out of these maxima.
Regret matrix | States of nature | Max | ||
Alternatives | No accident | Minor accident | Major accident | regret |
Take insurance | 100 | 0 | 0 | 100 |
Don't take insurance | 0 | 3,400 | 15,900 | 15,900 |
So, based on the opportunity-loss strategy, the best decision is to buy the insurance.