# Decision analysis Essay Example

1. In case of theft, what Danika would have to pay depends on the kind of policy he decides to take. The policy scenarios are outlined below together with the payable amount in case of theft;

1. Under the NoRegrets package, this is a comprehensive package meaning that the insurance company would pay the entire \$15,000 worth of head office contents. As such, Danika would not pay anything i.e.

Value of office contents stolen \$15,000

Value of compensation for theft \$15,000

Amount Dinka would pay \$0

1. Under the InsureNow package, the insurance company would require the insurance holder to pay the first \$5,000 of any losses incurred. Thus, Dinka would only be required to pay the first \$5,000 i.e.

Value of office contents stolen \$15,000

Value of compensation for theft \$10,000

Amount Dinka would pay \$5,000

1. Under the RiskIt package, the insurance company would only cover the loss up to 75% of the losses incurred. Thus, Dinka would pay the remaining 25% as follows;

Value of office contents stolen \$15,000

Value of compensation for theft 75%*15,000 \$11,250

Value of compensation for theft 25%* 15,000 \$3,750

1. The payoff table that models Danka’s problem is as shown below;

NB// The payoff table considers the fact that whether or not theft occurs, the package fees would have to be paid. As such, the amount paid by Dinka in case of theft under each package has been increased by the package fee as follows;

No regrets \$0+ \$2,000 = \$2,000

InsureNow \$5,000 +\$1,500 = \$6,500

RiskIt \$3,750 +\$1,000 = \$4,750

On the other hand, the amount paid in case of no theft includes the package fee as follows;

NoRegrets \$2,000

InsureNow \$1,500

Risk it \$1,000

NB// Since the probability of theft occurring is 0.05 or 5%, the probability that no theft occurs is hence 0.95% or 0.95 (Charlesworth, 2013).

NB// Since the amounts are payments, they have been put under a negative sign.

PAYOFF TABLE

 ALTERNATIVE PACKAGE NoRegrets InsureNow Probability

Optimal choice under

1. Maximin criterion

Using this criterion, Danika would choose the best of the worst payoff. In this case, the worst scenario would be if theft does occur. In this case,

 ALTERNATIVE PACKAGE NoRegrets InsureNow Probability

NoRegret guarantees a payoff of -\$2,000

InsureNow guarantees a payoff of — \$6,500

RiskIt guarantees a payoff of -\$4,750

Thus, Danika should prefer the NoRegret option as it minimizes the maximum loss in case of theft to just -\$2000 paid as insurance fee.

1. Maximax criterion

In this case, Danika should select the alternative that maximizes the maximum payoff available if the best happens. In this case, the best scenario is when there is no theft. In this case,

 ALTERNATIVE PACKAGE NoRegrets InsureNow Probability

NoRegret guarantees a payoff of -\$2,000

InsureNow guarantees a payoff of -\$1,500

RiskIt guarantees a payoff of -\$1,000

In this case, the best option for Danika is the RiskIt option since he pays the minimum of \$1,000 when no theft occurs.

1. Maximum criterion

This is the alternative with the highest payoff under most likely state of nature. In this case, the most likely state of nature is when no theft occurs with a probability of 0.95. In this case;

 ALTERNATIVE PACKAGE NoRegrets InsureNow Probability

NoRegret guarantees a payoff of -\$2,000

InsureNow guarantees a payoff of -\$1,500

RiskIt guarantees a payoff of -\$1,000

In this case, the best option for Danika is the RiskIt option that has the highest payoff of -\$1,000

1. The expected value criterion

This is the criterion that considers probability in choosing the best alternative as follows

 ALTERNATIVE PACKAGE NoRegrets InsureNow Probability

NoRegret expected value = (-\$2,000*.05) + (-\$2,000*.95) = -\$2,000

InsureNow expected value = (-\$6,500 *.05) + (-\$1,500*.95) = -\$1,750

RiskIt expected value = (-\$4,750*.05) + (-\$1,000 *.95) = -\$1187.5

In this case, Danika should choose the RiskIt criterion as it has the highest expected value bearing in mind that the expected values are in terms of payments (Brownley, 2013).

1. The package I would choose

The various criterion used above in choosing the best insurance alternative have arrived at RiskIt as the best option that Dinka should take in insuring his office contents. Another reason why the option would be preferable is because it is the cheapest option. However, other factors need to be put into consideration in deciding the best option that the company ought to take. First, though the likelihood of theft is very small at just 5%, one ought to consider the impact this would have on the company’s operations in case it does occur. For instance, choosing the RiskIt option will call for Danika to contribute \$3,750 towards replacing the office contents. What happens when the company does not have such money at the moment? It for such reasons that I would choose the NoRegret option despite it being the most expensive option (Institute for Operations Research and the Management Sciences, 2004). This is because incase theft occurs, I would not need to contribute anything towards replacing the office contents but the insurance company would replace all the contents. This means that whether I have money or not, the company’s operations will not be inconvenienced in case of theft but will go on as usual. Even if there was cash to replace the items, such cash would be used for business expansion. Therefore, I would advise Danika to choose the NoRegrets option as it is the best.

References

Charlesworth, D. (2013). Decision analysis for managers: A guide for making better personal and business decisions. New York: Business Expert.

Brownley, W. (2013) Multi-objective decision analysis: Managing trade-offs and uncertainty. New York, NY: Business Expert Press

Institute for Operations Research and the Management Sciences. (2004). Decision Analysis. Linthicum, Md: Institute for Operations Research

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