Question

Question 1             

A manufacturer of deodorant is about to expand production capacity to make a new product. Four alternative production processes are available. The table below shows estimated profits in pounds for these processes for each of three possible demand levels:

		State of Nature
		Low Demand	Moderate Demand	High Demand
Action	Process A	50000	250000	750000
	Process B	100000	300000	550000
	Process C	200000	350000	450000
	Process D	150000	300000	400000

1. Which action is chosen by the maximin criterion?
2. Which action is chosen by the maximax criterion?
3. Which action is chosen by the minimax regret criterion?
4. Suppose the manufacturer obtains information that 30% of products of this type have met high demand, 40% moderate demand and 30% low demand. According to the expected monetary value criterion, which process should be used?

Justify your answers.

Answer 1

Which action is chosen by the maximin criterion?

The conservative approach is to select the best of the worst possible payoffs.

The minimum payoff for each decision alternative is

		Minimum payoff
Action	Process A	50000
	Process B	100000
	Process C	200000
	Process D	150000

The alternative process C has the maximum of the minimum payoffs. Hence it is the recommended alternative.

ans: Using the maximin criterion, the manufacturer needs to chose the production process C.

Which action is chosen by the maximax criterion?

The optimistic approach, picks the alternative which provides the best of the best possible payoffs

The maximum payoff for each of the alternatives is

		Maximum payoff
Action	Process A	750000
	Process B	550000
	Process C	450000
	Process D	400000

We can see that the alternative, process A has the best payoff. Hence the recommended alternative is to go for Process A

ans: Using the maximax criterion, the manufacturer needs to chose the production process A.

Which action is chosen by the minimax regret criterion?

First we need to calculate the regret associated with each alternative and state of nature.

The regret is calculated as

Regret of the alternative for a demand type= (Best payoff for a given demand type) - (payoff for the alternative for a demand type)

The best payoff for each demand type is given below

		State of Nature
		Low Demand	Moderate Demand	High Demand
Action	Process A	50000	250000	750000
	Process B	100000	300000	550000
	Process C	200000	350000	450000
	Process D	150000	300000	400000
	Best Payoff	200000	350000	750000

The regret table calculated using

		State of Nature
		Low Demand	Moderate Demand	High Demand
Action	Process A	200000-50000=150000	350000-250000=100000	750000-750000=0
	Process B	200000-100000=100000	350000-300000=50000	750000-550000=200000
	Process C	200000-200000=0	350000-350000=0	750000-450000=300000
	Process D	200000-150000=50000	350000-300000=50000	750000-400000=350000

The maximum regret for each of the decision alternative is given below

		Maximum regret
Action	Process A	150000
	Process B	200000
	Process C	300000
	Process D	350000

The alternative Process A has the minimum regret of all. Hence the recommended alternative is process A.

ans: Using the minimax regret criterion, the manufacturer needs to chose the production process A.

Suppose the manufacturer obtains information that 30% of products of this type have met high demand, 40% moderate demand and 30% low demand. According to the expected monetary value criterion, which process should be used?

The expected value for Process A is

The expected value for Process B is

The expected value for Process C is

The expected value for Process D is

We can see that the decision alternative Process A has the highest expected payoff

ans: According to the expected monetary value criterion, Process A should be used