Question

1. ABC Inc. must make a decision on its current capacity for next year.  Estimated profits (in $000's) based on next year's demand are shown in the table below.

                      Next Year's

                        Demand

Alternative Low Medium  High
Expand         $100 $200         $250
Subcontract $50         $120         $125
Do Nothing $40         $50           $ 55

a. Which alternative should be chosen based on the maximax criterion?  

b. Which alternative should be chosen based on the maximin criterion?  

c. Which alternative should be chosen based on the Lapalce criterion?  

d. Which alternative should be chosen based on criterion of realism with alpha = 0.7?  

e. Which alternative should be chosen based on the minimax regret criterion?  

2. Refer to problem 1.  Assume that ABC Inc. has hired a marketing research firm that provided additional information regarding next year's demand.  Suppose that the probabilities of low and high demand are assessed as follows: P(Low) = 0.3, P(Medium)= 0.3 and P(High) = 0.4.

        a.  Which alternative should be chosen using the expected monetary value (EMV) criterion?

        b.  What is the expected value under perfect information (EVPI)?

        c.  Develop a Decision tree for this problem.

Answer 1

Answer 1 –

a.

Maximax criteria

In maximax decision criteria, select the maximum value from each state of nature (row) as best payoffs. From those best payoffs, select the maximum value as the best alternative.

	Low	Medium	High	Best Payoff
Expand	100	200	250	250
Subcontract	50	120	125	125
Do nothing	40	50	55	55

Based on Maximax criteria, we would choose the “Expand” alternative.

b.

Maximin criteria

Under the maximin decision criteria, select the minimum value from each state of nature (row) as the worst payoffs. From those worst payoffs, select the maximum value as the best alternative.

	Low	Medium	High	Worst Payoff
Expand	100	200	250	100
Subcontract	50	120	125	50
Do nothing	40	50	55	40

Based on Maximin criteria, we would choose the “Expand” alternative.

c.

Laplace criteria

Under the Laplace decision criteria, find the average payoffs for each decision alternative. From those average payoffs, select the maximum value as the best alternative.

Average payoff = Sum of values of all the three states of nature / 3

	Low	Medium	High	Average Payoff
Expand	100	200	250	(100+200+250)/3 = 183.33
Subcontract	50	120	125	(50+120+125)/3 = 98.33
Do nothing	40	50	55	(40+50+55)/3 = 48.33

Based on Laplace criteria, we would choose the “Expand” alternative.

d.

Criteria of realism with alpha = 0.7

Under the Criterion of Realism, multiplying the best outcome in the row by α, multiplying the worst outcome in the row by (1-α), and then add the two results together. From those calculated payoffs, select the maximum value as the best alternative

Here, α = 0.7

1- α = 1-0.7 = 0.3

	Low	Medium	High	Average Payoff
Expand	100	200	250	(250*0.7) + (100*0.3) = 205
Subcontract	50	120	125	(125*0.7) + (50*0.3) = 102.5
Do nothing	40	50	55	(55*0.7) + (40*0.3) = 50.5

Based on criteria with realism, we would choose the “Expand” alternative.

e.

MINIMAX REGRET

We will select a maximum value from all the alternatives available under the minimax regret criteria and then deduct each value from that selected value. Then we will select the maximum value from each state of nature as regrets. From those regrets, we will select the facility with minimum value.

The highest value in the table is 250. Deduct all the values from 250.

	Low	Medium	High	Best payoff
Expand	150 (250-100)	50	0	150
Subcontract	200	130	125	200
Do nothing	210	200	195 (250-55)	210

Based on MINIMAX REGRET criteria, we would choose the “Expand” alternative.