Question

Mick Karra is the manager of MCZ Drilling Products, which produces a variety of specialty valves for oil field equipment. Recent activity in the oil fields has caused demand to increase drastically, and a decision has been made to open a new manufacturing facility. Three locations are being considered, and the size of the facility would not be the same in each location. Thus, overtime might be necessary at times. The following table gives the total monthly profit (in $1,000s) for each possible location under each demand possibility. The probabilities for the demand levels have been determined to be 20% for low demand, 30% for medium demand, and 50% for high demand.

PAYOFFS	Outcomes
Alternatives	Demand is Low	Demand is Medium	Demand is High
Ardmore, OK	$85	$110	$150
Sweetwater, TX	$90	$100	$120
Lake Charles, LA	$110	$120	$130

1. Which location would be selected based on the optimistic criterion?
2. Which location would be selected based on the pessimistic criterion?
3. Which location would be selected based on the equally likely criterion?
4. Which location would be selected based on the realism criterion? (α=0.6)
5. Which location would be selected based on Expected Monetary Value (EMV)?
6. Which location would be selected based on the minimax regret criterion?
7. What is the expected value with perfect information in this situation (EVwPI)?
8. What is the expected value of perfect information in this situation (EVPI)?

Answer 1

Given data:

PAYOFFS (in $1000)
	Outcomes
Alternatives	Demand is Low	Demand is Medium	Demand is High
Ardmore, OK	85	90	110
Sweetwater, TX	110	100	120
Lake Charles, LA	150	120	130

1. Which location would be selected based on the optimistic criterion?

Optimistic criterion is the selection of the maximum of the maximum of all the courses of action. Also called as maximax criterion. The selection is done as shown in the table below:

PAYOFFS (in $1000)
	Outcomes
Alternatives	Demand is Low	Demand is Medium	Demand is High	Maximum of the options available	Maximum of the max course of action
Ardmore, OK	85	90	110	110	150
Sweetwater, TX	110	100	120	120
Lake Charles, LA	150	120	130	150

Hence under the optimistic criterion the location Lake Charles, LA is chosen with payoff values of $1,500,000

2. Which location would be selected based on the pessimistic criterion?

Under the pessimistic criterion, the decision maker chooses the action whose maximum loss is better than the least loss of all the other courses of action possible. Also referred to as the minimax criterion. In our case, we refer maximum loss as least profit and least loss as maximum profit. Hence the table follows as shown below:

PAYOFFS (in $1000)
	Outcomes
Alternatives	Demand is Low	Demand is Medium	Demand is High	Least of the possible courses of action available	Maximum of the max course of action
Ardmore, OK	85	90	110	85	120
Sweetwater, TX	110	100	120	100
Lake Charles, LA	150	120	130	120

Hence under the pessimistic criterion the location Lake Charles, LA is chosen with payoff values of $1,200,000

3. Which location would be selected based on the equally likely criterion?

Under this criterion, the decision maker maximizes the average payoff. The average payoff is calculated as shown below for Ardmore, OK location = = 95

Payoff(Lou) + Payoff(Med) + Payoff(High)

Similarly for other location ss as follows:

PAYOFFS (in $1000)
Probabilities associated	0.2	0.3	0.5
	Outcomes
Alternatives	Demand is Low	Demand is Medium	Demand is High	Average	Best of averages
Ardmore, OK	85	90	110	95	133
Sweetwater, TX	110	100	120	110
Lake Charles, LA	150	120	130	133

Hence under the equally likely criterion the location Lake Charles, LA is chosen with payoff values of $1,330,000

4. Which location would be selected based on the realism criterion? (α=0.6)

Under this criterion, the decision maker finds a compromise between the best and worst payoffs by choosing the best-weighted average based on the value of alpha called as the coefficient of realism.

= 0.60 is for best payoff and 1- = 0.40 is for the worst payoff.

Hence weighted average for example of Artmore, OT is * best payoff Ardmore + (1-) * worst payoff for Ardmore = 0.60 * 110 + 0.40 * 85 = 100 (in $1000)

Similarly, for other location, the table follows:

PAYOFFS (in $1000)
Probabilities associated	0.2	0.3	0.5
	Outcomes
Alternatives	Demand is Low	Demand is Medium	Demand is High	Weighted average	Best of averages
Ardmore, OK	85	90	110	100	138
Sweetwater, TX	110	100	120	112
Lake Charles, LA	150	120	130	138

Hence under the realistic criterion the location Lake Charles, LA is chosen with payoff values of $1,380,000

5. Which location would be selected based on Expected Monetary Value (EMV)?

Under this category, the highest value of EMV for each location is selected. EVM is calculated as below:

For example the EVM payoff for Ardmore, OK = Pr(Low) * Payoff for low demand at Ardmore +  Pr(Med) * Payoff for Med demand at Ardmore + Pr(High) * Payoff for High demand at Ardmore = 0.20 * 85 + 0.30 * 110 + 0.50 * 150 = $99 (in$1000).

Hence for other locations is as follows:

PAYOFFS (in $1000)
Probabilities associated	0.2	0.3	0.5
	Outcomes
Alternatives	Demand is Low	Demand is Medium	Demand is High	Expected Monetary value	Best of averages
Ardmore, OK	85	90	110	99	131
Sweetwater, TX	110	100	120	112
Lake Charles, LA	150	120	130	131

Hence under the EVM criterion the location Lake Charles, LA is chosen with payoff values of $1,310,000