. Greg Jones is running a manufacturing company that is experiencing a substanti
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Question
. Greg Jones is running a manufacturing company that is experiencing a substantial backlog. Greg is considering three alternatives. The correct choice will depend on the level of future demand. The various decision alternatives and the profits under different levels of future demand are as follows: DECISION ALTERNATIVES STATES OF NATURE (Levels of future demand) High demand Medium demand Low demand Arrange for subcontracting $100,000 $100,000 $20,000 Begin overtime production $200,000 $120,000 -$40,000 Construct new facilities $400,000 $40,000 -$300,000
a. Which decision alternative should Greg select using the MAXIMAX approach? What is the corresponding profit? b. Which decision alternative should Greg select using the MAXIMIN approach? What is the corresponding profit? c. Which decision alternative should Greg select using the Laplace (or equally likely) approach? What is the corresponding profit?
After consulting with the senior management at the company, Greg was able to estimate the probabilities for the three states of nature: P(high demand) = 0.40; P(medium demand) = 0.50; P(low demand) = 0.10. d. Construct a decision tree for this problem. e. If maximum expected monetary value (EMV) is used as the decision criterion, which decision alternative should Greg select? What is the corresponding expected profit? f. Compute the expected value of perfect information (EVPI) for Greg. g. If a sales forecasting firm claims to have the perfect information about the market demand and is offering its services for $71,500, would you advise Greg to accept the offer? Explain your reasoning
Explanation / Answer
Decision Table:
Profits under Different Demand Condition
High
Medium
Low
MAXIMAX
MAXIMIN
Laplace
Subcontracting
100000
100000
20000
100000
20000
74800
Overtime
200000
120000
-40000
200000
-40000
95200
New Facility
400000
40000
-300000
400000
-300000
47600
MAXIMAX approach (Optimistic Approach): Using this alternative decision maker chooses the course of action whose best possible payoff is better than the best gain of all other courses of action possible in given circumstances.
Decision: Go with New Facility
MAXIMIN approach (Pessimistic Approach): Using this alternative decision maker chooses the course of action whose best possible payoff is better than the worst gain of all other courses of action possible in given circumstances.
Decision: Go with Subcontracting
Laplace Approach (equally likely): Using this alternative decision maker chooses the course of action whose best possible payoff is better than the best gain of all other courses of action possible in given circumstances. Where all the course of the action has equal probability of occurring in given circumstances
Decision: Go with Overtime
Maximum Expected Monetary Value (EMV): Weightage average of the payoffs for a decision alternatives:
EMV = P1*Profit (High)+P2*Profit(Medium)+P3*Profit(Low)
Profits under Different Demand Condition
High
Medium
Low
EMV
Subcontracting
100000
100000
20000
92000
Overtime
200000
120000
-40000
136000
New Facility
400000
40000
-300000
150000
Probability
0.4
0.5
0.1
Expected Value of Perfect Information: It is the maximum amount you will be willing to pay for additional information about the state of nature before the decision is made:
Formula:
EVPI= EVwPI (Expected value with Perfect Information)-EVwoPI (Expected Value without Perfect Information)
EVwoPI= Maximum EMV
EVwPI= MAX(High)*P1+MAX(Medium)*P2+MAX(Low)*P3
Profits under Different Demand Condition
High
Medium
Low
EMV
EVwPI
EVPI
Subcontracting
100000
100000
20000
92000
222000
72000
Overtime
200000
120000
-40000
136000
New Facility
400000
40000
-300000
150000
Probability
0.4
0.5
0.1
EVPI= $72000
Yes Greg Should accept the deal as EVPI > 71500
Profits under Different Demand Condition
High
Medium
Low
MAXIMAX
MAXIMIN
Laplace
Subcontracting
100000
100000
20000
100000
20000
74800
Overtime
200000
120000
-40000
200000
-40000
95200
New Facility
400000
40000
-300000
400000
-300000
47600
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