Introduction to the Quantitative Analysis Approach for Linear Programming
Reviewer for MANSCIE
1. Introduction to Quantitative Analysis Approach
Quantitative Analysis involves the use of mathematical equations or relationships in analyzing a particular problem.
Steps in Quantitative Analysis Approach
1. Define the problem
2. Develop a model
3. Acquire input data
4. Develop a solution
5. Test the solution
6. Analyze the results
7. Implement the results
2. Decision Theory
Six steps in decision making
1. Define the problem
2. List possible alternatives
3. Identify possible outcome or state of nature
4. List the payoff or profit of each combination of alternatives and outcomes
5. Select one of the decision theory model
6. Apply the model and make decision
a. Decision-Making under certainty
In Decision-Making under certainty, decision makers know with certainty the consequences of every alternatives and decision choice. Ex. Bank saving account, time deposit, government treasury bills
b. Decision-Making under risk
In Decision-Making under risk, there are several possible outcomes for each alternatives, and the decision maker knows the probability of occurrence of each outcome.
1. Expected Monetary Value (EMV)
EMV is the weighted sum of possible payoffs for each alternatives.
EMV=(payoff of first state of nature)(probability of first state of nature)+(payoff of second state of nature)(probability of second state of nature)+...+(payoff of last state of nature)(probability of last state of nature)
1
Example: A basketball team is considering the following players with the following payoff to the team for each player from profits. The team believes there is 40% chance it will make the final four, 30% chance it will be competitive and 30% chance it will loss. What decision will the team make based on maximum expected value?
State of nature alternatives Loser
Competitive
Makes final four
EMV
Byrd
-3.2
1.3
4.4
1.19
Johnson
-2.7
0.7
5.8
1.72
Gordan
-6.3
-1.6
9.6
1.47 probability 30%
30%
40%
EMV=(-3.2)(30%)+(1.3)(30%)+(4.4)(40%)=1.19
1. Introduction to Quantitative Analysis Approach
Quantitative Analysis involves the use of mathematical equations or relationships in analyzing a particular problem.
Steps in Quantitative Analysis Approach
1. Define the problem
2. Develop a model
3. Acquire input data
4. Develop a solution
5. Test the solution
6. Analyze the results
7. Implement the results
2. Decision Theory
Six steps in decision making
1. Define the problem
2. List possible alternatives
3. Identify possible outcome or state of nature
4. List the payoff or profit of each combination of alternatives and outcomes
5. Select one of the decision theory model
6. Apply the model and make decision
a. Decision-Making under certainty
In Decision-Making under certainty, decision makers know with certainty the consequences of every alternatives and decision choice. Ex. Bank saving account, time deposit, government treasury bills
b. Decision-Making under risk
In Decision-Making under risk, there are several possible outcomes for each alternatives, and the decision maker knows the probability of occurrence of each outcome.
1. Expected Monetary Value (EMV)
EMV is the weighted sum of possible payoffs for each alternatives.
EMV=(payoff of first state of nature)(probability of first state of nature)+(payoff of second state of nature)(probability of second state of nature)+...+(payoff of last state of nature)(probability of last state of nature)
1
Example: A basketball team is considering the following players with the following payoff to the team for each player from profits. The team believes there is 40% chance it will make the final four, 30% chance it will be competitive and 30% chance it will loss. What decision will the team make based on maximum expected value?
State of nature alternatives Loser
Competitive
Makes final four
EMV
Byrd
-3.2
1.3
4.4
1.19
Johnson
-2.7
0.7
5.8
1.72
Gordan
-6.3
-1.6
9.6
1.47 probability 30%
30%
40%
EMV=(-3.2)(30%)+(1.3)(30%)+(4.4)(40%)=1.19