A decision is the act of deciding what single act among all alternatives is to be taken into account. Successful decision making comprises a number of steps to process:
1. Clearly define the problem.
2. Identify the possible alternatives and their outcomes.
3. List the profit for each combination of alternatives and outcomes.
4. Select one mathematica; decision theory model.
5. Apply the model and make your decision.
The success or failure that persons, companies, and management experience depends on the decision they make. Making use of quantities in decision-making helps a great deal in minimizing mistakes and failures. Some methods of computation should therefore be learned.
Decision theory is a general approach to decision making that is useful in many different aspects of operations management. It provides a framework for analysis of decision. It includes a number of different techniques that can classify according to the degree of uncertainty.
Decision under Certainty - when one knows with certainty which of the possible future conditions will actually happen, he simply chooses the alternative with the highest payoff under the state of nature.
Decision under Uncertainty - from certainty, the opposite extreme is uncertainty where there is no available information on how likely the various states of nature are. Under this condition, there are four possible decision criterions, namely :
a) Maximin - takes into account only the worst possible outcome for each alternative. This approach establishes a guaratee minimum.
b) Maximax - takes into account only the best possible outcome for each alternative.
c) Laplace - takes into account only the best average possible outcome for each alternative.
d) Minimax Regret - determines the worst regret for ach alternative, and chooses the alternative with the best worst.
DECISION TREES
Another useful technique for analyzing a decision situation is a decion tree. A decision tree, like the probability tree is a graphical diagram consisting of nodes and branches. However, rather than determining the probability of each branch as in a probability tree, in a decision tree the user computes the expected value of each outcome and makes a decision based on these expected values. The primary benefit of a decision tree is that it provides an illustration (or picture) of the decision-making process. This makes it easier to correctly compute the necessary expected values and to understand the process of making the decision.
The decision tree has two types of nodes: a square represents a decision point and a circle stands for a chance event. The tree is read left to right, and analyzed from right to left (starting with the last decision that might be made). For each decision, choose the alternative that will yield the greatest return. If chance events follow a decision, choose the alternative that has the highest expected value or the lowest expected loss.
1. T. Bone Puckett, a corporate raider, has acquired a textile company and is contemplating the future of one of its major plants located in South Carolina. Three alternative decisions are being considered: (1) expand the plant and produce lightweight, durable materials for possible sales to the military, a market with little foreigh competition; (2) maintain the status quo at the plant, continuing production of textile goods that are subject to heavy foreign competition; or (3) sell the plant now. If one of the first two alternatives is chosen, the plant will still be sold at the end of a year. The amount of profit that could be earned by selling the plant in a year depends on foreign market conditions, including the status of a trade embargo bill in Congress. The following payoff table describes this decision situation.
Decision States of Nature
Good Foreign Competitive Conditions Poor Foreign Competitive Condition
Expand 800,000 500,000
Maintain status quo 1,300, 000 -150, 000
Sell now 320,000 320, 000
a. Determine the best decision using the following decision criteria.
1. Maximax
2. Maximin
3. Minimaz regret
4. Hurwicz (alpha =0.3)
5. Equal likelihood
b. Assume that it is now possible to estimate a probability of 0.70 that good foreign competitive conditions will exist and a probability of 0.30 that poor conditions will exist. Determine the dest decision using the expected value and expected opportunity loss.
c. Compute the expected value of perfect information.
d. Develop a decision tree for this decision situation, with expected values at the probability nodes.
2. A farmer in Iowa is considering either leasing some extra land or investing in savings certificates at the local bank. If weather conditions are good next year, the extra land will allow the farmer to have an excellent harvest. However, if weather conditions are bad, the farmer will lose money. The savings certificates will result in the same return regardless of the weather conditions. The return for each investment given each type of weather condition is hown in the following payoff table.
Decision Weather
Good Bad
Lease land 90,000 -40,000
Buy savings certificate 10,000 10,000
Hurwicz (alpha = 0.4)
3. The owner of the Burger Doodle Restaurant is considering two ways to expand operations: operning a drive-up windom or serving breakfast. The increase in profits resulting from these proposed expansions depends on whether a competitor opens a franchise down the street. The possible profits from each expansion in operations given in both future competitive situations are shown in the following payoff table.
Decision Competitor
Open Not Open
Drive-up window -6,000 20,000
Breakfast 4,000 8,000
Hurwicz (alpha = 0.10)
4. Stevie Stone, a bellhop at the Royal Sundown Hotel in Atlanta, has been offered a management position. Although accepting the offer would assure him a job if there were a recession, if good economic conditionsprevailed he would actually make less money as a manager than as a bellhop (because of the large tips he gets as a bellhop). His salary during the next five years for each job given each economic condition is shown in the following payoff table.
Decision Economic Conditions
Good Recession
Bellhop 120,000 60,000
Manager 85,000 85,000
Hurwicz (alpha = 0.4)
5. Consider the following payoff table for three alternative investments, A, B, and C, under two future states of the economy, good and bad.
Investment Economic Conditions
Good Bad
A 70,000 25,000
B 120,000 -60,000
C 40,000 40,000
Hurwicz (0.3)
6. A farmer in Georgia must decide which crop to plant next year on his land: corn, peanuts, or soybeans. The return from each crop will be determined by whether a new trade bill with the USSR passes the Senate. The profit the farmer will realize from each crop given the two possible results on the trade bill is shown in the following payoff table.
Crop Trade Bill
Pass Fail
Corn 35,000 8,000
Peanuts 18,000 12,000
Soybeans 22,000 20,000
Hurwicz (0.3)
7. The owner of the Columbia Construction Company must decide among building a housing development, constructing a shopping center, or leasing all the company's equipment to another company. The profit that will result from each alternative will be determined by whether material costs remain stable or increase. The profit from each alternative given the two possibilities for material costs is shown in the following payoff table.
Decision Material Costs
Stable Increase
Houses 70,000 30,000
Shopping center 105,000 20,000
Leasing 40,000 40,000
Hurwicz (0.2)
8. An investor is considering investing in stocks, real estate, or bonds under uncertain economic conditions. The payoff table of returns for the investor's decision situation is shown below.
Investment Economic Conditions
Good Stable Poor
Stocks 5,000 7,000 3,000
Real estate -2,000 10,000 6,000
Bonds 4,000 4,000 4,000
Hurwicz (0.3)
9. A concessions manager at the Tech vs A and M football game must decide whether to have the vendors sell sun visors or umbrellas. There is a 30% chance if rain, a 15% chance of overcast skies, and a 55% chance of sunshine, according to the weather forecast in College Junction, where the game is to be held. The manager estimates the following profits will result from each decision given each set of weather conditions.
Decision Weather Conditions
Rain Overcast Sunshine
0.30 0.15 0.55
Sun visors -500 -200 1,500
Umbrellas 2000 0 -900
10. The Blitzkrieg Banking House in Berlin speculates in the money market. The status of the U.S dollar determines the return from investments in other currencies. The banking house will invest in the dollar, the yen, or other currencies. The banking house will invest in the dollar, the yen, or the mark. The return from each is shown in the following payoff table.
Currency Value of the Dollar
Increases (0.3) Remains stable(0.50) Declines(0.20)
Dollar 210,000 0 -170,000
Yen -10,000 20,000 80,000
Mark -40,000 35,000 150,000
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