Decision Analysis
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Decision AnalysisThere are two very basic models used for decision analysis - decision tables and decision trees.
The decision table can be used to find the expected value, the maximin(minimax) and/or the maximax(minimin) when several decision options are available and there are several scenarios that might occur. In addition the expected value under certainty, the expected value of perfect information and the regret or opportunity cost can be computed.
The general framework for decision tables is given by the number of options which are available to the decision maker and the number of scenarios which might occur. In addition, we must choose whether the objective is to maximize profits or to minimize costs.
Scenario Probabilities. For each scenario it is possible (but not required) to enter a probability. The expected value measures (expected monetary value, expected value under certainty, expected value of perfect information) require probabilities while the maximin(minimax) and maximax (minimin) do not.
Profits or costs. The profit(cost) for each combination of options and scenarios is to be given.
Hurwicz Alpha. Above the data is a scrollbar/textbox combination for entering the value for Hurwicz alpha. The Hurwicz value is used to give a weighted average of the best and worst outcomes for each strategy (row).
Example. The example below presents 3 decision options which are to subcontract, to use overtime or to use part time help. The possible scenarios are that demand will be low, normal or high or that there will be a strike or a work slowdown. The table contains profits as indicated. The first row in the table represents the probability that each of these states will occur. The remaining three rows represent the profit that we accrue if we make that decision and the state of nature occurs. For example, if we select to use overtime and there is high demand then our profit will be 180.
Solution
The results screen shown below contains both the data and the results for this 3 by 5 example. On the screen the data can be distinguished from the solution by color or boldness.
Expected values. The expected values for the options have been computed and appear in a column labeled "EMV" (expected monetary value) which has been appended to the right hand side of the data table.
Row minimum. For each row the minimum element has been found and listed. This element is used to find the maximin or minimin.
Row maximum. For each row the maximum element in the row has been found and listed. This number is used for determining the maximax or minimax.
Maximum expected value. Because this is a profit problem we are interested in finding the maximum values. The maximum expected value is the largest number in the expected value column which in this example is 124.5.
Maximin. The maximin is the largest (MAXImum) number in the MINimum column. In this example the maximin is 100.
Maximax. The maximax is the largest value in the table or the largest value in the maximum column. In this example it is 190.
Hurwicz. These represent 40% times the best outcome plus 60% times the worst outcome for each row. For example for subcontracting the Hurwicz is
.4 * 140 + .6 * 100 = 116.
Perfect values. An extra row labeled "Perfect Information" has been added at the bottom of each scenario. In this row, we have listed the best outcome for that scenario.
Perfect*probability (Expected value under certainty). The expected value under certainty is computed as the sum of the products of the probabilities multiplied by the best outcomes. In the example this is:
EV(Certainty)= .2*120 + .3*150 + .25*190 + .15*120 + .1*130 = 147.50
Expected Value of Perfect Information. The expected value of perfect information (EVPI) is the difference between the best expected value (124.5) and the expected value under certainty (147.5) which in this example is 23.
Table Values. The values in the table are for each column computed as the cell value subtracted from the best value in the column in the data. For example, under low demand the best outcome is 120. If we subcontract and get 100 then our regret is 20.
| 1. Introduction | 2. Example | 3. Main Menu | 4. Printing | 5. Graphs | 6. Modules |
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