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Decision Analysis

Decision Theory is a general approach to decision making when the outcomes associated with alternatives are often in doubts. It helps operational manager with decision on process capacity,location, and inventory because such decisions are about an uncertain future. Decision analysis can also be used by managers in other functional areas. There 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), or the maximax (minimin) when several decision options are available and there are several scenarios that might occur. Also, the expected value under certainty, the expected value of perfect information, and the regret (opportunity cost) can be computed.

The general framework for decision tables is given by the number of options (or alternatives) that are available to the decision maker and the number of scenarios (or states of nature) that might occur. In addition, the objective can be set to either maximize profits or to minimize costs.

 

The following example presents three decision options: (1) subcontract, (2) use overtime, or (3) use part-time help. The possible scenarios (states of nature) 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, the profit will be 180. The objective is to maximize profits.

 

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The general framework for decision tables is given by the number of options (or alternatives) that are available to the decision maker and the number of scenarios (or states of nature) that might occur. In addition, the objective can be set to either maximize profits or to minimize costs.

 

The following example presents three decision options: (1) subcontract, (2) use overtime, or (3) use part-time help. The possible scenarios (states of nature) 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, the profit will be 180. The objective is to maximize profits.

Decision Tree

A decision tree is a schematic model of alternatives available to the decision maker along with their possible consequences. The name derives from the tree-like appearance. The Decision tree analysis is widely used in strategic decision making. Let’s consider the following example. A retailer must decide whether to build a small or a large facility at a new location. Demand at the location can be either small or large with probabilities to be .4 and .6. If a small facility is built and demand proves to be high, the manager may choose not to expand or to expand. If a small facility is built and demand is low, there is no reason to expand and the payoff is $200,000. If a large facility is built and demand proves to be low, the choice is to do nothing or to stimulate demand through local advertising. The response to advertising may be either modest or sizable, with their probabilities estimated to be .3 and .7 respectively. Below diagram shows the decision variables and its estimated payoff of each event.

 

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The Solution: 

Based on the estimated probabilities and expected payoff, the retailer should build the large facility with expected payoff of $544 compare to small facility with expected payoff of $242. If demand is low, the retailer should advertise rather than do nothing as the expected payoff of advertising (payoff = 160) is higher than doing nothing. This analysis is very useful when management faced with multiple options and the likely probability of occurrence and consequences ( e.g profits/costs) associate with it.