A decision tree is a graphical display of the decision process that indicates decision alternatives and their respective payoffs.
A company which manufactures car audio system is investigating the possibility of building a new plant. It has the options of either constructing a large of a small plant. The market for the product produced – car audio system – can be either favorable or unfavorable.
With a favorable market, a large facility will give the company a net profit of $200,000. If the market is unfavorable, a $180,000 net loss will occur. A small plant will result in a net profit of $100,000 in a favorable market, or a net loss of $20,000 in an unfavorable market. The company can, of course, choose not to do anything.
The probability of a favorable market is 0.60. The probability of an unfavorable market is 0.40.(Click to enlarge.)
We will compute the Expected Monetary Value (EMV) for each alternative. The EMV for an alternative is given by the formula below:
EMV = (payoff of favorable market) x (probability of favorable market)
+ (payoff of unfavorable market) x (probability of unfavorable market)
A completed and solved decision tree is presented below:
(Click to enlarge.)
Based on the decision tree, a small plant should be built because it yields the highest EMV.
Jay Heizer & Barry Render, “Operations Management”, 8th edition