Decision Tree Decision making under uncertainty Operation Research December 29, 2014 RS and GISc, IST, Karachi

Decision Tree When a series of decisions at different points in time are made A decision tree enables a decision maker to decompose a large complex decision problem into several smaller problems

In the absence of a market study, Colaco believes that Chocola has a 55% chance of being a national success and a 45% chance of being a national failure. If Chocola is a national success, Colaco’s asset position will increase by $300,000, and if Chocola is a national failure, Colaco’s asset position will decrease by $100,000 If Colaco performs a market study (at a cost of $30,000), there is a 60% chance that the study will yield favorable results (referred to as a local success) and a 40% chance that the study will yield unfavorable results (referred to as a local failure). If a local success is observed, there is an 85% chance that Chocola will be a national success. If a local failure is observed, there is only a 10% chance that Chocola will be a national success. If Colaco is risk-neutral (wants to maximize its expected final asset position), what strategy should the company follow?

Decision Tree: Decision Fork The decision tree is constructed with two kinds of forks: decision forks (denoted by ) and event forks (denoted by ). A decision fork represents a point in time when Colaco has to make a decision. Each branch emanating from a decision fork represents a possible decision

Decision Tree: Event Fork An event fork is drawn when outside forces determine which of several random events will occur Each branch of an event fork represents a possible outcome, and the number on each branch represents the probability that the event will occur

Decision Tree: Terminal Branch A branch of a decision tree is a terminal branch if no forks emanate from the branch