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What do you think we should do? We’re down by 10 with 5 minutes left—plenty of time to get the ball back,”pondered Ken Kendall, head coach of West Highin talking to offensive coach Craig Russell. West was facing fourth down and short yardage for another first down from their opponent’s 9-yard line. “Should we try for the first down or go for the field goal?” Craig noted that statistically a run is better than a field goal attempt inside the 10-yard line. Ken wasn’t so sure, trying to weigh the risk of not getting the first down or a touchdown instead of an almost sure field goal.
Decision analysis is the formal study of how people make decisions, particularly when faced with uncertaininformation, as well as a collection of techniques to support the analysis of decision problems.
Applications:• Product selection• Facility capacity expansion and location• Inventory analysis• Technology and process selection
Applying Decision Analysis Tools• Decision analysis techniques apply when
decisions• Are important• Are probably unique• Allow some time for study • Are complex• Involve uncertainty and risk
Uncertainty refers to not knowing what will happen in the future. Risk is the uncertainty associated with an undesirable outcome, such as financial loss.
1. Maximax—choose the decision that will maximizethe maximum possible profit among all events. Thisis an aggressive, or risk-taking, approach.2. Maximin—choose the decision that will maximize the minimum possible profit among all events. This is a conservative, or risk-averse, approach.3. Minimax regret—choose the decision that will minimize the maximum opportunity loss associated with the events.
1. Minimin—choose the decision that will minimize the minimum possible cost among all events. 2. Minimax—choose the decision that will minimize the maximum possible cost among all events. 3. Minimax regret—choose the decision that will minimize the maximum opportunity loss associated with the events. When the output measure is cost is that the “best” payoff is the lowest cost, not the highest profit.
The expected value of perfect information, or EVPI, is the difference between the expected payoff under perfect information and the expected payoff of the optimal decision without perfect information.
A decision tree is a graphical schematic of the logical order with which decisions are made and events occur. Nodes refer to the intersections, or junction points, of the tree. Arcs are the connectors between the nodes. Arcs are sometimes called branches.
Trendy’s Pies Case Study 1. Use these cost, revenue, and probability
estimates along with the decision tree to identify the best decision strategy for Trendy’s Pies.
2. Suppose that Trendy is concerned about her probability estimates of the consumer response to the regional test market. Although her estimates are .7 for a high response and .3 for a low response, she is not very confident of these values. Determine how the decision strategy would change if the probability of a high response varies from .1 to .9 in increments of .1. How sensitive is the best strategy in Question 1 to this probability assumption?