The organizers of a music festival may use video from the Friday concert to create a DVD to sell to those who come to the Saturday concert. Attendance on Saturday is uncertain, as is the percentage of those who attend on Saturday who will buy the DVD. Is this a good project? If so, what number of DVDs should be burned early Saturday morning and offered for sale at that evening's performance? By that time, Friday attendance is known, as well as whether it rained on Friday, and there is a forecast for whether it will rain on Saturday. Historical information on these variables may help us predict Saturday attendance using multiple regression; together with the results of a marketing survey, such analysis will help us make better purchasing decisions. This case series (see also the A case, UVA-QA-0707) can be used to illuminate a multitude of concepts that are covered in basic decision-analysis courses. The series starts by examining the role of uncertainty in decision making, proceeds through the estimation of probability distributions from sample data with multiple regression, culminates in the development of a full decision model, and ends with a qualitative and quantitative analysis (with a tornado diagram) of how to add value and reduce risk. Key pitfalls for students are failing to recognize both limits on sales (supply and demand), incomplete reasoning in the determination of the attendance probability distribution, and oversimplifying the full forecast model (i.e., averaging the Saturday rain/no Saturday rain outcomes, rather than incorporating the uncertainty explicitly into the simulation).
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