Decision Models -- Prof. Juran16 Each of the branches at the far right of the diagram is characterized by two elements: a probability and a payoff value. For example, the Sell 100 branch has a probability of 0.05 and a payoff (in the case of having purchased 100 units of shoes) of $2,500 (see cell B8 in the payoff table). These entries are tedious, so we want to use copy-and- paste as much as possible. The payoffs will vary across the different purchase quantities, but the probabilities will not.
Decision Models -- Prof. Juran21 PrecisionTree uses True and False to indicate which branch of a decision node is optimal. Here, the best policy is to order 400 units and have an expected profit of $7,550.
Decision Models -- Prof. Juran22 Example 2: TV Production Witkowski TV Productions is considering a pilot for a comedy series for a major television network. The network may reject the pilot and the series, or it may purchase the program for one or two years. Witkowski may decide to produce the pilot or transfer the rights for the series to a competitor for $100,000.
Decision Models -- Prof. Juran23 Witkowskis profits are summarized in the following profit ($1000s) payoff table: If the probability estimates for the states of nature are P (Reject) = 0.20, P (1 Year) = 0.30, and P (2 Years) = 0.50, what should Witkowski do?
Decision Models -- Prof. Juran25 Value of Perfect Information
Decision Models -- Prof. Juran26 Perfect information (if it were available) would be worth up to 125 - 100 = 25 thousand dollars to Witkowski. This is referred to as expected value of perfect information.
Decision Models -- Prof. Juran27 For a consulting fee of $2,500, the ODonnell agency will review the plans for the comedy series and indicate the overall chance of a favorable network reaction.
Decision Models -- Prof. Juran32 What should Witkowskis strategy be? What is the expected value of this strategy? The best thing to do is to forget about ODonnell and sell the rights for $100,000.
Decision Models -- Prof. Juran33 What is the expected value of the ODonnell agencys sample information? Is the information worth the $2,500 fee? What is the efficiency of ODonnells sample information?
Decision Models -- Prof. Juran36 Decision Alternative Expected Value Produce Pilot 99.65 Optimal Favorable ODonnell Report Sell to Competitor 97.50 Produce Pilot -4.20 Unfavorable ODonnell Report Sell to Competitor 97.50 Optimal The overall expected value with sample information ( EVwSI ) is: 2211 IPIEVIPI 98. 31.0*5.9769.0*65.99 (Note that we are assuming here that we will always adopt the optimal strategy in light of whatever information ODonnell provides.)
Decision Models -- Prof. Juran38 Expected Value of Sample Information
Decision Models -- Prof. Juran39 What is the expected value of the ODonnell agencys sample information? Is the information worth the $2,500 fee? If we pay ODonnell the $2,500 fee, our overall expected value drops by $1,020. This implies that the ODonnell report is worth We would be willing to pay up to (but no more than) $1,480 for the ODonnell report. (This is one way to address the question, How much should Witkowski be prepared to pay for the research study?)
Decision Models -- Prof. Juran40 Efficiency of Sample Information The efficiency of sample information is calculated using this formula: In other words, the market research project gives us information with less than 6% of the utility of having perfect information.
Decision Models -- Prof. Juran41 Conclusions Dont buy the ODonnell report Sell the script to the competitor Earn $100,000
Decision Models -- Prof. Juran42 Summary Decision Analysis Uncertain Future Events Perfect Information Partial Information –The Return of Rev. Thomas Bayes