Charles River Jazz Festival

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Decision tree for Friday pressing Mr. Ward is trying to decide on how many CDs to press on the first night of the festival. His intuition combined with his experience allowed him to make some predictions of demand. These take the form of probabilities. “The probabilities may be subjective estimates from managers or from experts in a particular field, or they may reflect historical frequencies. If they are reasonably correct, they provide a decision maker with additional information that can dramatically improve the decision-making process. Since the problem is limited to Ward’s expected demands for CDs, we can say that our recognizable states of nature are the following:

  • Saturday Demand = 1000 and Sunday Demand = 1000
  • Saturday Demand = 1000 and Sunday Demand = 3000
  • Saturday Demand = 3000 and Sunday Demand = 1000
  • Saturday Demand = 3000 and Sunday Demand = 3000

The minimum total demand for both Saturday and Sunday would be 2000 CDs, whereas the maximum total demand for both Saturday and Sunday would be 6000 CDs.

The intermediate total demand however is consistent at 4000 CDs. We can consolidate them to 3 states of nature:

  • Saturday Demand + Sunday Demand = 2000
  • Saturday Demand + Sunday Demand = 4000
  • Saturday Demand + Sunday Demand = 6000

Let’s call these states of nature d2, d4 and d6. We use the TreePlan software to create the decision tree for Ward’s problem. We specified the initial costs of productions as $24,000, $33,000 and $42,000.

Additionally, we make sure to deduct the royalties from the sales revenue, since they are considered as future expenses (after the sales occur). Please see below for the decision tree.

Maximization of Expected Monetary Value as a criterion

The average or expected payoff of each alternative is a weighted average: the state of nature probabilities are used to weight the respective payoffs. ? Therefore the expected monetary value for each alternative is as follows: EMVp2 = $ 6,000

EMVp4 = $ 12,000 EMVp6 = $ 10,500 According to the maximization of Expected Monetary Value criterion, we can say that the director of the festival should press 4000 CDs on Friday night, since the Expected Monetary Value of that decision is optimal at $12,000.

Paying for perfect information

If Ward could obtain information about the demand for CDs prior to committing to the CD production, there will be an upper bound on the sum of money it would be reasonable to spend.

The most Ward should pay for perfect information about the two-day demand for CDs can be calculated using the Expected Value of Perfect Information: EVPI = EPC – EMV, where EPC is the expected payoff under certainty, and EMV is expected monetary value with alternative p4. We calculate EPC as: EPC = 0. 5 * 6000 + 0. 25 * 27000 + 0. 25 * 48000 = $ 21,750 EMV = $ 12,000 Total value of perfect information: EVPI = $ 9750 It would be reasonable to pay $9,750 dollars to obtain perfect information. It is thus not worthwhile to spend more than that amount of money to obtain ‘perfect’ information.

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