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# Assuming Roper would not charge for his review services, determine the optimal strategy based on the expected value criterion, and state its expected value

1. Film scenario. A Hollywood film producer named John Mogul is evaluating a script for a potential film.  Mogul estimates that the probability of a film based on that script being a hit is .10 and probability of it being a flop is .90.  The studio accounting department estimates that if a hit, the film will make \$25 million in profit, but if a flop, will lose \$8 million.  Before deciding whether or not to produce a film based on that script, Mogul needs to decide whether or not to hire film critic Dick Roper to evaluate the script.  Over many reviews of scripts in the past, Roper film would be a hit (of the scripts) for 70% of the films (based on the scripts) that turned out to be hits, and had predicted film was a flop (of the scripts) for 80% of the films (based on the scripts) that turned out to be flops. [adapted from Taylor (2004)]
• Assuming Roper would not charge for his review services, determine the optimal strategy based on the expected value criterion, and state its expected value (Draw and solve the Decision Tree below).

At a decision node, the branch that has the highest ending node value represents the optimal decision

Beginning with the rightward decision nodes, we can determine the expected value by using the probability.

Branch 1: Hiring Dick Ropper

Node 4 = (0.8)(25) + (0.2)(-8) = \$18.4 M

Node 2 = (0.7)(25) – (0.3)(18.4) = \$11.98

\$18.4M – \$11.98M = \$6.42M.

Branch 2: Not Hiring Dick Ropper

Node 7 = Difference between Decision node 8 and decision node 9

Node 8 = (0.1)(25) = \$2.5M

Node 9 = (0.9)(-8) = -\$7.2M

Value of the branch = \$2.5 – \$7.2 = \$-4.7M

According to the above value, hiring Dick Ropper has the higher ending value, therefore is the optimal decision.

The expected value of the optimal decision using probability is \$6.42M.

• Determine EVSI (with Roper regarded as the sample information).

EVSI = ERSI – EREV

EVSI = \$6.42M – \$4.7M = \$1.72M

• If Roper were to charge \$100,000 for his review, what would be the optimal strategy and its expected value?

Branch 1: Hiring Dick Ropper

Node 4 = (0.8)(24.9) + (0.2)(-8) = \$18.32 M

Node 2 = (0.7)*(24.9) – Node 4

\$17.43M – \$18.32M = -\$0.89M.

Branch 2: Not Hiring Dick Ropper

Node 7 = Difference between Decision node 8 and decision node 9

Node 8 = (0.1)(25) = \$2.5M

Node 9 = (0.9)(-8) = -\$7.2M

Value of the branch = \$2.5 – \$7.2 = \$-4.7M

The optimal decision would be hiring Dick Ropper,

The decision expected value is -\$0.89M.

Machine shop scenario.  A machine shop owner wants to decide whether to purchase a new drill press, new lathe, or new grinder.  As shown in the following table, the profit from each purchase will vary depending on whether or not the owner wins a government contract, with the owner estimating a probability of .60 of winning the contract:

Before deciding which item to purchase, the owner needs to decide whether or not to hire a military consultant to assess whether the shop will get the government contract.  The track record of the military consultant in predicting whether companies would win government contracts is as follows:  For 90% of the companies that won contracts, the consultant had predicted they would win, and for 70% of the companies that lost contracts, the consultant had predicted they would lose. [adapted from Taylor (2004)]

• Assuming the consultant would not charge for his assessment, determine the optimal strategy based on the expected value criterion, and state its expected value. (Draw then solve the Decision Tree below)

The branch that has the highest ending node value represents the optimal decision

Beginning with the rightward decision nodes, we can determine the expected value by using the probability.

Branch 1: Hiring Consultant

Decision code 3

0.9(40000+20000+12000) – 0.1(-8000+4000+10000).

=\$64800 – \$600 = \$64200.

Decision code 6

0.7(-8000+4000+10000) – 0.3(40000+20000+12000).

= -\$17400.

Decision code 2 on hiring a consultant = \$64200 – \$17400 = \$46800.

Branch 2: Not hiring a consultant

Branch code 9

0.6(40000+20000+12000) – 0.4(-8000+4000+10000)

= \$40800.

Hiring a consultant is the optimal strategy and the expected value is \$46800

• Determine EVSI (with the consultant regarded as the sample information).

EVSI = ERSI – EREV

EVSI = \$46800 – \$40800

= \$6000.

• If the consultant were to charge \$5,000 for his assessment, what would be the optimal strategy and its expected value?

Branch 1: Hiring Consultant

Decision code 3

0.9(35000+15000+7000) – 0.1(-13000-1000+5000).

= \$50400.

Decision code 6

0.7(-13000+-1000+5000) – 0.3(35000+15000+7000).

= -\$23400.

Decision code 2 on hiring a consultant = \$50400 – \$23400 = \$27000.

Branch 2: Not hiring a consultant

Branch code 9

0.6(40000+20000+12000) – 0.4(-8000+4000+10000)

= \$40800.

Not Hiring a consultant is the optimal strategy and the expected value is \$40800

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