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Arizona State University, Tempe *
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SCM517
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Mathematics
Date
Feb 20, 2024
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docx
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Uploaded by HighnessWallabyMaster375
Problem Set #1
TEM494/598: Data Driven Decision Making
Format: word, pdf
You are permitted to use Excel or other computing programs.
You are allowed to do the assignment handwritten (as long as I can read it; if it’s illegible, it will be marked incorrect), but you must convert it over to pdf.
1.
10 pts. This is a question about process. You have decided to become a professional opera singer. Make a roadmap with at least 5 major milestones to measure progress (1 milestone can be where you start; one where you end up). At each milestone, say what it is, why it is a milestone, and in each transition arrow, say what processes you are going through.
2.
10 pts. Quick shots. These are questions based on this week’s readings.
Why is Christian and Griffiths Algorithms to Live By useful for decision making? 1 pts
What is: 8 pts
the 37 percent rule
Look then Leap
Full Information
Threshold Rule
Explore/Exploit
Win-Stay, Lose Shift
Regret Minimization
Gittins Index
Do you use any of the terms presented here apply to your life?
i.
3.
15pts. The following is a probability distribution of a weighted die.
10
9
8
Weight
7
6
5
4
3
2
1
1
2
3
4
5
6
Die Number
a.
(5 pts) What is the probability of rolling a 1, 2, 3, 4, or 5?
b.
(5 pts) What is the standard deviation of this distribution?
c.
(5 pts) Rolling 2 of these die at the same time, you are trying to roll a total of 2 or 3. What has better odds: getting a heads on flipping a coin or rolling a 2 or 3 with two of these die?
4.
Game Show (15 pts)
You are on the Game Show, Who wants to be a Millionaire.
You are up to the $250,000 level question. You are stuck. Your options are:
Skip the question and take $100,000 and go home.
Guess what the correct answer is. You have it down to two answers, but have no idea which answer is right. If you are wrong, you walk away with $32,000.
Use a lifeline. Call a friend for help before answering. Your friend has an 80% chance of being right; however, there is only a 70% chance you will agree with them. If you disagree with them (30% of the time), then you will pick the opposite answer.
a)
Draw a decision tree for each case. Show the final expectation. (5 pts)
b)
What would you do? Explain your reasoning. Is your answer rational, bounded rational or motivational? (10 pts)
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5.
Drug choice (15 pts)
The probability of a drug of moving from one step to the next step is shown below:
P
Phase I to Phase II
63.2%
Phase II to Phase III
30.7%
Phase III to NDA
58.1%
NDA/BLA to market
85.2%
a.
What is the probability that a drug will pass from Phase I to market? (4 pts)
b.
There are 3 companies with the following drug portfolios:
Number of Drugs
Worth/ drug ($k)
Number of Drugs
Worth/ drug ($k)
Number of Drugs
Worth/ drug ($k)
Phase I
3
700,000
0
0
Phase II
0
0
7
700,000
3
300,000
Phase III
1
500,000
0
2
600,000
NDA
1
500,000
0
1
200,000
Gougeorian
Moneyprinter
RUonDrugs
The drugs are at different phases (some companies have multiple drugs at one step). This is also
called the pipeline. Calculate the expected return for each company if all the drugs in their pipeline pay off. (8pts)
c.
You have $100,000 to invest. i. Which company would you invest in? ii. What criteria did you use? iii. How did you treat the risk? (8 pts)
6.
15 pts The game Yahtzee is one of the classic table games. Accidently invented in 1954 by a Canadian couple, Yahtzee sells over 50 million games per year.
The objective of the game is to score points by rolling five
dice
to make certain combinations. The winner is the person with the most points.
The dice are rolled 3 times; after each roll, the player has a choice of which die he wants to keep and which he wants to roll again. After the three rolls are completed, the player chooses a scoring category. The scoring categories have varying point values, some of which are fixed values and others for which the score depends on the value of the dice. Points are awarded based on whether the die match the chose scoring category. Yahtzee is the highest scoring roll with five-of-a-kind. The winner is the player who scores the most points.
More details on how the game is played can be found here:
https://en.wikipedia.org/wiki/Yahtzee
https://www.ultraboardgames.com/yahtzee/game-rules.php
a.
5 pts On the first roll of the game, you have thrown the following combination:
Which combination should you go for? Which die should you keep for the second roll? Why?
b.
5 pts On the first roll of the game, you have thrown the following combination:
Which combination should you go for? Which die should you keep for the second roll? Why?
c.
In the figure below, Dr Cho has the following scorecard; his opponent’s score (Bigfoot) is to the column to the right. His roll, which is the first roll of your turn, is shown at the bottom. 5 pts
Which combination should you go for? Which die should you keep for the next roll? Why?
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7.
20 pts. Pyles Snow has a problem. He is in the bidding for the CEO position of the biomedical firm Costello Technology. His division received an injunction from the FDA to halt production on
its serum. There is an issue of whether hepatitis is a contaminant in the system.
Snow has consulted his manufacturing people and to meet the FDA’s requirements would cost the division about $100MM. Snow is in competition for the CEO position with a rival from another division. If this problem occurs during the CEO process, it has a 90% chance of killing his bid to become the next CEO.
Snow is confident that its process kills the virus and this is mostly a documentation issue. If he is wrong, this could be several hundred million dollars. The product brings in about $100MM in
profit every year. Snow doesn’t know what he should do. So he starts mapping out his options.
He could do nothing and hope there will be no penalties. The maximum penalty that the FDA ever handed down was $50MM, but there is a 50% chance the penalty could reach as high as $100MM and they would still have to spend the $100MM to clean the facility up, which could take up to a year. There’s a 80% chance the product would get pulled off the market for 1 years and a 20% chance for 2 years. In this case, there’s a 70% chance FDA would rule in 10 months, 20% in 1 year and 10% in 2 years.
He could try and do a little (spend about $5MM/yr) and hope that will make the FDA happy. If he can string this process out, he can become CEO and deal with it then. However, companies that string along the FDA along tend to get hit with maximum fines ($100MM) and suspension of their products for 3 years. However, Pyles can string this process out for 2 years before the FDA would get impatient.
He could just try and be honest and fix the problem. It would cost the company $100MM, but at least the product would still be selling. The CEO position will be decided in 1 year. There’s a 50% chance they could finish in 9 months.
a.
Draw a decision tree based on the penalties to the company. Calculate the expected penalties for each option. What is the best decision for the company? b.
Draw decision tree based on Pyles getting the CEO position. What is the best decision for Pyles?
Summarize your results in the following table:
Choice
Financial Penalty
Probability will become CEO