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GSU / OTHER / MGMT 3100 / What is a decision alternative?

What is a decision alternative?

What is a decision alternative?

Description

School: Georgia State University
Department: OTHER
Course: Business Analysis
Professor: Wendy roth
Term: Fall 2016
Tags: business, analysis, EV, EOL, EVUPI, EVPI, EVUII, EVS, decision making, decision, Trees, making, under, uncertainty, Ignorance, Payoffs, alternatives, States, Of, nature, Maximax, Minimax, Laplace, and Regret
Cost: Free
Name: Chapter 6 Notes: Decision Analysis
Description: These notes go over the take-home video of chapter 6. This chapter goes over Decision Analysis and the different basic concepts of how to make a decision given certain alternatives.
Uploaded: 10/24/2016
18 Pages 327 Views 0 Unlocks
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Decision Analysis Chapter 6: 1A Quantitative Methods to Help Make Decisions Chapter 6 Topics 1. States of Nature, Decision Alternatives, and Outcomes or Payoffs 2. Decision Making under Certainty:  3. Decision Making under Ignorance: a. Maximax, Maximin, LaPlace, minimax regret 4. Decision Making under Risk: a. EV, EOL, EVUPI, EVPI, EVS 5. Decision Trees 6. Bayes’ Theorem  When analyzing different decision alternatives, there are three things  that come into play:  1. Decision Alternative: your choices, different choices of what you can do 2. States of Nature: what can happen, not something that you  get to pick,  3. Payoffs: what you get based on the decision alternative you  picked, and the state of nature you end up in  -Your choices are your Decision Alternatives -The different possible future conditions are called States of  Nature; various possible future conditions -Based on the decision alternative, which you choose, and the  state of nature that happens, which you don’t have control over, you  will get some results. These are your payoffs. We can create a table containing this information, which we will use to  analyze the possible different decision alternatives.  Decision Payoff Table

States of Nature Decision  Alternatives High Demand Low Demand Produce 30k 29 -12 Produce 20k 18 8 Produce 12k 3 11


If you know that the demand will be High, what would you pick?



Say we are trying to decide how many widgets to produce. We can  make either 12,000, 20,000, or 30,000 widgets. We get to pick one of  these decision alternatives. The column on the left contains all of the  possible decision alternatives. How much demand we have is not  certain, and we don’t get to pick which state of nature we are in. The  economy could be doing very well and we don’t have a lot of  competition, so we have High Demand. The economy could be doing  poorly and our competitors come out with a cheaper alternative to our  product, so we could have Low Demand. The row across the top  shows the different States of Nature. What we pick, our Decision  Alternative, and what happens, what we don’t get to pick, our States of Nature, will result in a specific Payoff. The part of the table that  contains the numbers is the Payoffs. It contains a cell for every  combination of a Decision Alternative and a State of Nature. Basically  they each represent possible outcomes of the choice we make, from our Decisions Alternatives, and what can happen, that we can’t control, our State of Nature. This information is summarized in our Decision  Payoff Table. This helps to layout our problem. W will use this table and learn some various methods that can be used to take this data to help  us make better decisions.  Depending on the amount of information we have, our ability to make  better decisions will vary. We know our payoffs, and we get to choose  which decision alternatives we want. The thing we would like to know  more about is which state of nature will occur.  Decision-making can be classified by the amount of information we  have about the likelihood of the various states of nature occurring.  Here are some classifications: 1. Decision Making (DM) under Certainty: decision maker  knows what will happen (they know what state of nature will  prevail.) 2. Decision Making (DM) under Ignorance: knows more than one state of nature, but not the probability that will occur.  3. Decision Making (DM) under Risk: knows probability of  states of nature occurring2. Decision Making (DM) under Certainty  

States of Nature Decision  Alternatives High Demand Low Demand Produce 30k 29 -12 Produce 20k 18 8 Produce 12k 3 11


-What if the probabilities aren’t as simple as flipping a coin or rolling a dice?



Don't forget about the age old question of How to connect the fourier series?

When you know the state of nature that will occur. All you need to do is select the best alternative. If you know that the demand will be High,  what would you pick? You would choose the production option that  would make you the most money (Produce 30k; has the highest  payoff) If you know your demand is Low, you will choose to produce  only 12k because it the highest payoff when there’s low demand.  Unfortunately, we seldom get to make decisions under certainty. And  most examples of this are probably illegal.  3. Decision Making (DM) under Ignorance Methods for Decision Making under Ignorance: 1. Maximax 2. Maximin 3. LaPlace 4. Minimax Regret Sally needs to decide what to do with her software company.  She has three decision alternatives:  MaxiMax Decision Alternativ es Extrem e Success Above Average Success Moderat e Success Failure MaxiMax Sell  Company 100,00 0 100,000 100,000 100,000 100,000 Form Joint Venture 600,00 0 350,000 50,000 0 600,000 Sell  Software  Herself 800,00 0 500,000 70,000 (110,000) 800,000


How do we look at these two and compare them to figure out which one is a better choice?



We also discuss several other topics like What is the number or product and variables raised to powers called?

On this chart we have created a decision payoff table.  -She has three decision alternatives. (Sell Company, Form Joint  Venture, Sell Software Herself). -There are 4 possible states of nature of what could happen in the  future (Extreme Success, Above Average Success, Moderate Success,  Failure). -For the MaxiMax method we look at each decision alternative, and find the maximum return for that decision.  -Then we pick the Maximum of the payoffs (800,000) MaxiMin Max of the Minimum Decision Alternativ es Extrem e Success Above Average Success Moderat e Success Failure MaxiMin Sell  Company 100,00 0 100,000 100,000 100,000 100,000 Form Joint Venture 600,000 350,000 50,000 0 0 Sell  Software  Herself 800,000 500,000 70,000 (110,000 ) (110,000 )

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You just take the maximum of the minimums in MaxiMin Most conservative LaPlace Average of all possible payoffs Decision Alternativ es Extrem e Success Above Average Success Moderat e Success Failure LaPlace Sell  Company 100,000 100,000 100,000 100,000 100,000 Form Joint Venture 600,000 350,000 50,000 0 250,000 Sell  Software  Herself 800,000 500,000 70,000 (110,000) 315,000

1. (100,000 + 100,000 + 100,000 + 100,000) / 4 = 100,000 2. (600,000 + 350,000 + 50,000 + 0) / 4 = 250,000 3. (800,000 + 500,000 + 70,000 + (110,000)) / 4 = 315,000 Then you pick the largest Payoff (315,000) MiniMax Regret Regret Table: when you want to focus on avoiding the regret  that comes from missing out on a better alternative Decision Alternativ es Extrem e Success Above Average Success Moderat e Success Failure MiniMax Regret Sell  Company 100 100 100  100  100,000 Form Joint Venture 600 350 50 0 250,000 Sell  Software  Herself 800  500  70 (110) 315,000

You need to look at all of the states of nature and determine which  would be your best decision Decision Alternativ es Extrem e Success Above Average Success Moderat e Success Failure MiniMax Regret Sell  Company 800-100 = 700 500-100 = 400 100-100 = 0 100-100 = 0 700 Form Joint Venture 800-600 = 200 500-350 = 150 100-50 = 50 100-0 = 100 200 Sell  Software  Herself 800-800 = 0 500-500 = 0 100-70 = 30 100-(- 110) = 210 210

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You just take your best choices and you subtract it from the actual  values that are in those states of nature.  Whatever your answer is your regret.  You then choose your maximum regret (in red) Higher numbers are BAD, so you choose the lowest regret number  (200) 4. Decision Making (DM) under Risk-When your outcome is uncertain, there is a risk (risk you wont get the  outcome you’re looking for). To be able to make a decision when there  is risk, you need to know the probabilities of the different possible  outcomes. Under decision making under risk, we now have the  probabilities of different states of nature occurring.  -What if the probabilities aren’t as simple as flipping a coin or rolling a  dice? Here are two options with various payoffs and various  probabilities. How do we look at these two and compare them to figure  out which one is a better choice? Which would you choose? ∙ Option 1 Payoff Probability $1000 1.8% $100 50% $100,000 1.2% 0 48%

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∙ Option 2 Payoff Probability $2,456 2.8% $450,607 .2% $567 24.5% 0 72.5%

We want a way to compare option 1 & 2 and pick which one is better.  That way is called: Expected Value (EV):  -Basically is it the idea that if you have a situation that has a  number of different possible outcomes, if you were to repeat the situation over and over again, and found the average of all your results, that would be the Expected Value. ∙ The long-run average of the results of many independent  repetitions of an experiment.  ∙ The weighted average of all possible values that this random  variable can take ∙ Mean  ∙ The principle is that the value of a future gain should be directly  proportional to the chance of getting it ∙ We will also refer to is as Expected Return  Decision Making Under Risk: We know the probabilities of the  States of Natures, so we can calculate the Expected Return.  

Extreme Success Above Average Success Moderate Success Failure Expected Return Probabiliti es 0.05 0.15 0.50 0.30

Sell  Company 100,000 100,000 100,000 100,000

Form Joint  Venture 600,000 350,000 50,000 0

Sell  Software  Herself 800,000 500,000 70,000 (110,000)

Don't forget about the age old question of How does Roger Lancaster view machismo?

Sally has gone to a consultant who has told her each likelihood of the  states of nature occurring. All of the probabilities of the states of  nature add to 1, they have to add to 1 because with probabilities, 1 =  100%.  Expected Value Under Perfect Information (EVUPI):

Extreme Success Above Average Success Moderate Success Failure Probabilities 0.05 0.15 0.50 0.30 Sell Company 100,000 100,000 100,000  100,000 Form Joint  Venture 600,000 350,000 50,000 0 Sell Software Herself 800,000  500,000  70,000 (110,000)

You just pick the best alternative (most profitable) payoff in the states  of nature.  Extreme Success = 800,000 Above Average Success = 500,000 Moderate Success = 100,000 Failure = 100,000 -The difference when we looked at decision-making under certainty is  here, we get to pick the best choice for state of nature, but we still  have to live within these probabilities of when we will end up in these  states of nature.  -To Calculate the EVUPI, you take the best outcome of each state,  and multiply it by the likelihood of that state of nature occurring.  (0.05*800,000) + (0.15*500,000) + (0.50*100,000)  +(0.30*100,000) = 195,000 Expected Value Under Imperfect Information (EVUII)

Extreme Success Above Average Success Moderate Success Failure Expected Return Probabiliti 0.05 0.15 0.50 0.30

es

Sell  Company 100,000 100,000 100,000 100,000 100,000 Form Joint  Venture 600,000 350,000 50,000 0 107,500 Sell  Software  Herself 800,000 500,000 70,000 (110,000) 117,000

We do not know which state of nature we are going to be in, so we cant just pick our best choice for each state of nature. We must consider  all the different states of nature that can happen and their payoff for  each of those states of nature.  -For the decision alternative of Selling the Company, we take each of the payoffs of each of the states of nature and multiply them by how  likely that particular state of nature will occur.  0.05*100,000 + 0.15*100,000 + 0.50*100,000 + 0.30*100,000 = 100,000 And so on for the next alternatives: 0.05*600,000 + 0.15*350,000 + 0.50*50,000 + 0.30*0 =  107,500 0.05*800,000 + 0.15*500,000 + 0.50*70,000 + 0.30*(110,000)  = 117,000 Now we can compare these different alternatives because we have  something that looks at the probabilities and the various payoffs. We  are going to pick the one that has the HIGHEST Expected Return. Decision Making Under Risk (Overview) ∙ EVUPI: Expected Value Under Perfect Information o (pick the Payoff for each state of nature) ∙ EVUII: Expected Value Under Imperfect Information o (from all decision alternatives, pick the HIGHEST Expected  Return) ∙ EVPI: Expected Value of Perfect Information o EVUPI – EVUII o What this is telling you is that EVUII is where you  am now, if you could do some marketing research or somehow get some additional information, how  much are you willing to pay for it. If it could get you  closer to EVUPI (making a perfect decision), how  much is that information worth.  o EVUPI = 195,000 o EVUII = 117,000 o EVPI = 195,000 – 117,000 = 78,000 o If we could get perfect information, the most we  would be willing to pay for it is 78,000 o Anything over than that is not worth it Expected Opportunity Lost (EOL)

Extrem e

Above Average Moderat e

Failure EOL

Success Success Success

Probabiliti es 0.05 0.15 0.50 0.30

Sell  Company 800-100 = 700 500-100 = 400 100-100 = 0 100-100 = 0 95 Form Joint Venture 800-600 = 200 500-350 = 150 100-50 = 50 100-0 = 100 87.5 Sell  Software  Herself 800-800 = 0 500-500 = 0 100-70 = 30 100-(- 110) = 210 78

Take the regret table and combine with the probabilities of the given  states of nature. Take the highest payoff for each states of nature and  subtract is from each alternative in that state of nature to give you the  amount of regret for that specific decision alternative in that state of  nature. Now we take those regret values and combine them with the  probability, just like we did in the previous section of expected return. But now, instead of dealing with payoffs, were dealing with regrets or  loss, and so it is called Expected Opportunity Loss (EOL).  Remember, regret represents how bad we feel for not making a  different choice, which can also be thought of as an opportunity we  gave up or lost.  Sell Company = 0.05*700 + 0.15*400 +0.50*0 +0.30 *0 = 95 Form Joint Venture = 0.05*200 + 0.15*150 +0.50*50 +0.30  *100 = 87.5 Sell Software Herself = 0.05*0 + 0.15*0 +0.50*30 +0.30 *210 = 78 Units in $1,000We take the LOWEST number since regret is BAD (78) 5. Decision Trees ∙ Converting our Decision Making Under Risk  Information into a Decision Tree State of Nature  State of Nature  1Payoff: 11 Payoff: 11 e e ccii) ) ooVVhhEEDecision  Decision  Alternative 1 Alternative 1 Decision  Decision  Alternative 2 Alternative 2 1 State of Nature  State of Nature  2Payoff: 12 Payoff: 12 2 State of Nature  State of Nature  1Payoff: 21 Payoff: 21 1 State of Nature  State of Nature  2Payoff: 22 Payoff: 22 CC( ( 2 t t sseeBBDecision  Decision  Alternative 3 Alternative 3 State of Nature  State of Nature  1Payoff: 31 Payoff: 31 1 State of Nature  State of Nature  2Payoff: 32 Payoff: 32 2 -We take our three parts of the original decision path table and put  them into a tree -We have our Decision Alternatives, States of Nature, and our Payoffs-If you read it from left to right, you want to make the best choice you  have from the three decision alternatives,  -Depending on which state of nature you are in, you get a certain  payoff -We have three different decision alternatives, we have only two states  of nature, and they are the same for all three decision alternatives -Depending on the decision alternative and a specific state of nature,  we get a unique payoff (that’s why they have numbers) Decision Making Under Risk

Extreme Success Above Average Success Moderate Success Failure Expected Return Probabiliti es 0.05 0.15 0.50 0.30

Sell  Company 100,000 100,000 100,000 100,000 100,000 Form Joint  Venture 600,000 350,000 50,000 0 107,500 Sell  Software  Herself 800,000 500,000 70,000 (110,000) 117,000

We then put it in a tree   State of Nature  PayoffDecision  Decision  Alternative Alternative Sell  Sell  Company Company Form Joint  Form Joint  Venture Venture Sell Software  Sell Software  Herself  Herself  Extreme  Extreme  (0.05) 100,000 100,000 (0.05) Above  Above  Average  (0.15)100,000 100,000 Average  (0.15) Moderate  Moderate  (0.50) 100,000 100,000 (0.50) Failure (0.30) Failure (0.30) 100,000 100,000 Extreme  Extreme  (0.05) 600,000 600,000 (0.05) Above  Above  Average  (0.15)350,000 350,000 Average  (0.15) Moderate  Moderate  (0.50) 50,000 50,000 (0.50) Failure (0.30) Failure (0.30) 00 Extreme  Extreme  (0.05) 800,000 800,000 (0.05) Above  Above  Average  (0.15)500,000 500,000 Average  (0.15) Moderate  Moderate  (0.50) 70,000 70,000 (0.50) Failure (0.30) Failure (0.30) -110,000 -110,000 To get your Expected Return using the tree, you must start on  the left-hand side and move to the right 1. Payoff*Probabilities 2. Sum all of the answers together for that alternative to get  your Expected Return. 3. Choose the highest value of Expected Return Sell Company = 100,000 Form Joint Venture = 107,500 Sell Software Herself = 117,000
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