Chapter 14 Decision Making

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Chapter 14 Decision Making

• Applying Probabilities to the Decision-Making
  Process in the face of uncertainty.

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In order to make the best decision, with the
information available, the decision maker
utilizes certain decision strategies to evaluate
the possible benefits and losses of each
alternative.
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When making a decision in the face of
uncertainty, ask

• What are my possible Alternatives or Courses of
  Action?
• 2) How can the future affect each action?

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What are my possible Alternatives or Courses of
Action?

• Before selecting a course of action, the decision
  maker must have at least two possible
  alternatives to evaluate before making his choice.

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Example I want to invest 1 million for 1 year.
I narrow my choices to three alternatives
(actions)

• Alternative 1 Invest in guaranteed income
  certificate paying 10.
• Alternative 2 Invest in a bond with a coupon
  value of 8.
• Alternative 3 Invest in a well-diversified
  portfolio of stocks.

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The Alternatives (Actions) are under the decision
makers control.
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How can the future affect each alternative
(action)?
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Unless youve got a crystal ball

• Future uncertainties may derail the most perfect
  of plans.

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These future events are also referred to as
States of Nature
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Example Economic conditions, foremost among
which is interest rates.

• Interest rates increase.
• Interest rates stay the same.
• Interest rates decrease.

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To account for future uncertainties (events)

• We assign probabilities to measure the likelihood
  of a future event occurring.

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Example Probabilities
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Future events (states of nature or outcomes), are
out of the decision makers control and often
strictly a matter of chance.
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Yet, the impact of these events

• Affect the payoffs/losses which determine the
  decision making process.

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Important Distinction!

• The action (alternative) is under the decision
  makers control.

• The event (state of nature) that ultimately
  occurs is strictly a matter of chance.

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Associated with each alternative (action) and
event (state of nature) is a corresponding payoff
or profit.
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• If I could predict the future with certainty,
• I would choose the alternative with the highest
  payoff (profit).

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Instead of focusing on profits, I could look at
the Opportunity Loss associated with each
combination of an alternative and the economic
condition affecting that alternatives
profitability.
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Opportunity Loss

• The difference between the profit I made on the
  alternative I chose and the profit I could have
  made had the best decision been made.

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• NOTE
• Since Opportunity Loss is the difference between
  two decisions, it can not be expressed as a
  negative number.

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If I could predict the future with certainty,

• I would choose the alternative (action) with the
  highest payoff or lowest loss.

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In many decision problems, it is impossible to
assign Empirical probabilities to the economic
events, or states of nature, that affect profits
and losses. In many cases, probabilities are
assigned Subjectively.
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Using probabilities, we calculate the Expected
Monetary Value for each alternative or action.

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Expected Monetary Value (EMV)
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To maximize profits, choose the Alternative with
the highest EMV.
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What does the EMV represent?
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If the investment is made a large number of times
(infinite)

• with bonds,
• 20 of the investments will result in a 50,000
  loss,
• 50 will result in an 80,000 profit, and
• 30 will result in 180,000 profit.
• The average of all these investments is the EMV
  of 84,000.

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Expected Opportunity Loss Decision (EOL)
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Expected Opportunity Loss (EOL)
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To minimize losses, choose the Alternative with
the lowest EOL.
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Example

• A vendor at a baseball game must determine
  whether to sell ice cream or soft drinks at
  todays game. The vendor believes that the profit
  made will depend on the weather.

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Based on past experience at this time of year,
the vendor estimates the probability of warm
weather as 60.
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1. Compute the EMV for selling soft drinks and
   selling ice cream.
2. Compute the EOL for selling soft drinks and ice
   cream.
3. Based on the previous results, which should the
   vendor sell, ice cream or soft drinks? Why?

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EMV

• EMV (soft drinks) .4(50) .6(60)
• 20 36
• 56
• EMV (ice cream) .4(30) .6(90)
• 12 54
• 66
• Sell ice cream

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Stay tuned
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The Value of Additional Information

• If we knew in advance which future event or state
  of nature would occur, we would capitalize on
  this knowledge and maximize our profits/minimize
  our losses.

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• But our knowledge of future events or states of
  nature is sometimes tenuous at best.
• Leaving us to ask ourselves, Am I making the
  best decision?

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To determine which course of action (alternative)

• to select, we assign probabilities to the
  likelihood of each future event occurring.

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Probabilities are assigned based on

• past data,
• the subjective opinion of the decision maker,
• Or knowledge about the probability distribution
  that the event may follow.

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• Better information makes better decisions.

But what are you willing to pay?
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Data is costly to acquire

• Money time
• Cognitive energy
• Staff effort
• Opportunity costs of failing to do other things
  with the money or time.

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Goal is to gather data as long as

• the MARGINAL COST is NO MORE than the MARGINAL
  BENEFITS of the additional data.

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• At some point, data gathering must stop and the
  decision must be made.

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The Value of Additional Information
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Expected Payoff with Perfect Information (EPPI)

• EPPI is the maximum price that a decision maker
  should be willing to pay for perfect information.

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With perfect information,

• I would know what to expect so I would select
  the optimum course of action for each future
  event.

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Expected Payoff With Perfect Information (EPPI)
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If the Expected Profit Under Certainty (EPPI) is
the profit I expect to make if have perfect
information about which event will occur, how
much should I be willing to pay for this
perfect information?
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• The 134,000 does NOT represent the MAXIMUM
  amount Id be willing to pay for perfect
  information because I could have made an expected
  profit of EMV 100,000 WITHOUT perfect
  information.

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Expected Value of Perfect Information

• EVPI EPPI EMV
• 134,000 - 100,000
• 34,000
• If perfect information were available, the
  decision maker should be willing to pay up to
  34,000 to acquire it.

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Besides profits losses, is there something else
we should consider?
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Variability!

• When comparing two or more actions, especially
  with vastly different means, evaluate the
  relative risk associated with each action.
• Coefficient of Variation (CV)
• Return to Risk Ratio (RRR)

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Coefficient of Variation (CV)

• Measures the relative size of the variation
  compared with the arithmetic mean (EMV).
• CV s EMV
• s vS (x- µ)2 P (X)
• Where µ EMV

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CV s EMV s vS (x- µ)2 P (X) Where µ
EMV
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• EMV 100,000
• sstocks vS (x- µ)2 P (X)
• v(150,000 100,000) 2 (.2) (90,000
  100,000) 2 (.5)
• (40,000 100,000) 2 (.3)
• 40,373

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• EMV 100,000
• sbonds vS (x- µ)2 P (X)
• v(-50,000 100,000) 2 (.2) (80,000
  100,000) 2 (.5)
• (180,000 100,000) 2 (.3)
• 81,363

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Coefficient of Variation

• CVstocks (s EMV) 100
• (40,373 100,000) 100
• 40.4
• CVbonds (s EMV) 100
• (81,363 100,000) 100
• 81.4

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Return-to-Risk Ratio (RRR)

• RRR EMV s
• RRR stocks 100,000 40,373 2.48
• RRR bonds 100,000 81,363 1.23

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Although Bonds stocks have a comparable EMV,
the RRR for stocks is substantially higher than
bonds the stocks CV much smaller than that of
bonds.
RRR stocks 100,000 40,373 2.48 RRR bonds
100,000 81,363 1.23
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Homework

• A baker must decide how many specialty cakes to
  bake each morning. From past experience, she
  knows that the daily demand for cakes ranges from
  0 to 3. Each cake costs 3.00 to produce and
  sells for 8.00, and any unsold cakes are thrown
  in the garbage at the end of the day.

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Set up a payoff table to help the baker decide
how many cakes to bake.
Payoff Table
Produce Produce Produce Produce
Demand Bakeo Bake1 Bake2 Bake3
Sello 0 -3.00 -6.00 -9.00
Sell1 0 5.00 2.00 -1.00
Sell2 0 5.00 10.00 7.00
Sell3 0 5.00 10.00 15.00
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• Opportunity Loss Table

Produce Produce Produce Produce
Demand Bakeo Bake1 Bake2 Bake3
Sello 0 3.00 6.00 9.00
Sell1 5.00 0 3.00 6.00
Sell2 10.00 5.00 0 3.00
Sell3 15.00 10.00 5.00 0
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Assuming probability of each event is equal Sell
.25

• EMV(0) 0
• EMV(1) .25(-3) .25(5) .25(5) .25(5)
• 3.00
• EMV(2) .25(-6) .25(2) .25(10) .25(10)
• 4.00
• EMV(3) .25(-9) .25(-1) .25(7) .25(15)
• 3.00
• EMV decision is to bake 2 cakes.

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Assuming probability of each event is equal Sell
.25

• EOL(0) .25(0) .25(5) .25(10) .25(15)
• 7.50
• EOL(1) .25(3) .25(0) .25(5) .25(10)
• 4.50
• EOL(2) .25(6) .25(3) .25(0) .25(5)
• 3.50
• EOL(3) .25(9) .25(6) .25(3) .25(0)
• 4.50
• EOL decision is to bake 2 cakes.

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EVPI EPPI EMV

• EPPI .25(-3) .25(5) .25(10) .25(15)
• 6.75
• EMV 4.00
• EVPI 6.75 4.00 2.75

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Homework

• The manager of a large shopping center in Buffalo
  is in the process of deciding on the type of snow
  clearing service to hire for his parking lot. Two
  services are available. The White Christmas
  Company will clear all snowfalls for a flat fee
  of 40,000 for the entire winter season. The
  Weplowmen Company charges 18,000 for each
  snowfall it clears.

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Set up the payoff table to help the manager
decide, assuming that the number of snowfalls per
winter season ranges from 0 to 4.
Payoff Table
Demand Flat Fee Pay per snowfall
of Snowo -40,000 0
of Snow1 -40,000 -18,000
of Snow2 -40,000 -36,000
of Snow3 -40,000 -54,000
of Snow4 -40,000 -72,000
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Using subjective assessments, the manager has
assigned the following probabilities to the
number of snowfalls. Determine the optimal
decision.

• p(0) .05
• p(1) .15
• p(2) .30
• p(3) .40
• p(4) .10

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EMV (flat fee) - 40,000EMV (pay per snowfall)
.5(0) .15(-18,000) .3(-36,000) .4(
-54,000) .1(-72,000) -42,000EMV is flat fee
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Hopefully, something hit home