Decision Analysis Part 3

1
Chapter 14

• Decision Analysis Part 3

2
Restaurant Decision

• A company plans to open a restaurant/bar in
  Newark. It is considering 3 locations, A, B and
  C. Location A is furthest from campus, B is next
  closest and C is adjacent to the campus. The
  closer to campus, the greater the chance the
  restaurant will NOT get a liquor license which
  will greatly impact revenues. The company plans
  to request a special vote to obtain a license.
  The vote could be favorable or unfavorable.

3
Restaurant Decision

• The following payoff table shows the potential
  revenue for each location given the vote outcome

4
Restaurant Decision

• If the company has determined that the likelihood
  of a favorable vote is .55 and unfavorable is
  .45, then EMVs could be calculated as follows
• EMVA 60(.55) 50(.45)
• EMVB 80(.55) 30(.45)
• EMVC 100(.55) 0(.45)

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Restaurant Decision - EVPI

• If the company has determined that the likelihood
  of a favorable vote is .55 and unfavorable is
  .45, then the EVPI could be calculated as
  follows
• EVPI EPPI EMV
• EVPI (100)(.55) (50)(.45) 57.5
• EVPI

6
Sensitivity Analysis

• In many cases, probabilities and payoffs are
  based on subjective assessments and can vary over
  time.
• Sensitivity analysis can be used to determine how
  changes to these inputs impact your decision
• If a small change in one of the inputs causes a
  change in the recommended decision alternative,
  extra effort and care should be taken in
  estimating the input value. The inverse is true
  as well!

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Sensitivity Analysis Example

• Assume a reversal of the likelihoods from our
  restaurant example Favorable .45, Unfavorable
  .55.
• Now EMVs could be calculated as follows
• EMVA 60(.45) 50(.55)
• EMVB 80(.45) 30(.55)
• EMVC 100(.45) 0(.55)

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Sensitivity Analysis Example

• When likelihood of Favorable is larger, choose B
  smaller, choose A. Question is up to what
  point?
• In the situation with 2 states of nature, can
  determine ranges using the following formula
• P(S2) 1- P(S1) 1-P

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Sensitivity Analysis Example

• EV(A) P(S1)(60) P(S2)(50)
• p(60) (1-p)(50)
• 60p 50 50p
• 10p 50
• Use the same process for each alternative
• EV(B) 50p30
• EV(C) 100p

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Sensitivity Analysis Example

• Can use these equations to graph the EMVs across
  varying likelihoods to determine ranges of
  optimal selections
• Identify graphing coordinates for each by setting
  p equal to extreme likelihoods p 1 and p 0

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Sensitivity Analysis Example
EV
Alt B highest EV
Alt C highest EV
120 100 80 60 40 20 0 -20
Alt A highest EV
EVC
EVB
EVA
.2 .4 .6 .8
1.0 p
How do you determine the points where you would
change your mind?
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Sensitivity Analysis Example

• Set equations equal to determine points of
  intersection
• EVA EVB 10p50 50p30 .50
• EVB EVC 50p30 100p .60
• Conclusion If likelihood for Favorable Vote is
• lt50 - Choose location A
• 50 - 60 - Choose location B
• 60 - Choose location C

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Sensitivity Analysis Example

• Can also use sensitivity analysis to test payoff
  values
• Identify best and 2nd best alternatives
• Best Choice B with EMV of 57.5
• 2nd Best Choice A with EMV of 55.5
• Can state that Choice B will remain optimal as
  long as EVB 55.5
• Up to what point will this be true?

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Sensitivity Analysis Example

• Let F the payoff of decision B when a favorable
  vote is encountered
• Let U the payoff of decision B when an
  unfavorable vote is encountered
• EVB .55F .45U
• .55F .45U 55.5
• .55F .45(30) 55.5
• .55F 13.5 55.5
• .55F 42
• F 76.4

What does this mean to you?
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Sensitivity Analysis Example

• Let F the payoff of decision B when a favorable
  vote is encountered
• Let U the payoff of decision B when an
  unfavorable vote is encountered
• EVB .55F .45U
• .55F .45U 55.5
• .55(80) .45U 55.5
• 44 .45U 55.5
• .45U 11.5
• U 25.5

What does this mean to you?
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Reviewing Our Decision

• Have alternatives ?
• Have payoff information ?
• Have initial assumptions re likelihoods ?
• Have EVPI information can decide whether or not
  to get new information to revise or update our
  assumptions ?
• What happens if our new information changes our
  initial assumptions?

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New Information

• Prior to deciding on a location, the company must
  decide whether to conduct a lobbying effort among
  the Newark authorities. The outcome of the
  lobbying effort can be positive or negative with
  the following likelihoods
• P(positive lobbying effort) .75
• P(negative lobbying effort) .25

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New Information

• If the lobbying effort is positive, the company
  has determined that the likelihood for a
  favorable vote would increase with new
  likelihoods as follows
• P(Favorable vote given a positive lobbying
  effort) .95
• P(Unfavorable vote given a positive lobbying
  effort) .05

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New Information

• If the lobbying effort is negative, the company
  has determined that the likelihood for a
  favorable vote would decrease with new
  likelihoods as follows
• P(Favorable vote given a negative lobbying
  effort) .35
• P(Unfavorable vote given a negative lobbying
  effort) .65

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New Information

• If NO lobbying effort is conducted, the PRIOR
  probabilities are still applicable
• P(favorable) .55
• P(unfavorable) .45

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Decision Strategy with New Information

• Can now create a new decision tree that reflects
  the alternate courses of action and revised
  (posterior) probabilities and SOLVE
• LETS GO TO THE BOARD

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Fav .95
60 50 80 30 100 0
A
Unfav .05
Positive .75
B
Fav .95
Unfav .05
C
Fav .95
Lobby Effort
Unfav .05
Fav .35
60 50 80 30 100 0
A
Unfav .65
B
Fav .35
Unfav .65
Negative .25
C
Fav .35
Unfav .65
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Fav .55
60 50 80 30 100 0
A
Unfav .45
B
Fav .55
Unfav .45
No Lobby Effort
C
Fav .55
Unfav .45
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Fav .95
60 50 80 30 100 0
A
Unfav .05
Positive .75
B
Fav .95
Unfav .05
C
Fav .95
Lobby Effort
Unfav .05
Fav .35
60 50 80 30 100 0
A
Unfav .65
B
Fav .35
Unfav .65
Negative .25
C
Fav .35
Unfav .65
25
Fav .55
60 50 80 30 100 0
A
Unfav .45
B
Fav .55
Unfav .45
No Lobby Effort
C
Fav .55
Unfav .45
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Expected Value of Sample Information

• If we chose to do the lobbying effort, the EV
  84.625
• If we chose NOT to do the lobbying effort, the EV
  57.5
• The difference between these EVs is the Expected
  Value of Sample Information
• EVSI EVwSI EVwoSI

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Expected Value of Sample Information

• EVSI EVwSI EVwoSI
• EVSI 84.625 57.5 27.125
• Conducting the lobbying effort adds 27,125 to
  the location decision EV.

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Efficiency of Sample Information

• Since we cant be sure that the sample
  information will yield us PERFECT information,
  its helpful to consider the efficiency of the
  information we do receive.
• Assuming that perfect information yields an
  efficiency of 100, we can calculate
• Efficiency (EVSI / EVPI) x 100

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Efficiency of Sample Information

• Efficiency (EVSI / EVPI) x 100
• 27.125 x 100 135
• 20
• This value means that the lobbying effort is 135
  as efficient as perfect information so we would
  definitely want to pursue it!

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For Next Class

• Read balance of Chapter 14 (Bayes Theorem) and
  Utility Theory