Transcript HCM540-Modeling-3-DecisionAnalysis

Decision Making
Under Uncertainty
Let’s stop pretending
we know things
Decision Analysis
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A formal technique for framing and analyzing decisions under
uncertainty that have a dynamic component
 Make decision, then uncertainty revealed, make next decision,
…
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Draws on probability, statistics, economics, psychology
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Useful for big decisions with a manageable number of
alternatives and uncertain elements
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Like many modeling techniques, process of careful analysis
may be as valuable as “results”
 DA is great tool for helping to structure decision problems
 DA process leads to useful communications tools describing
the problem in a “common language”
Objectives for this Session
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Help you become an educated consumer of
basic decision analyses
Use DA to generate broadly applicable
fundamental insights regarding decision
making
As a consumer, you should be able to
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Identify opportunities for DA to help frame
and analyze tough decisions
Play important role in analyzing decision
problems by integrating technical analyses
with managerial expertise and experience
Understand DA principles sufficiently to
manage and interact with staff carrying out
such analyses
Warning! Decision and risk
analysis is a radical concept
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People, in general, are not comfortable with
probabilistic reasoning
Most people commonly use point estimates for
uncertain quantities and then may carry out a limited
1 or 2 variable sensitivity analysis
Everyone will say, “too much thinking and planning
required, don’t have time in the real world”
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but somehow, people have time to revisit the messes they
make with “seat of the pants” decision making
Why Important to Model
Uncertainty?
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The world is uncertain
Replacing random quantities with averages
or single “guesstimates” can be dangerous
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Allows prediction of distribution of results
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The Flaw of Averages
Not just one predicted number or outcome
Sensitivity analysis of outputs to inputs
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Which inputs really affect the outputs?
Common Decision Making
Biases
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Poor framing – glass ½ full or glass ½ empty
Recency effects – the last word
Poor probability estimation – uncertain about
uncertainty
Overconfidence – too certain about uncertainty
Escalation phenomena – ignoring sunk cost
Association bias – a hammer in search of nails
Group think – power in numbers
Random variables (RV) and
probability distributions
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A variable whose value depends on the outcome of an
uncertain event
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Probability of various outcomes determined by probability
distribution associated with the RV
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Low bid by competing firms
Demand for some service next year
Number of patients requiring open heart surgery next month at
Hospital H
Cost of Drug X in December, 2003
As modelers, we select appropriate distributions
Probability distributions
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mathematical functions
Assign numeric probabilities to uncertain events modeled by
the distribution
See “Distributions, Simulation and Excel Functions” handout that Doane created.
Discrete Probability Distributions
Discrete Probability Distribution of Demand
DistributionReview.xls
0.35
0.30
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Countable # of outcome values
Each possible outcome has an
associated probability
Probability
0.25
0.20
0.15
0.10
0.05
0.00
100
Demand
100
150
200
250
300
172.5
Expected Demand
Probability
0.30
0.20
0.30
0.15
0.05
1.00
Total Probability
150
200
250
300
Demand
Expected Value of Discrete RV
n
E[ X ]   xi P[ X xi ]
i 1
 A few discrete distributions
 Empirical
 Binomial – BINOMDIST()
 Poisson – POISSON()
Decision Making Elements
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Although there is a wide variety of contexts in decision
making, decision making problems have three main
elements:
1.
the set of decisions (or strategies) available to the
decision maker
2.
the set of possible outcomes and the probabilities of
these outcomes for all random variables
3.
a value model that prescribes results, usually monetary
values, for the various combinations of decisions and
outcomes.
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Once these elements are known, the decision maker can
find an “optimal” decision.
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With respect to some decision making objective
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THEN DO SENSITIVITY ANALYSIS
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Tornado diagrams
Example – Capacity Planning for
Portable Monitoring Devices
How many devices should we purchase?
We need to decide how
many monitoring devices to
purchase.
Here’s our model of demand
– a discrete RV.
If we’re “short”, we must
rent from a supplier at a cost
premium.
We charge $100/day and
incur an estmated cost of
$20/day for each monitor
we own.
Decision Analysis Strategy
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Identify our alternatives
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Identify and quantify random variables
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Demand – we have somehow estimated distribution of
daily demand for devices
Create payoff matrix for all combinations of
alternatives and uncertain outcomes
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Purchase 0, 1, 2, 3, 4, or 5 devices
Excel well suited for this
Can also graph the risk profile for each alternative
Explore “optimal” decision under different objective
functions
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Maximin – maximize the worst possible return (pessimistic)
Maximax – maximize the best possible return (optimistic)
Expected monetary value – pick the alternative that gives
the highest expected return
Payoff Matrix
Daily device cost
Revenue
Total Shortage cost
# short
How many devices
should we purchase?
What does the
expected demand
suggest we do?
Let’s look at PortMonitoring.xls
Conclusions
This comment is in PortMonitoring.xls file.
Effect of Increased Rental Cost
Risk Profiles
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A risk profile simply lists all
possible monetary values and
their corresponding probabilities.
Risk profiles can be illustrated on
a bar chart. There is a bar above
each possible monetary value with
height proportional to the
probability of that value.
Making a decision is basically a
choice of which risk profile you
wish to accept.
4 Devices
3 Devices
5 Devices
The Flaw of Averages
http://www.stanford.edu/~savage/flaw/
Math Speak
A non-linear function of a random variable, evaluated at the
average of the random variable, is not the average of the function.
The Math
F(E(X)) ≠ E(F(X) if F is a nonlinear function
Practical Interpretation
When you plug average values into a spreadsheet, you don’t get
average outputs unless the model is linear (and most people don’t
know if their models are linear or not).
Savage, S., 2003, Weapons of Mass Instruction, OR/MS Today, August, pp. 36-40.
Example of Flaw of Averages
This function,
probability that the
unit is full is NOT a
linear function of the
birth volume.
The Flaw of Averages
Number of post-partum beds:
Births
Probability[unit full]
1200
0.6%
1500
3.9%
1800
14.7%
2100
38.4%
2400
78.4%
Average
1800
16
Average
6.4%
Probability[unit full] - 16 Beds
90.0%
80.0%
70.0%
NOT equal to
each other.
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
0
500
1000
1500
Birth Volume
2000
2500
3000
Sensitivity Analysis
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Sensitivity analysis (SA) a big part of Decision
Analysis (DA)
SA = “What matters in this decision?”
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which variables might I want to explicit model as
uncertain and which ones might I just as well fix to my
best guess of their value?
On which variables should we focus our attention on
either changing their value or predicting their value?
No “optimal” SA procedure exists for DA
SA can help identify Type III errors - solving the
wrong problem
Some SA Techniques
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Scenarios – base, pessimistic, optimistic
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1-way and 2-way data tables and associated
graphs
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as in the Break Even spreadsheet
Tornado diagrams
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How did we do with “scenario planning”?
a one variable at a time technique
Top Rank –Excel add-in for simple “What if?”
Risk Analysis or Spreadsheet Simulation
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direct modeling of uncertainty through probability
distributions
@Risk , CrystalBall – sophisticated Excel add-ins
Tornado Diagrams
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Graphical sensitivity analysis technique
Create base, low and high value scenarios for
each input variable
Set all variables at base value
“Wiggle” each variable to its low and high values,
one at a time.
A one-way sensitivity analysis technique
Calculate total profit for each scenario
Create “tornado diagram” - Excel
JCHP-BreakEven-Tornado.xls
OBMODELS-HCM540-TopRank.XLS
From “Making Hard Decisions” by Clemen
Sensitivity Analysis with
TopRank
Big bars means
high impact
Some of the broadly applicable
insights...
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Explicit incorporation and quantification of risks and uncertainties is
often important
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Quantification of risk is difficult and subject to common human
decision biases
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Humans have hard time with uncertainty
It’s important to guard against decision biases
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Be wary of clairvoyant analysts!
Several methods for trying to incorporate uncertainty in analysis
Awareness is half the battle
It’s OK to say “I DON’T KNOW”
Not all information is worth the cost or equally valid
Obtaining data for some of these modeling approaches can be
difficult
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probability estimation can be tough
historical data may or may not exist