Decision Making
ADMI 6510
Decision Analysis Models
Key Sources:
Data Analysis and Decision Making (Albrigth, Winston and Zappe)
An Introduction to Management Science: Quantitative Approaches to Decision
Making (Anderson, Sweeny, Williams, and Martin), Essentials of MIS (Laudon and
Laudon), Slides from N. Yildrim at ITU, Slides from Jean Lacoste, Virginia Tech,
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Outline
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Basic concepts
Payoff table
Decision making
Expected value DA models
Decision trees
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Basics
• Decision Support Systems (DSS) use a variety
of mathematical approaches to analyze
business processes/ problems/ decisions.
– Generate alternatives.
– Visualize environment, effect of the environment.
– Estimate cost and benefit of the alternatives.
– Use data from customers, sales, economic factors
to forecast.
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Basics
Data
Data
Cost Analysis
Model
Forecast
Models
Forecast and
Probabilities
Decision
Options
Decision
Alternatives
Model
Decision
Analysis Model
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Basics
• Decision Analysis models have the following
structure:
– Decision alternatives (DA): different options
related to a system/ product.
– States of nature (SN): future events, not under the
control of the decision maker, which may occur.
• States of nature should be defined so that they are
mutually exclusive and collectively exhaustive.
– For each DA and SN combination there is an effect
($) called a payoff. Could be a profit or a cost.
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Basics
http://www.dilbert.com/
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Payoff tables
• Decisions have an associated sets of
costs/profits.
• States of nature have an effect on those
costs, profits, … performance level.
State of
nature 1
State of
nature 2
State of
nature 3
Decision option 1
$
$
$
Decision option 2
$
$
$
Decision option 3
$
$
$
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Payoff table – Example 1
– You are getting into the Xmas
trees selling business.
– Decision, how many
containers to buy?
– System characteristics/
constraints
• Each container has 400 trees
and costs $10,000 (delivered).
• Other costs are “fixed” at
$6,000 for the season
(location, salaries, marketing).
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Payoff table – Example 1
– States of nature:
• Low demand, low prices: Market for about 1,200 at an
average of $35/each.
• Medium demand/ medium prices: Market for about
1,500 at an average of $45/each.
• High demand/ high prices: Market for about 2,100 at an
average of $50/each.
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Payoff table – Example 2
• Select from 3 leasing options for a copy machine.
– System characteristics/ options:
• Lease 1: $5,000 per year; $0.035 per copy.
• Lease 2: $8,000 per year; $0.015 per copy.
• Lease 3: $10,000 per year; first 80,000 are “free”, after that
$0.009 per copy.
– States of nature:
• 5,000 copies per month.
• 7,000 copies per month.
• 15,000 copies per month.
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Decision making
• Rules that do not take into account the
likelihood (probability) of each SN.
– Optimistic: the best possible payoff.
– Conservative: maximize the minimum payoff.
• Minimize the maximum cost.
• Maximize the minimum profit.
– Minimize maximum regret: avoid the maximum
mistake.
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Decision making
Costs
sn1
sn2
sn3
d1
190
120
130
d2
90
140
200
d3
70
150
300
Optimistic: d3
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Decision making
– For each decision the worst result is listed.
– Select the best of the worst results.
sn1
sn2
sn3
max cost
d1
190
120
130
190
d2
90
140
200
200
d3
70
150
300
300
Conservative: d1
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Decision making
Minimize Maximum Regret
– Build a Regret table
• For each SN, ID the
best payoff.
• Table items:
Regret = difference
between each payoff
and best payoff.
– Select the minimum
of the maximum
regrets.
sn1
sn2
sn3
d1
190
120
130
d2
90
140
200
d3
70
150
300
sn1
sn2
sn3
Max.
Regret
d1
120
0
0
120
d2
20
20
70
70
d3
0
30
170
170
MinMax: d2
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Expected value DA models
• Expected value of a random variable is the
weighted average of all possible values that
this random variable can take on.
• The weights used in computing this average
correspond to the probabilities in case of a
discrete random variable,
• What is the expected value when rolling a 6 sided dice?
• What if it was a rigged dice and the “one” side has a
probability of 55%, the “six” side has a probability of
5%, and the other four sides have a probability of 10%
each.
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Expected value DA models
• Example 1 Probabilities
– Low demand/prices: 50%
– Medium demand/prices: 30%
– High demand/prices: 20%
• Example 2 Probabilities
– 5,000 copies/mo: 15%
– 7,000 copies/mo: 60%
– 15,000 copies/mo: 25%
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Sensitivity analysis
• Sensitivity analysis (or post-optimality
analysis) is used to determine how the
optimal solution is affected by changes:
– To the objectives
– To the constraints
• Sensitivity analysis is important to the
manager who must operate in a dynamic
environment with imprecise estimates.
• Sensitivity analysis is about asking what-if
questions about the problem.
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Sensitivity analysis
• Assume that the probability of high
demand/prices is fixed at 20%.
• And that pSN=low + pSN=medium = 80%.
• What is the sensitivity of the optimal solution
to changes in pSN=low ?
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Decision trees
• Graphical representation of decisions
– Could be used to represent multi-level/time decisions
or states of nature.
– Useful for models where decisions are based on
expected values.
• Each decision tree has two types of nodes; round nodes for
SNs, square nodes correspond to DA.
• The branches leaving each round node represent the
different states of nature while the branches leaving each
square node represent the different decision alternatives.
• At the end of each limb of a tree are the payoffs attained
from the series of branches making up that limb.
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Decision trees – example
• Sourcing of a critical component.
• Considering two vendors.
– DA1: all requirements to vendor A.
– DA2: all requirements to vendor B.
– DA3: split requirements; 50% vendor A, 50%
vendor B.
– States of nature based on the following events:
vendor delivers or a vendor fails to deliver.
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Decision trees – example
Use A only
Use B only
Use both
Requirement per cycle is 1,000 units.
Loss costs = $400/unit not available.
Vendor A delivers
Vendor A fails to deliver
Vendor B delivers
Vendor B fails to deliver
Vendor A delivers and Vendor B delivers
Vendor A delivers, Vendor B fails
Vendor A fails, Vendor B delivers
Both vendors fail
Vendor A
Vendor B
Cost per unit
$100
$95
Delivery probability
96%
92%
Additional delivery capacity
150 units
0 units
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Decision trees – example
• Each decision has an expected value based on
the applicable SNs.
A delivers
Use A only
A fails to deliver
B delivers
Use B only
B fails to deliver
EV =
96% ($100 x 1,000) +
4%($400 x 1,000)
EV =
92% ($95 x 1,000)
+ 8%($400 x 1,000)
$112,000
$119,400
Use both
A delivers & B delivers
A delivers, B fails
A fails, B delivers
Both vendors fail
EV =
(96%)(92%) ($100 x 500 + $95 x 500)
+ (96%)(8%) ($100 x 650 + $400 x 350)
+ (4%)(92%) ($400 x 500 + $95 x 500)
+ (4%)(8%) ($400 x 1,000)
$112,244
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Decision trees – example
• Sensitivity to Loss cost
160,000
150,000
140,000
130,000
A
120,000
B
110,000
A&B
100,000
90,000
80,000
0
100
200
300
400
500
Loss cost/ unit
600
700
800
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