1 decision making admi 6510 decision analysis models key sources: data analysis and decision making...
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Decision Making ADMI
6510Decision 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• Basic concepts• Payoff table• Decision making• Expected value DA models• Decision trees
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
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Data
Forecast and Probabilities
Forecast Models
Decision Alternatives
Model
Data
Cost AnalysisModel
Decision Options
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.
Basics
6 http://www.dilbert.com/
Payoff tables
• Decisions have an associated sets of costs/profits.
• States of nature have an effect on those costs, profits, … performance level.
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State of nature 1
State of nature 2
State of nature 3
Decision option 1 $ $ $
Decision option 2 $ $ $
Decision option 3 $ $ $
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
sn1 sn2 sn3
d1 190 120 130
d2 90 140 200
d3 70 150 300
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Costs
Optimistic: d3
Decision making
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sn1 sn2 sn3 max cost
d1 190 120 130 190
d2 90 140 200 200
d3 70 150 300 300
Conservative: d1
– For each decision the worst result is listed.– Select the best of the worst results.
Decision making
– 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.
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sn1 sn2 sn3
d1 190 120 130
d2 90 140 200
d3 70 150 300
Minimize Maximum Regret
sn1 sn2 sn3 Max. Regret
d1 120 0 0 120
d2 20 20 70 70
d3 0 30 170 170
MinMax: d2
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.
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
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Use A only
Use B only
Use both
Vendor A deliversVendor A fails to deliverVendor B deliversVendor B fails to deliver
Vendor A delivers and Vendor B deliversVendor A delivers, Vendor B failsVendor 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
Requirement per cycle is 1,000 units.Loss costs = $400/unit not available.
Decision trees – example• Each decision has an expected value based on
the applicable SNs.
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Use A only
Use B only
Use both
A delivers
A fails to deliver
B delivers
B fails to deliver
A delivers & B delivers
A delivers, B fails
A fails, B delivers
Both vendors fail
EV = 96% ($100 x 1,000) + 4%($400 x 1,000)
EV = 92% ($95 x 1,000) + 8%($400 x 1,000)
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)
$112,000
$119,400
$112,244
Decision trees – example• Sensitivity to Loss cost
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80,000
90,000
100,000
110,000
120,000
130,000
140,000
150,000
160,000
0 100 200 300 400 500 600 700 800Loss cost/ unit
A
B
A&B