Operations
Management
Decision-Making Tools
Module A
A-1
Outline
Decision Making & Models.
Decision Tables.
Decision making under uncertainty.
 Decision making under risk.
 Expected value of perfect information (EVPI).

Decision Trees.
A-2
The Decision-Making Process
Quantitative Analysis
Problem
Logic
Historical Data
Marketing Research
Scientific Analysis
Modeling
Qualitative Analysis
Emotions
Intuition
Personal Experience
and Motivation
Rumors
A-3
Decision
Models and Scientific Management
 Can Help Managers to:
 Gain deeper insights into the business.
 Make better decisions!
 Better assess
alternative plans and actions.
 Quantify, reduce and understand the
uncertainty surrounding business plans
and actions.
A-4
Steps to Good Decisions
 Define problem and influencing factors.
 Establish decision criteria.
 Select decision-making tool (model).
 Identify and evaluate alternatives using
decision-making tool (model).
 Select best alternative.
 Implement decision.
 Evaluate the outcome.
A-5
Benefits of Models
 Allow better and faster decisions.
 Less expensive and disruptive than
experimenting with the real world system.
 Allow managers to ask “What if…?” questions.
 Force a consistent and systematic approach to
the analysis of problems.

Require managers to be specific about constraints and
goals.
A-6
Limitations of Models
 May be expensive and time-consuming to develop
and test.
 May be unused, misused or misunderstood (and
feared!).

Due to mathematical and logical complexity.
 May downplay the value of qualitative
information.
 May use assumptions that oversimplify the real
world.
A-7
Decision Theory
Terms:
Alternative: Course of action or choice.
Decision-maker chooses among alternatives.
State of nature: An occurrence over which the
decision maker has no control.
A-8
Decision Table
States of Nature
State 1
State 2
Alternative 1
Outcome 1
Outcome 2
Alternative 2
Outcome 3
Outcome 4
A-9
Example - Decision Making Under
Uncertainty
A firm has two options for expanding production of a product: (1)
construct a large plant; or (2) construct a small plant. Whether or not
the firm expands, the future market for the product will be either
favorable or unfavorable.
If a large plant is constructed and the market is favorable, then the
result is a profit of $200,000. If a large plant is constructed and the
market is unfavorable, then the result is a loss of $180,000.
If a small plant is constructed and the market is favorable, then the
result is a profit of $100,000. If a small plant is constructed and the
market is unfavorable, then the result is a loss of $20,000. Of course,
the firm may also choose to “do nothing”, which produces no profit or
loss.
A-10
Example - Decision Making Under
Uncertainty
States of Nature
Alternatives Favorable Unfavorable
Construct
large plant
Construct
small plant
Market
$200,000
Market
-$180,000
$100,000
-$20,000
$0
$0
Do nothing
A-11
Decision Making Under
Uncertainty - Criteria
 Maximax - Choose alternative that maximizes
the maximum outcome for every alternative
(Optimistic criterion).
 Maximin - Choose alternative that maximizes
the minimum outcome for every alternative
(Pessimistic criterion).
 Expected Value - Choose alternative with the
highest expected value.
A-12
Example - Maximax
States of Nature
Alternatives Favorable Unfavorable
Construct
large plant
Construct
small plant
Market
$200,000
Market
-$180,000
$100,000
-$20,000
$0
$0
Do nothing
Maximax decision is to construct large plant.
A-13
Example - Maximin
States of Nature
Market
$200,000
Market
-$180,000
Minimum
in Row
-$180,000
$100,000
-$20,000
-$20,000
$0
$0
$0
Alternatives Favorable Unfavorable
Construct
large plant
Construct
small plant
Do nothing
Maximin decision is to do nothing.
(Maximum of minimums for each alternative)
A-14
Decision Making Under Risk
 Probabilistic decision situation.
 States of nature have probabilities of
occurrence.
 Select alternative with largest expected
value (EV).

EV = Average return for alternative if decision were
repeated many times.
A-15
Expected Value Equation
Number of states of nature
N
EV
( Ai ) =
Value of Payoff
 V i * P (V i )
Probability of payoff
i =1
= V 1 * P (V 1 ) + V 2 * P (V 2 ) + ... +V N * P (V N )
Alternative i
A-16
Example - Expected Value
Suppose: Probability of favorable market = 0.5
Probability of unfavorable market = 0.5
States of Nature
Market
$200,000
Market
-$180,000
Expected
Value
$10,000
$100,000
-$20,000
$40,000
$0
$0
Alternatives Favorable Unfavorable
Construct
large plant
Construct
small plant
Do nothing
Decision is to “Construct small plant”.
A-17
$0
Example - Expected Value
Suppose: Probability of favorable market = 0.7
Probability of unfavorable market = 0.3
States of Nature
Market
$200,000
Market
-$180,000
Expected
Value
$86,000
$100,000
-$20,000
$64,000
$0
$0
Alternatives Favorable Unfavorable
Construct
large plant
Construct
small plant
Do nothing
Now, decision is to “Construct large plant”.
A-18
$0
Example - Expected Value
Over what range of values for probability of favorable
market is “Construct large plant” preferred?
States of Nature
Alternatives Favorable Unfavorable
Construct
large plant
Construct
small plant
Do nothing
Expected Value
Market
$200,000
Market
-$180,000
380,000x - 180,000
$100,000
-$20,000
120,000x - 20,000
$0
$0
Solve for x: 380000x-180000 > 120000x-20000
A-19
Example - Expected Value
Over what range of values for probability of favorable
market is “Construct large plant” preferred?
Solve for x: 380000x - 180000 > 120000x - 20000
x > 0.6154
So, as long as probability of a favorable market
exceeds 0.6154, then “Construct large plant”.
A-20
Expected Value of Perfect
Information (EVPI)
 EVPI places an upper bound on what one
would pay for additional information.

EVPI is the maximum you should pay to learn the
future.
 EVPI is the expected value under certainty
(EVUC) minus the maximum EV.
EVPI = EVUC - maximum EV
A-21
Expected Value Under Certainty
(EVUC)
n
EVUC =  (Best outcome for the state of nature j) * P(S j )
j =1
where:
P(Sj ) = The probability of state of nature j.
n = Number of states of nature.
A-22
Example - EVUC
States of Nature
Alternatives Favorable Unfavorable
Construct
large plant
Construct
small plant
Do nothing
Market
$200,000
Market
-$180,000
$100,000
-$20,000
$0
$0
Best outcome for Favorable Market = $200,000
Best outcome for Unfavorable Market = $0
A-23
Expected Value of Perfect
Information
Suppose: Probability of favorable market = 0.5
Probability of unfavorable market = 0.5
EVPI = EVUC - max(EV)
= ($200,000*0.50 + 0*0.50) - $40,000
= $60,000
Thus, you should be willing to pay up to $60,000 to
learn whether the market will be favorable or not.
A-24
Expected Value of Perfect
Information
Now suppose: Probability of favorable market = 0.7
Probability of unfavorable market = 0.3
EVPI = EVUC - max(EV)
= ($200,000*0.70 + 0*0.30) - $86,000
= $54,000
Now, you should be willing to pay up to $54,000 to
learn whether the market will be favorable or not.
A-25
Decision Trees
 Graphical display of decision process.
 Used for solving problems with several sets of
alternatives and states of nature (sequential
decisions).

Decision tables can not be used for more than one
decision.
 Expected Value criterion is used.
A-26
Using Decision Trees
 Define the problem.
 Draw the decision tree.
 Assign probabilities to all states of nature.
 Estimate payoffs for each combination of
alternatives and states of nature.
 Solve the problem:

Compute expected values for each state-of-nature
node moving right to left.

Select decisions that maximize expected value.
A-27
Decision Theory
Terms:
 Alternative: Course of action or choice.
 State of nature: An occurrence over which the
decision maker has no control.
Symbols used in decision tree:
 A decision node from which one of several
alternatives may be selected.
 A state of nature node out of which one state of
nature will occur.
A-28
Decision Tree
State 1
1
State 2
State 1
2
Decision
Node
State 2
Outcome 1
Outcome 2
Outcome 3
Outcome 4
State of Nature Node
A-29
Decision Tree for Example
Favorable Mkt (0.7)
Unfavorable Mkt (0.3)
Favorable Mkt (0.7)
Unfavorable Mkt (0.3)
$200,000
-$180,000
$100,000
-$20,000
$0
A-30
Decision Tree for Example Solution
$86,000
Favorable Mkt (0.7)
Unfavorable Mkt (0.3)
$64,000
Favorable Mkt (0.7)
Unfavorable Mkt (0.3)
$0
$200,000
-$180,000
$100,000
-$20,000
$0
A-31
Decision Tree Example
A firm can build a large plant or small plant initially (for a new product).
Demand for the new product will be high or low initially. The probability
of high demand is 0.6. (The probability of low demand is 0.4.)
If they build “small” and demand is “low”, the payoff is $40 million. If
they build “small” and demand is “high”, they can do nothing and payoff
is $45 million, or they can expand. If they expand, there is a 30%
chance the demand drops off and the payoff will be $35 million, and a
70% chance the demand grows and the payoff is $48 million.
If they build “large” and demand is “high”, the payoff is $60 million. If
they build “large” and demand is “low”, they can do nothing and payoff
is -$10 million, or they can reduce prices and payoff is $20 million.
Determine the best decision(s) using a decision tree.
A-32
Decision Tree Example
Three decisions:
1. Build “Large” or “Small” plant initially.
2. If build “Small” and demand is “High”, then “Expand”
or “Do nothing”.
3. If build “Large” and demand is “Low”, then decide to
“Reduce prices” or “Do nothing”.
Two states of nature:
1. Demand is “High” (0.6) or “Low” (0.4) initially.
2. If build “Small”, demand is “High”, and decision is
“Expand”, then demand “Grows” (0.7) or demand
“Drops” (0.3).
A-33
Decision Tree
Demand grows (0.7)
Demand drops (0.3)
$48
$35
2
$45
$40
1
$60
Reduce prices
3
Do nothing
A-34
$20
-$10
Decision Tree Solution
Work right to left (from end back to beginning).
Start with Decision 3:
“Reduce prices” or “Do nothing”.
Choose “Reduce prices” (20 > -10).
A-35
Decision Tree
Demand grows (0.7)
Demand drops (0.3)
$48
$35
2
$45
$40
1
$60
$20
3
Reduce prices
Do nothing
A-36
$20
-$10
Decision Tree Solution
Consider Decision 2: “Expand” or “Do nothing”.
To compare outcomes we need expected value if
we “Expand”: (48*0.7) + (35*0.3) = 44.1
Choose “Do nothing” (45 > 44.1).
A-37
Decision Tree
$44.1
Demand grows (0.7)
Demand drops (0.3)
$45
2
$45
$48
$35
$45
$40
1
$60
$20
3
Reduce prices
Do nothing
A-38
$20
-$10
Decision Tree
$44.1
Demand grows (0.7)
Demand drops (0.3)
$45
2
$45
$43
$48
$35
$45
$40
1
$60
$44
$20
3
Reduce prices
Do nothing
A-39
$20
-$10
Decision Tree Final Solution
Decisions:
1. Build “Large”.
2. If demand is “Low”, then “Reduce prices”.
Expected payoff = $44 million.
A-40
Larger Decision Tree
$10
0.4
2
0.2
0.6
0.3
$8
$12
$9
0.5
1
$11
0.4
0.6
3
0.4
0.3
0.3
A-41
$6
$12
$8
$9
$8
Larger Decision Tree - Solution
$10
$10.4
2
$10.4
0.2
$10.28
0.4
0.6
0.3
$8
$12
$9
0.5
1
$9.6
$11
0.4
0.6
$9.6
3
$8.3
0.4
0.3
0.3
A-42
$6
$12
$8
$9
$8