Decision Analysis

Decision Analysis

represents a general approach to decision making

which is suitable for a wide range of projects
management decisions, including:

Capacity product and

planning service design

location equipment
planning selection

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 Problem Formulation

A decision problem is characterized by decision

alternatives, states of nature, and resulting payoffs.

The decision alternatives are the different possible,

feasible strategies the decision maker can employ.

The states of nature refer to future events, not

under the control of the decision maker, which
may occur.

For every decision alternative and state of nature,

there is a resulting payoff.

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 Payoff Tables

The consequence resulting from a specific combination

of a decision alternative and a state of nature is a
payoff.

A table showing payoffs for all combinations of

decision alternatives and states of nature is a payoff
table.

Payoffs can be expressed in terms of profit, cost, time,

distance or any other appropriate measure.

A decision is said to dominate another decision if the

payoff of the first is greater than the payoff of the
other.
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 PDC Condominium Project Example

PDC is planning building a condominium complex with three alternatives:

• D1: small complex
• D2: medium complex
• D3: large complex
There may be a strong demand or a weak demand

A payoff table was constructed based on expected profits for each

alternative and each state of nature

There may be probabilities associated with each state of nature

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 Decision Tree

A decision tree is a visual representation of the decision

problem choices, consequences and opportunities.

Each decision tree has two types of nodes; round nodes

correspond to the states of nature while square nodes
correspond to the decision alternatives.

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 Tree

Box is used to show a choice that the

manager has to make.

Circle is used to show that a probability

outcome will occur.

Lines connect outcomes to their choice

or probability outcome.

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PDC Example – Decision Tree

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 Decision Making without Probabilities

Three commonly used criteria for decision making

when probability information regarding the
likelihood of the states of nature is unavailable are:
• the optimistic approach (Maximax)
• the conservative approach (Maximini)

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 Optimistic Approach

The optimistic approach would be used by an

optimistic decision maker.

The decision with the largest possible payoff is

chosen.

If the payoff table was in terms of costs, the decision

with the lowest cost would be chosen.

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 Conservative Approach

A conservative decision maker.

For each decision the minimum payoff is listed and then the
decision corresponding to the maximum of these minimum
payoffs is selected. (Hence, the minimum possible payoff is
maximized.)
If the payoff was in terms of costs, the maximum costs would
be determined for each decision and then the decision
corresponding to the minimum of these maximum costs is
selected. (Hence, the maximum possible cost is minimized.)

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 Example

Consider the following problem with three

decision alternatives and three states of nature with
the following payoff table representing profits:

States of Nature
s1 s2 s3

d1 4 4 -2
Decisions d2 0 3 -1
d3 1 5 -3

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 Example: Optimistic Approach

An optimistic decision maker would use the

optimistic (maximax) approach. We choose the
decision that has the largest single value in the
payoff table.

Maximum
Decision Payoff
Maximax d1 4 Maximax
decision d2 3 payoff
d3 5

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 Example: Conservative Approach

A conservative decision maker would use the

conservative (maximin) approach. List the minimum
payoff for each decision. Choose the decision with
the maximum of these minimum payoffs.

Minimum
Maximin Decision Payoff Maximin
decision d1 -2 payoff
d2 -1
d3 -3

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 Decision Making with Probabilities

Expected Value Approach

• If probabilistic information regarding the states
of nature is available, one may use the expected
value (EV) approach.

• Here the expected return for each decision is

calculated by summing the products of the
payoff under each state of nature and the
probability of the respective state of nature
occurring.

• The decision yielding the best expected return is

chosen.
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 Expected Value of a Decision Alternative

The expected value of a decision alternative is the

sum of weighted payoffs for the decision alternative.

The expected value (EV) of decision alternative di is

defined as:
N
EV( d i ) =  P( s j )Vij
j =1

where: N = the number of states of nature

P(sj ) = the probability of state of nature sj
Vij = the payoff corresponding to decision
alternative di and state of nature sj

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 Example: Burger King

Burger King Restaurant is considering opening a new

restaurant on Main Street. It has three different
models, each with a different seating capacity.
Burger King estimates that the average number of
customers per hour will be 80, 100 or 120 with a
probability of 0.4, 0.2 or 0.4, respectively. The payoff
table for the three models is below

Average Number of Customers Per Hour

s1 = 80 s2 = 100 s3 = 120

Model A $10,000 $15,000 $14,000

Model B $ 8,000 $18,000 $12,000
Model C $ 6,000 $16,000 $21,000
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 Expected Value Approach

Calculate the expected value for each decision.

The decision tree on the next slide can assist in this
calculation. Here d1, d2, d3 represent the decision
alternatives of models A, B, C, and s1, s2, s3 represent
the states of nature of 80, 100, and 120.

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 Decision Tree

Payoffs
s1 .4
10,000
s2 .2
2 s3 15,000
.4
d1 14,000
s1 .4
d2 8,000
1 s2 .2
3 18,000
d3 s3 .4
12,000
s1 .4
6,000
s2 .2
4 16,000
s3
.4
21,000

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 Expected Value for Each Decision

EV = .4(10,000) + .2(15,000) + .4(14,000)

d1 = $12,600
2

EV = .4(8,000) + .2(18,000) + .4(12,000)

Model B d2 = $11,600
1 3

d3 EV = .4(6,000) + .2(16,000) + .4(21,000)

= $14,000
4

Choose the model with largest EV, Model C.

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 Expected Value of Perfect Information

The expected value of perfect information (EVPI) is

the increase in the expected profit that would result if
one knew with certainty which state of nature would
occur.

The EVPI provides an upper bound on the expected

value of any sample or survey information.

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 Expected Value of Perfect Information

EVPI Calculation
• Step 1:
Determine the optimal return corresponding to
each state of nature.

• Step 2:
Compute the expected value of these optimal
returns.

• Step 3:
Subtract the EV of the optimal decision from the
amount determined in step (2).

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 Expected Value of Perfect Information

Calculate the expected value for the optimum payoff for

each state of nature and subtract the EV of the optimal
decision.

EV = 14,000
Potential EV with perfect information =
= .4(10,000) + .2(18,000) + .4(21,000)

EVPI= .4(10,000) + .2(18,000) + .4(21,000) - 14,000 = $2,000

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 Example

FCC has a new product idea. Managers believe that

there is 20% chance that sales will be large, 55% that
sales will be moderate and 25% chance that sales will be
low.

Because the idea is risky, FCC is not sure whether to

produce and sell the product itself or license it to
another company and collect a royalty on all sales.

If FCC produces the product itself, managers believe

that the present value of future profits will be 26 million
$ if it is large, 10 million $ if it is moderate, and a loss of
6 million $ if it is low.

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FCC can license the product for 3 years to another
company and receive a royalty, which will be 8 million
$, 3 million $ or 0 $, according to sales (20% large, 55%
moderate and 25% low).

After 3 years, FCC could renew the license and receive

another 8 million $, 3 million $ or 0 $ with certainty.
Alternatively, FCC could take over the production and
earn an additional 11 million $ if sales are large and 4
million $ if they are moderate.

1. Determine the best strategy for FCC.

2. Suppose that for 2 million $ FCC could determine in
advance, with complete accuracy, what the sales will
be . Should FCC buy this information?
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 Payoffs
Decision Tree
+8 +8
+19
4
+8 +11
+3+3
+7.65 +7
2 Moderate .55
5
+3+4
+9.20
0
1
6 License +0+0

+9.20
+26
3 Moderate .55
+10
-6
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1. The best strategy for FCC is to produce the product
itself.

2. Payoff without information = 9.20 million $

Payoff with information = 26×0.20 + 10×0.55 + 0×0.25
= 10.7 million $

EVPI = 10.7 – 9.20 = 1.5 million $

So it is better for FCC not to buy the information.

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