Decision Analysis
Decision Analysis
MGS 3100
Business Analysis
i
l i
y A Rational and Systematic Approach to Decision Making
k
y Decision Making: choose the “best” from several available alternative courses of action
il bl lt
ti f ti
y Key Element is Uncertainty of the outcome
Chapter 8
Decision Analysis I
Decision Analysis—I
y We, as decision makers, control the decision
y Outcome of the decision is uncertain to and uncontrolled by decision maker (it is controlled by nature)
Decision Analysis
Example of Decision Analysis
Example of Decision Analysis
Components of Decision Problem
ou a e $ 0,000 o
est g o e o t e t ee
You have $10,000 for investing in one of the three options: Stock, Mutual Fund, and CD. What is the best choice?
y Alternative Actions—Decisions
y There are several alternatives from which we want to choose the best
y States of Nature—Outcomes
y There are several possible outcomes but which one will occur is uncertain to us
y Payoffs
y Numerical (monetary) value representing the (
y)
p
g
consequence of a particular alternative action we choose and a state of nature that occurs later on
Question: Do you know all the choices?
Do you know the best choice?
What is the uncertainty?
How do you make your choice? Decision Analysis
2
3
Decision Analysis
4
A E
l
An Example
Payoff Table
State of Nature
State of Nature
S2
…
Sm
r12
r1m
…
S1
r11
A2
r21
r22
…
r2m
…
…
…
…
…
An
rn1
rn2
…
rnm
S1
Rain
Alte
ernative
e
Alternative
A1
S2
No Rain
Outcome (A1S1)
Don’t gget wet but a
little inconvenient.
(80)
Outcome (A2S1)
A2
No Umbrella Get wet (and
possibly get sick)
( 40)
(-40)
A1
Umbrella
Outcome (A1S2)
Cumbersome and
inconvenient
(-20)
Outcome (A2S2)
The best!
(100)
Decision Analysis
Decision Analysis
Decision Making Under Certaint
Decision Making Under Certainty
Three Classes of Decision Models
Decision Variable
U it tto b
Units
build
ild
y Decision Making Under Certainty
y Only one state of nature (or we know with 100% sure what will happen)
pp )
y Decision Making Under Uncertainty (ignorance)
y Several possible states of nature, but we have no idea about the likelihood of each possible state
Parameter Estimates
Costt tto b
C
build
ild (/unit)
(/ it)
Revenue (/unit)
Demand (units)
y Decision Making Under Risk
y Several possible states of nature, and we have an estimate of the probability for each state
Decision Analysis
6
5
7
Decision Analysis
150
$
$
6 000
6,000
14,000
250
Consequence Variables
Total Revenue
T t l Cost
Total
C t
$ 2,100,000
$ 900,000
900 000
Performance Measure
Net Re
Revenue
en e
$ 1,200,000
1 200 000
8
Th N
d M
d l
The
Newsvendor
Model
Decision Making Under Ignorance
y the AJC newspapers
p p for 40 cents
A newsvendor can buy
each and sell them for 75 cents.
y Maximax (Assume the Best State of Nature)
(
)
y Select alternative that maximizes the maximum payoff (expect the best outcome optimistic)
(expect the best outcome‐‐
p p before he knows
However,, he must buyy the papers
how many he can actually sell. If he buys more papers
than he can sell, he disposes of the excess at no
additional cost. If he does not buy enough papers, he
loses potential sales now and possibly in the future.
y Maximin (Assume the Worst State of Nature)
y Select alternative that maximizes the minimum payoff (expect the worst situation‐‐pessimistic)
y LaPlace (Assume Equal Likely States of Nature)
(
q
y
)
y Select alternative with the best average payoff
Suppose that the loss of future sales is captured by a
loss of goodwill cost of 50 cents per unsatisfied
customer.
t
Assume
A
that
th t the
th maximum
i
demand
d
d is
i 3.
3
Decision Analysis
9
d
ff bl
Newsvendor Payoff Table
Order
quantity
Decision Analysis
10
l Newsboy
b Problem
Example:
Payoff Table
Payoff Table
Demand
0
1
2
3
State of Nature (Demand)
0
1
Alternative
(Order)
0
1
2
3
0
0
-50
-100
-150
1
-40
35
-15
-65
2
-80
-5
70
20
3
-120
-45
30
105
2
3
Payoff = 75(# sold) ‐ 40(# ordered) ‐ 50(unmet demand)
where (# sold) = MIN{demand, order quantity}
q
y
(unmet demand) = MAX{0, (demand ‐ order quantity)}
Decision Analysis
Decision Analysis
11
12
E
l Newsboy
N
b Problem
P bl
Example:
Example: Newsboy Problem
Maximax Criterion
Maximin Criterion
State of Nature (Demand)
State of Nature (Demand)
Alternative
(Order)
0
1
2
3
Max
Alternative
(Order)
0
1
2
3
Min
0
0
-50
-100
-150
0
0
0
-50
-100
-150
-150
1
-40
35
-15
-65
35
1*
-40
35
-15
-65
-65*
2
-80
-5
70
20
70
2
-80
-5
70
20
-80
3*
-120
-45
30
105
105*
3
-120
-45
30
105
-120
Decision Analysis
13
14
Decision Making Under Risk
Example: Newsboy Problem
LaPlace Criterion
• In this situation,
situation we have more information about
the uncertainty—probability
State of Nature (Demand)
Alternative
(Order)
0
1
2
3
Mean
0
0
-50
-100
-150
1
-40
35
-15
2*
-80
-5
3
-120
-45
Decision Analysis
Decision Analysis
State of Nature
S2
…
r12
…
-75
Alternative
A1
S1
r11
-65
-21.25
A2
r21
r22
…
r2m
70
20
1.25*
…
…
…
…
…
30
105
-7.5
An
rn1
rn2
…
rnm
Probability
p1
p2
Sm
r1m
pm
15
Decision Analysis
16
Decision Making Under Risk
Decision Making Under Risk
Example: Newsboy Problem
Expected Return
y Maximize Expected Return
Maximize Expected Return* (ER)
ERi = ∑ (pj × rij) = p1ri1 + p2ri2 +…+ pmrim
State of Nature (Demand)
Alternative
((Order))
0
1
2
3
ER
0
0
-50
-100
-150
-85
1
-40
40
35
-15
15
-65
65
-12.5
12 5
2*
-80
-5
70
20
22.5*
3
-120
-45
30
105
7.5
Probability
y
0.1
0.3
0.4
0.2
Where ERi = Expected return if choosing the ith
alternative ((Ai)), (i =
( 1, 2, …, n))
pj = The probability of state j (Sj)
rij = The payoff if we choose alternative Ai
and Sj state of nature occurs (j=1, …, m)
* Also referred to as Expected Value (EV) or Expected
Monetary Value (EMV)
Decision Analysis
18
17
Expected Value of Perfect Information
Expected Value of Perfect Information
Example: Newsboy Problem
Calculate EVPI
y If we could have the perfect information regarding the state of nature, we could improve our decision. EVPI measures how much better we could do if we were always given the perfect information
y EVPI also measures the maximum worth (value) of the “Perfect Information” that we should pay for in p y
order to improve our decisions
EVPI = ER w/ perfect info – ER w/o perfect info.
EVPI = ER w/ perfect info. –
ER w/o perfect info
y ER w/ perfect info (EVUPI or EVwPI) = ∑ pj × max(rij)
y ER w/o perfect info. (EVUII ) = max(ERi) = max(∑ pj × rij) Decision Analysis
State of Nature (Demand)
Alternative
((Order))
0
1
2
3
ER
0
0
-50
-100
-150
-85
1
-40
35
-15
-65
-12.5
2
-80
-5
70
20
22.5
3
-120
-45
30
105
7.5
Best
0
35
70
105
59.5
Probability
0.1
0.3
0.4
0.2
37.0
Decision Analysis
19
ER w/o PI
ER w/ PI
EVPI
20
Spreadsheet for Calculating EVPI
1
2
3
4
5
6
7
8
9
10
11
12
13
A
B
C
D
E
Demand
Order Quantity
0
1
2
3
0
0
-50
-100
-150
1
-40
35
-15
-65
2
-80
-5
70
20
3
-120
-45
30
105
Probabilities
0.1
0.3
0.4
0.2
Best
=MXA(B3:B6) =MXA(C3:C6) =MXA(D3:D6) =MXA(E3:E6)
Decision Analysis
EV w PI
EV w/o PI
EVPI
F
Expected Return
=SUMPRODUCT(B3:E3,$B$7:$E$7)
=SUMPRODUCT(B4:E4,$B$7:$E$7)
=SUMPRODUCT(B5:E5,$B$7:$E$7)
=SUMPRODUCT(B6:E6,$B$7:$E$7)
=SUMPRODUCT(B8:E8,$B$7:$E$7)
=MAX(F3:F6)
=F10-F11
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