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CJ 316 – Research Methods in Criminal Justice
Component #3 – Research Design/Conclusion
Due by midnight on Saturday, February 24, 2018
Here you will explain the design for your proposed research.
There are 3 elements to this section.
1. Hypothesis- after your literature review and problem
statement you should have a clear thesis question
that you are intending to answer. This should be your first
sentence under this section backed up by a
few supporting details that illustrates this claim.
a. Example: Community orientated polices has been a major
contributor for decreasing crime in
inner cities. This fact has been cited throughout the literature
over the years and has been seen as
an effective strategy (Please add more details, this is just an
example).
b. Side note: You should have around 5 sentences, one stating
your hypothesis/ thesis question, and
the other sentences should involve supporting details about your
hypothesis.
2. Operationalization- Please discuss the variables that you will
be using in your study. Each study should
contain a dependent and independent variable. In addition if you
chose to use a theory to explain your
thesis question then please explain why your chose that theory.
a. Example: crime rate depends on community policing
practices. The crime rate is the dependent
variable and community policing is the independent variable.
b. In addition, please include any issues of Validity, Reliability,
or Ethics that pertain to your
operationalizing. Each of these elements should be broken off
into separate paragraphs.
3. Research design/ Data and Methods- please describe your
proposed research design. This should
include:
• The units of analysis
• Sampling frame
• Sampling procedure
• Sample size
• Methods of collection
Example:
With the evolution of the criminal justice system and its
continued reliance on technology, the electronic
monitoring system is a safer and more effective way to keep
track of criminals and reduce the recidivism of
the probationers. With probation officers under increasing
caseloads and having to keep track of more and
more probationers, the people on probation are followed less
and have less supervision while on probation.
This gives the probationers the opportunity to break their rules
with a less likely chance that the overworked
officer will catch them. The ankle electronic monitoring system
helps the officer keep track of more cases
easier and track the probationers more closely.
There are a few variables that are part of the electronic
monitoring research. The independent variable of
the research is the electronic monitoring devices and the
dependent variable is the reduction of recidivism.
The reduction of recidivism directly relates to the use of the
ankle monitoring device. With the ankle
monitor, it convinces the probationer to stick to his clean ways
because the probation officer will be notified
of the user’s actions. Without the electronic monitoring device
the people on probation could be tempted to
break their rules because the officer is overworked and sees
them less.
There are a few threats to the internal validity of this research.
The first threat is history, unknown
external events such as unexpected visits from old friends who
are against the probation rules, this would
cause them to break their probation and go back to jail. Another
threat is instrumentation, the constant
upgrade of ankle monitoring devices and the wide variety
available to the probation officers can cause a
reliability issue in the tracking of the probationers. A third
threat is the selection biases; this is a problem
because there is a higher likelihood that rich, white people will
be selected for the use of the monitoring
system. These people are less likely to recidivate due to their
social status.
There is construct validity threats as well. With this research it
has to be sure that the ankle monitoring
devices are actually the things that are reducing recidivism.
There could be other things that could cause a
reduction in recidivism, such as a group of individuals that
made a mistake once, or an over active probation
officer could keep track of the probationers so well that they
have no chance to break their probation.
Reliability can become an issue in this research. When
researching you want to make sure that the
results that are produced can yield the same result if the
experiment is done over and over in different areas.
When gathering information on whether the electronic ankle
monitoring devices actually affect the
recidivism of probationers the data needs to be reliable. The
way to avoid the reliability issues in this
experiment is to use interrater reliability. This way the results
could be compared to other results gathered
by other researchers to see if the data is reliable. Also, the test-
retest method could be applied to make sure
that the data gathered is reliable and accurate.
The research being done dose have some ethical considerations
to be dealt with. First, since it is a
research project it would have to be cleared by the Institutional
Review Board. They would make sure that
there were no issues with the project. Some issues would be that
the people being studied would be
considered special populations and thus would require informed
consent before starting the study. Another
ethical problem that could occur is asking them about what they
do on probation and trying to get the
information from them without tricking or deceiving them. If
the subjects are deceived then the data will not
be reliable.
In the data and methods section of the research design, the units
of analysis would be individuals. The
thing that is being studied are probationers, and they are people
that are the same. The sampling procedure
would be a disproportionate stratified sampling. This is the
procedure for this research because not everyone
is on probation, so it is not something common or a
representative of the population. The people for the
research have to be chosen from select cases where the people
are on probation.
The sample size of this research proposal would hopefully be
bigger than smaller. Other research on this
topic has had over fifty thousand people in their research. The
one that is proposed would have about ten
thousand participants in it. This is smaller than most of the
other sample sizes so there would be less
spurious data. But, it will have enough participants that the data
will not be skewed in one way or another.
With the methods of collection, the data would be collected
through a mostly qualitative survey. This form
of collection would be used because trying to discover whether
the electronic ankle monitoring device
actually influences people not to break their probation and
actually decrease recidivism wouldn’t require
numerical data. A longitudinal study would also be conducted
during this study; a survey would be
conducted just as the people got onto probation and when they
received the ankle monitoring system. Then
another survey would be presented to the subjects at the end of
their probation period to see the results.
There are some consequences to using this type of sample.
Using a smaller sample size can sometimes
be more accurate but has a tendency to more easily be skewed
by outliers; it can also have a higher sampling
error. A larger sample size on the other hand tends to average
out the outliers and creates a larger picture
that dose not really show the real data. Using a cross sectional
study gives a real in depth view of the
subjects during one point in time, but times always change so
the data produced can quickly become
obsolete. The longitudinal study covers the subjects over a
longer period of time so it does not become old
as quickly but does not go into as much depth as the other one
dose. Lastly, using an experiment can cause
unexpected problem among the subjects, such as the Stanford
prison experiment where the subjects ended
up suffering mental problems, causing the experiment to end
quickly. A control on the other hand can
produce results that are false. Placebos can trick people into
thinking that they are actually feeling the results
the real drug or treatment were supposed to produce.
For the surveys given to the participants, it would be broken up
into two different surveys. The first
survey would be given at the start of their probation. It would
ask on whether they had the electronic ankle
monitor as part of their probation, how long their probation is
and other questions along those lines. The
second survey would be sent to the house of the person on
probation and ask whether they felt it influenced
them to not break probation, if they thought about breaking
their probation, and whether they finished their
probation without breaking any of the rules. Assistants and
sending the surveys with a return envelope and
postage will be the methods of handing out and collecting the
surveys for this research. The positives of this
process are that the subjects don’t have to gather at a certain
place to take the survey and it is easier for
them. But, at the same time this does not make the survey seem
important and they could not fill it out. Also
the people on probation could lie on the survey skewing the
results. This format was chosen due to its easy
style to answer for the participants and would show whether the
electronic ankle monitoring devices
actually have an influence on the recidivism of the users.
The intended results from this research project would show that
the use of electronic ankle monitoring
devices used in probation actually reduces recidivism and makes
the probation officers job easier. The
device convinces the wearer that if they were to try and run
away from their sentence or to go into areas that
are off limits, the probation officer would quickly learn of it
and they would break their rules of probation
and head back to jail. With this success of reduced recidivism,
the monitoring device should be more widely
used than the amount it is now. It could help cut back crimes
and pull back the prison population which is
stressing our corrections area. The thought of someone watching
them during their probation causes the
subjects to change their habits for the better, so that by the time
they are free people their bad habits have
been changed to ones that won’t send them back to prison.
Conclusion
Please explain your intended results and the significance for
developing this study.
Sheet1AlternativesOptimistic ConditionsRealistic
ConditionsPessimistic ConditionsApartment
Building420000290000-90000Office Building240000110000-
200000Warehouse310000190000-
60000Probability0.250.650.1Fee for Survey12000Probability of
survey results positive0.52Probability of survey results
negative0.48If the analysis report results positiveOptimistic
ConditionsRealistic ConditionsPessimistic
Conditionsprobability0.520.370.11If the analysis report results
negativeOptimistic ConditionsRealistic ConditionsPessimistic
Conditionsprobability0.150.270.58
CASE PROBLEM ‘BICYCLE SHOP’ 1
Assignment 2:
Case Problem – Bicycle Shop
Tom Grady
Boston University
AD715 Quantitative and Qualitative Decision-Making
Richard Maltzman, PMP
11 MARCH 2016
CASE PROBLEM ‘BICYCLE SHOP’ 2
Table of Contents
Executive Summary
...............................................................................................
.................. 3
The Bicycle Shop Case Problem
.............................................................................................
4
Payoff Table and Decision Tree Analysis
.......................................................................... 4
Should Jerry Conduct and Use Marketing Research?
..................................................... 6
Sensitivity Analysis
...............................................................................................
............... 7
Conclusion
.................................................................................. .............
............................. 7
References
...............................................................................................
.................................. 8
APPENDIX A
...............................................................................................
............................ 9
APPENDIX B
...............................................................................................
.......................... 10
CASE PROBLEM ‘BICYCLE SHOP’ 3
Executive Summary
This managerial report aims to analyze Jerry Smith’s problem
as to whether he should
start a bicycle shop business either by opening a small shop, a
large shop or no shop at all.
Further analysis was done on whether he should engage his old
marketing professor to
conduct a marketing research study before starting his new
business venture with a fee of
$5,000. As such, payoff table, decision tree analysis and
sensitivity analysis were used in
analyzing Jerry’s problem and coming up with a decision on
which alternative to be carried
out. The result from the analysis in this managerial report
indicates that Jerry should engage
his old marketing professor to conduct a market research study
with the fee of $5,000 with
the condition that the probability of a favorable market research
is more than 0.3 as shown in
the sensitivity analysis. If the result of the market research
study is favorable, Jerry should
open a large shop as the expected monetary value (EMV) is
$45,000 and if the research result
is not favorable, Jerry should not open any shop at all as it has
the best EMV of negative
$5,000.
CASE PROBLEM ‘BICYCLE SHOP’ 4
The Bicycle Shop Case Problem
Jerry Smith had been contemplating on whether to start a new
business venture by
opening a bicycle shop in his hometown as he had found the
right building at the perfect
location to operate his business. The profit from the new
business venture will depend on the
size of the shop and whether there is a market for Jerry’s
product. As such, Jerry has to make
a few key decisions which are listed below before he could
move forward.
(1) Jerry has an alternative to either open a small shop, a big
shop or no shop at all; and
(2) Jerry could engage his old marketing professor to conduct a
marketing research study
with a fee of $5,000 before deciding the alternative stated in (1)
above.
Payoff Table and Decision Tree Analysis
As Render et al. (2015) mentioned, a good decision is a
decision that is based on
logic, considers all available data and possible alternatives as
well as applying quantitative
approach. In order to make the best decision, Jerry has done
some analysis on the profitability
of the bicycle shop. He determined that there are only two
possible outcomes – the market for
bicycles could be favorable or it could be unfavorable, both the
outcomes have a 0.5
probability. Jerry thinks that a large bicycle shop will earn
$60,000 in a favorable market or
loses $40,000 if the market is unfavorable. A small bicycle shop
will result in a $30,000
profit in a favorable market and a loss of $10,000 in an
unfavorable market. Not opening a
shop would result in $0 profit/loss in either market. The payoff
table for Jerry’s conditional
values is shown in table 1.
Alternatives
State of Nature
Favorable Market ($) Unfavorable Market ($)
Small Shop 30,000 -10,000
Large Shop 60,000 -40,000
No Shop 0 0
Probability 0.5 0.5
Table 1: Payoff Table with Conditional Values for the Bicycle
Shop
CASE PROBLEM ‘BICYCLE SHOP’ 5
Buckley and Dudley (1999) stated that in some cases where
decisions have to be
made, certain alternative choices could be clear. However, the
consequences of these choices
may not be readily apparent. As such, one possible tool that
could be use in such a situation is
the decision tree analysis whereby the payoff table could be
graphically illustrated. Figure 1
shows the payoffs and probabilities for Jerry’s decision
situation.
Figure 1: Bicycle Shop’s Decision Tree
The most popular method of making decision under risk where
a decision is made in
which several possible states of nature occurs and its
possibilities are known is by selecting
the alternative with the highest expected monetary value (EMV)
(Render et al. 2015). As
reflected in the decision tree in Figure 1, both the small shop
and large shop has the same
highest EMV of $10,000 whereas the EMV for no shop is $0.
The calculations are as follow:
EMV (small shop) = ($30,000)(0.5) + (-$10,000)(0.5) = $10,000
EMV (large shop) = ($60,000)(0.5) + (-$40,000)(0.5) =
$10,000
EMV (no shop) = ($0)(0.5) + ($0)(0.5) = $0
Jerry’s initial analysis on the payoff for the alternatives and
probability for the market
conditions yielded the same EMV for both small shop and large
shop which is $10,000. If
0.5 TreePlan.com
Favorable Market
$30,000
Small Shop $30,000
$10,000 0.5
Unfavorable Market
-$10,000
-$10,000
0.5
Favorable Market
$60,000
1 Large Shop $60,000
$10,000
$10,000 0.5
Unfavorable Market
-$40,000
-$40,000
No Shop
$0
$0
1
2
CASE PROBLEM ‘BICYCLE SHOP’ 6
Jerry uses the information from the marketing research
conducted by his old marketing
professor with a fee of $5,000, the expanded decision tree is as
shown in Figure 2 in
Appendix A. Examining the decision tree in Figure 2, it is
apparent that the best EMV is to
conduct the market research with a value of $25,000 as
compared to an EMV of $10,000 if
market research was not conducted. So the best choice would be
to conduct a market
research. If the market research result is favorable, Jerry should
open a large shop as
indicated with an EMV of $45,000. However, if the research
result is negative, Jerry should
not open any shop at all as it has the best EMV of negative
$5,000.
Should Jerry Conduct and Use Marketing Research?
As reflected in the decision tree in Figure 2, the best choice is
to conduct a marketing
research study. If Jerry were to engage his old marketing
professor to conduct the marketing
research study, it could change his situation from one of
decision making under risk to one of
decision making under certainty (Render et al. 2015). However,
before engaging his old
professor, Jerry should calculate the maximum that he would
pay for that information using
the expected value of perfect information (EVPI). The
calculation is as follows,
EVPI = Expected Value with Perfect Information (EVwPI) –
Best EMV
= [(best payoff in favorable market)(probability of favorable
market) + (best
payoff in unfavorable market)(probability of unfavorable
market)] - Best EMV
= [($60,000)(0.5) + ($0)(0.5)] - $10,000 = $20,000
Therefore, the maximum amount that Jerry should pay for the
perfect information is $20,000.
Thus, the rate of $5,000 for the service that Jerry’s professor is
charging to conduct a market
research study is reasonable and Jerry should take the
opportunity to carry out and use the
marketing research.
CASE PROBLEM ‘BICYCLE SHOP’ 7
Sensitivity Analysis
Render et al. (2015) states that “sensitivity analysis
investigates how our decision
might change given a change in the problem data”. As such, we
could use the sensitivity
analysis to evaluate the impact that a change in the probability
value of a favorable marketing
research would have on the decision facing Jerry since he is
unsure that the 0.6 probability of
a favorable marketing research result is correct.
In order to compute the sensitivity of the data, let ‘p’ be the
probability of the
favorable market research results and ‘1 – p’ is the probability
for the unfavorable results.
The equation for EMV of conducting the market research which
is node 1 is as follows,
EMV (node 1) = ($45,000)p + (-$5,000) (1 – p) = $50,000p –
$5,000
Jerry will maintain indifferent with his decision to conduct the
market research when
the EMV for node 1 (conducting market research) is the same as
the EMV of not conducting
a market research with a value of $10,000. The indifference
point is calculated as follows,
$50,000p – $5,000 = $10,000
p = $15,000 / $50,000 = 0.3
By referring to the sensitivity analysis, it indicates that the
probability of the favorable market
research has to be less than 0.3 (as shown in point 1 in the
graph of the EMV values in Figure
3 – Appendix B), in order for Jerry to change his decision to not
conduct a market research.
Conclusion
With the above analysis, Jerry can finally decide to proceed
with engaging his old
marketing professor to conduct a market research study with a
fee of $5,000 as long as the
probability of the favorable market research is more than 0.3. If
the result of the study is
favorable, than Jerry should open a large shop. However, if the
research result is negative,
Jerry should not open any shop at all.
CASE PROBLEM ‘BICYCLE SHOP’ 8
References
Buckley, J. &. (1999). How Gerber Used a Decision Tree in
Strategic Decision-Making.
Graziadio Business Review, 2(3). Retrieved from
https://gbr.pepperdine.edu/2010/08/how-gerber-used-a-decision-
tree-in-strategic-
decision-making/
Render, Stair, Hanna & Hale (2015). Quantitative Analysis for
Management, 12 Edition.
Pearson Education. Chapter 3: Decision Analysis, pages 65 - 95
CASE PROBLEM ‘BICYCLE SHOP’ 9
APPENDIX A
Figure 2: Bicycle Shop’s Decision Tree with Market Research
0.9 TreePlan.com
Favorable Market
$25,000
Small Shop $25,000
$21,000 0.1
Unfavorable Market
-$15,000
-$15,000
0.6 0.9
Favorable Market
$55,000
2 Large Shop $55,000
$45,000
$45,000 0.1
Unfavorable Market
-$45,000
-$45,000
No Shop
-$5,000
-$5,000
0.12
$25,000 Favorable Market
$25,000
Small Shop $25,000
-$10,200 0.88
Unfavorable Market
-$15,000
-$15,000
0.4 0.12
Favorable Market
$55,000
3 Large Shop $55,000
-$5,000
-$33,000 0.88
Unfavorable Market
-$45,000
-$45,000
1
$25,000
No Shop
-$5,000
-$5,000
0.5
Favorable Market
$30,000
Small Shop $30,000
$10,000 0.5
Unfavorable Market
-$10,000
-$10,000
0.5
Favorable Market
$60,000
1 Large Shop $60,000
$10,000
$10,000 0.5
Unfavorable Market
-$40,000
-$40,000
No Shop
$0
$0
Favorable
Survey Result
Unfavorable
Survey Result
Conduct
Market
Research
Do Not
Conduct
Market
Research
1
2
3
4
5
6
7
CASE PROBLEM ‘BICYCLE SHOP’ 10
APPENDIX B
Figure 3: Sensitivity Analysis for the Probability of Favorable
Market Research for the Bicycle Shop
-$10,000
$0
$10,000
$20,000
$30,000
$40,000
$50,000
0 0.5 1
EX
P
EC
TE
D
M
O
N
ET
A
R
Y
V
A
LU
E
(E
M
V
)
PROBABILITY OF FAVORABLE MARKET RESEARCH (P)
SENSITIVITY ANALYSIS - BICYCLE SHOP
Conduct Market Research Do Not Conduct Market Research
point 1
0.3
Week 5: Summary
Week 6, Lecture 6: Decision Analysis and Support in
Organizations
Bb Discussion W6: Quantitative Analysis and Decision Making
in an Organization
Preparation for Assignment 2 (Due Monday Oct-28 by 11:59pm)
– Q&A
Individual Exercise: Working with the Tutorial for AD715
“Decision Trees in TreePlan”
AD 715: Quantitative and Qualitative Decision-Making
Week 6, Class 6 (10/8/2019)
Boston University MET AD715 © Dr. Zlatev, 2019
B
C
D
1
A
AGENDA
F
B
Boston University MET AD715 © Dr. Zlatev, 2019 2
Week 6
C D
Decision making and decision analysis – an introduction
Decision making under certainty and uncertainty
- an
example
decision tree problems
1
3
4
2
F
The Six Steps in
Decision Making: Decision
Analysis Prospective
1. Clearly define the problem
at hand
2. List the possible
alternatives
3. Identify the possible
outcomes or states of
nature
4. List the payoff (typically
profit) of each
combination of
alternatives and outcomes
5. Select one of the
mathematical decision
theory models
6. Apply the model and
make your decision
Step 1:
Recognize the
Need of a Decision
Step 2:
Generate
Alternative
Step 3:
Assess
Alternative
Step 4:
Choose Among Alternatives
Step 5:
Implement the
Chosen Alternative
Step 6:
Learn from
Feedback
Decision
Making
Process
The Steps in the Managerial Decision Making Process
Decision Making and Decision Analysis – An Introduction
4
B 1
Boston University MET AD715 © Dr. Zlatev, 2019
Demonstration of the Decision Making
Process as a Step-By-Step Analytical Approach
Step 3 – Identify possible outcomes or
states of nature
• The market could be favorable or
unfavorable
Step 5 – Select the decision model
• Depends on the environment
and amount of risk and
uncertainty
Decision Making and Decision Analysis – An Introduction
Business Running Case:
Thompson Lumber Company
Step 1 – Define the problem
• Consider expanding by
manufacturing and marketing a new
product – backyard storage sheds
Step 2 – List possible alternatives
• Construct a large new plant
• Construct a small new plant
• Do not develop the new
product line
Step 4 – List the payoffs
• Identify conditional values for the
profits for large plant, small plant,
and no development for the two
possible market conditions
Step 6 – Apply the model to the
data
5
B 1
Boston University MET AD715 © Dr. Zlatev, 2019
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
Construct a large plant 200,000 –180,000
Construct a small plant 100,000 –20,000
Do nothing 0 0
Decision Making and Decision Analysis – An Introduction
Business Running Case:
Thompson Lumber Company
Step 3 – Identify possible outcomes or
states of nature
• The market could be favorable or
unfavorable
Step 2 – List possible alternatives
• Construct a large new plant
• Construct a small new plant
• Do not develop the new
product line
States of Nature:
Outcomes over
which the decision
makers has little
or no control
Decision Table (Payoff Table)
with Conditional Values
The easiest way to present
the combination of
decision alternatives,
possible states of nature,
and conditional values for
each one of the possible
decision alternatives and
states of nature is called
decision table or payoff
table.
6
B 1
Boston University MET AD715 © Dr. Zlatev, 2019
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
Construct a large plant 200,000 –180,000
Construct a small plant 100,000 –20,000
Do nothing 0 0
Decision Table (Payoff Table) with Conditional Values
Decision Making and Decision Analysis – An Introduction
Business Running Case:
Thompson Lumber Company
Conditional Values:
Possible combination of
alternatives and outcomes,
also called payoffs.
Payoffs can be based on
money or any appropriate
means of measuring
benefits.
Step 4 – List the payoffs
• Identify conditional values
for the profits for large
plant, small plant, and no
development for the two
possible market conditions
Net profit of $200,000 is a conditional value
because receiving the money is conditional
upon both building a large factory and
having a good (favorable) market
Net loss of $180,000 is a conditional value
because receiving the money is conditional
upon both building a large factory and
having a unfavorable market
7
B 1
Boston University MET AD715 © Dr. Zlatev, 2019
Types of Decision-Making Environments
• Decision making under certainty
– The decision maker knows with certainty the consequences of
every alternative or decision choice
• Decision making under uncertainty
– The decision maker does not know the probabilities of the
various
outcomes
• Decision making under risk
– The decision maker knows the probabilities of the various
outcomes
Decision Making and Decision Analysis – An Introduction
8
B 1
Boston University MET AD715 © Dr. Zlatev, 2019
Decision Making Under Certainty
9
Example:
You have $10,000 to invest for a one year period
Existing alternatives to invest in two equally secure and
guaranteed investments:
Consequences
(Return after 1 year in interest)
• Alternative #1 is to open a saving account paying 4% interest
$400
• Alternative #2 is to invest in a government Treasury bond
paying 6% interest $600
Decision Choice: Select Alternative #2 ($600 > $400)
The decision makers know with certainty the
consequence of every alternative or decision choice
B 2
Boston University MET AD715 © Dr. Zlatev, 2019
Decision Making Under Uncertainty
Criteria for making decisions under uncertainty
1. Maximax (optimistic)
2. Maximin (pessimistic)
3. Criterion of realism (Hurwicz)
4. Equally likely (Laplace)
5. Minimax regret
10
B 2
Boston University MET AD715 © Dr. Zlatev, 2019
Optimistic
Used to find the alternative that maximizes the
maximum payoff – maximax criterion
– Locate the maximum payoff for each alternative
– Select the alternative with the maximum
number
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
MAXIMUM
IN A ROW ($)
Construct a
large plant
200,000 –180,000 200,000
Construct a
small plant
100,000 –20,000 100,000
Do nothing 0 0 0
Maximax Decision
Maximax
11
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
MINIMUM IN
A ROW ($)
Construct a
large plant
200,000 –180,000 -180,000
Construct a
small plant
100,000 –20,000 -20,000
Do nothing 0 0 0
Maximin
Business Running Case: Thompson Lumber Company
Maximin Decision
Used to find the alternative that maximizes the
minimum payoff – maximin criterion
– Locate the minimum payoff for each alternative
– Select the alternative with the maximum
number
Pessimistic
Decision Making Under Uncer
B 2
Boston University MET AD715 © Dr. Zlatev, 2019
Criterion of Realism (Hurwicz)
Often called weighted average
– Compromise between optimism and pessimism
– Select a coefficient of realism ɑ, with 0 ≤ a ≤ 1
a = 1 is perfectly optimistic
a = 0 is perfectly pessimistic
– Compute the weighted averages for each
alternative
– Select the alternative with the highest value
–
12
nt alternative using ɑ = 0.8
(0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000
(0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
CRITERION
OF REALISM
(a = 0.8) $
Construct a
large plant
200,000 –180,000 124,000
Construct a
small plant
100,000 –20,000 76,000
Do nothing 0 0 0
Criterion of Realism Decision
Realism
Business Running Case:
Thompson Lumber Company
Decision Making
Decision B 2
Boston University MET AD715 © Dr. Zlatev, 2019
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
ROW
AVERAGE ($)
Construct a
large plant
200,000 –180,000 10,000
Construct a
small plant
100,000 –20,000 40,000
Do nothing 0 0 0
Equally Likely (Laplace)
Considers all the payoffs for each alternative
– Find the average payoff for each alternative
– Select the alternative with the highest average
Equally Likely Decision
Equally likely
13
Decision Making Under Uncertainty
Business Running Case:
Thompson Lumber Company
Boston University MET AD715 © Dr. Zlatev, 2019
Minimax Regret
fference between
the optimal profit and actual payoff for a decision
1. Create an opportunity loss table by determining the
opportunity loss from not choosing the best alternative
2. Calculate opportunity loss by subtracting each payoff in
the column from the best payoff in the column
3. Find the maximum opportunity loss for each alternative
and pick the alternative with the minimum number
14
Decision Making Under Uncertainty
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
Construct a
large plant
200,000 - 200,000 0 – (–180,000)
Construct a
small plant
200,000 - 100,000 0 – (–20,000)
Do nothing 200,000 - 0 0 - 0
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
Construct a
large plant
0 180,000
Construct a
small plant
100,000 20,000
Do nothing 200,000 0
Business Running Case:
Thompson Lumber Company Determining Opportunity Losses
Opportunity Loss Table
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
MAXIMUM
IN A ROW
($)
Construct a
large plant
0 180,000 180,000
Construct a
small plant
100,000 20,000 100,000
Do nothing 200,000 0 200,000
Minimax Decision Using Opportunity Loss
Minimax
(Opportunity Loss)
B 2
Boston University MET AD715 © Dr. Zlatev, 2019
Decision Making Under Risk
Expected Monetary Value (EMV)
When there are several possible states of nature and the
probabilities associated with each possible state are
known
– Most popular method – choose the alternative
with the highest expected monetary value (EMV)
EMV(alternative) = X iP(X i )å
where
Xi = payoff for the alternative in state of nature i
P(Xi) =probability of achieving payoff Xi
(i.e., probability of state of nature i)
∑ = summation symbol
15
Expanding the equation
EMV (alternative i) = (payoff of first state of nature)
x (probability of first state of nature)
+ (payoff of second state of nature)
x (probability of second state of nature)
+ … + (payoff of last state of nature)
x (probability of last state of nature)
Boston University MET AD715 © Dr. Zlatev, 2019
• Each market outcome has a probability of
occurrence of 0.50
• Which alternative would give the highest EMV?
EMV (large plant) = ($200,000)(0.5) + (–$180,000)(0.5)
= $10,000
EMV (small plant) = ($100,000)(0.5) + (–$20,000)(0.5)
= $40,000
EMV (do nothing) = ($0)(0.5) + ($0)(0.5)
= $0
Business Running Case:
Thompson Lumber Company (EMV)
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($) EMV ($)
Construct a
large plant
200,000 –180,000 10,000
Construct a
small plant
100,000 –20,000 40,000
Do nothing 0 0 0
Probabilities 0.5 0.5
Decision Table with Probabilities and EMVs
Best EMV
Decision Making Under Risk
16
EMVB 3
Boston University MET AD715 © Dr. Zlatev, 2019
Expected Value of Perfect Information (EVPI)
EVPI places an upper bound on what you
should pay for additional information
EVwPI is the long run average return if we have
perfect information before a decision is made
EVwPI = ∑(best payoff in state of nature i) (probability of state
of nature i)
Decision Making Under Risk
Expanded EVwPI becomes EVwPI = (best payoff for first state
of nature)
x (probability of first state of nature)
+ (best payoff for second state of nature)
x (probability of second state of nature)
+ … + (best payoff for last state of nature)
x (probability of last state of nature)
EVPI = EVwPI – Best EMV
and
17
Boston University MET AD715 © Dr. Zlatev, 2019
• Scientific Marketing, Inc. offers analysis
that will provide certainty about market
conditions (favorable)
• Additional information will cost $65,000
Business Running Case: Thompson Lumber Company (EVPI)
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($) EMV ($)
Construct a
large plant
200,000 –180,000 10,000
Construct a
small plant
100,000 –20,000 40,000
Do nothing 0 0 0
Probabilities 0.5 0.5
With Perfect
Information 200,000 0 100,000
Decision Table with Perfect Information
Best EVwPI
Best EMV The maximum EMV without additional
information is $40,000
EVwPI = $200,000 x 0.5 + $0 x 0.5 = $100,000
where $200,000 is best payoff for first state of nature
$0 is the best payoff for second state of nature
EVPI = EVwPI – Best EMV = $100,000 - $40,000 = $60,000
Therefore, the maximum Thompson should
pay for the additional information is $60,000
SOLUTION: Thompson should not pay
$65,000 for this information
Should Thompson Lumber
purchase the information?
Decision Making Under Risk
18
Boston University MET AD715 © Dr. Zlatev, 2019
Expected Opportunity Loss
Expected opportunity loss (EOL) is the cost of not picking the
best solution
– Construct an opportunity loss table
– For each alternative, multiply the opportunity loss by the
probability of
that loss for each possible outcome and add these together
– Minimum EOL will always result in the same decision as
maximum EMV
– Minimum EOL will always equal EVPI
19
Decision Making Under Risk
Business Running Case: Thompson Lumber Company
EOL (large plant) = (0.50)($0) + (0.50)($180,000) = $90,000
EOL (small plant) = (0.50)($100,000) + (0.50)($20,000) =
$60,000
EOL (do nothing) = (0.50)($200,000) + (0.50)($0) = $100,000
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
EOL
($)
Construct a
large plant
0 180,000 90,000
Construct a
small plant
100,000 20,000 60,000
Do nothing 200,000 0 100,000
Opportunity
Loss Table
Probabilities 0.5 0.5
Best EOL
EOL Table
Opportunity Loss)
B 3
Boston University MET AD715 © Dr. Zlatev, 2019
EMV & Sensitivity Analysis
EMV(large plant) = $200,000P – $180,000)(1 – P)
= $200,000P – $180,000 + $180,000P
= $380,000P – $180,000
If P = 1 then EMV = $380,000x1 - $180,000 = $200,000
If P = 0 then EMV = $380,000x0 - $180,000 = -$180,000
EMV(small plant) = $100,000P – $20,000)(1 – P)
= $100,000P – $20,000 + $20,000P
= $120,000P – $20,000
If P = 1 then EMV = $120,000x1 - $20,000 = $100,000
If P = 0 then EMV = $120,000x0 - $20,000 = -$20,000
EMV(do nothing) = $0P + 0(1 – P)
= $0
20
$300,000
$200,000
$100,000
0
–$100,000
–$200,000
EMV Values
EMV (large plant)
EMV (small plant)
EMV (do nothing)
Point 1
Point 2
.167 .615 1
Values of P
Business Running Case:
Thompson Lumber Company
B 3
Boston University MET AD715 © Dr. Zlatev, 2019
Probabilities P (1-P)
EMV & Sensitivity Analysis
EMV(large plant) = $200,000P – $180,000)(1 – P)
= $200,000P – $180,000 + $180,000P
= $380,000P – $180,000
EMV(small plant) = $100,000P – $20,000)(1 – P)
= $100,000P – $20,000 + $20,000P
= $120,000P – $20,000
EMV(do nothing) = $0P + 0(1 – P)
= $0
21
D
$300,000
$200,000
$100,000
0
–$100,000
–$200,000
EMV Values
EMV (large plant)
EMV (small plant)
EMV (do nothing)
Point 1
Point 2
.167 .615 1
Values of P
Point 1: EMV(do nothing) = EMV(small plant) Point 2:
EMV(small plant) = EMV(large plant)
0 = $120,000P - $20,000
20,000
P = ------------- = 0.167
120,000
$120,000P - $20,000 = $380,000P - $180,000
160,000
P = ------------- = 0.615
260,000
Business Running Case:
Thompson Lumber Company
B 3
Boston University MET
AD715 © Dr. Zlatev, 2019
EMV & Sensitivity Analysis
22
$300,000
$200,000
$100,000
0
–$100,000
–$200,000
EMV Values
EMV (large plant)
EMV (small plant)
EMV (do nothing)
Point 1
Point 2
.167 .615 1
Values of P
Business Running Case:
Thompson Lumber Company
BEST ALTERNATIVE
RANGE OF
P VALUES
Do nothing Less than 0.167
Construct a small plant 0.167 – 0.615
Construct a large plant Greater than 0.615
CONCLUSIONS:
B 3
Boston University MET AD715 © Dr. Zlatev, 2019
Problem (Text, p.p.75 - 77):
A department will be signing three year lease for a new copy
machine and three different machines are being considered
• For each of the machines, there is a monthly fee (incl. monthly
fee & charge per each copy)
• The department has estimated that the number of copies/Mo
could be 10,000 or 20,000 or 30,000
• The monthly cost for each machine based on the offers and the
three levels of activities is shown in the table below
Which machine should be selected?
10,000 COPIES
PER MONTH
20,000 COPIES
PER MONTH
30,000 COPIES
PER MONTH
Machine A 950 1,050 1,150
Machine B 850 1,100 1,350
Machine C 700 1,000 1,300
TABLE 3.12 – Payoff Table
23
Q/A: Costs Minimization - An ExampleB 3
Boston University MET AD715 © Dr. Zlatev, 2019
10,000
COPIES PER
MONTH
20,000
COPIES PER
MONTH
30,000
COPIES PER
MONTH
BEST PAYOFF
(MINIMUM)
WORST
PAYOFF
(MAXIMUM)
Machine A 950 1,050 1,150 950 1,150
Machine B 850 1,100 1,350 850 1,350
Machine C 700 1,000 1,300 700 1,300
TABLE 3.13 – Best and Worst Payoffs
24
Q/A: Costs Minimization - An Example
Using Best Payoff (Minimum) vs Worst Payoff (Maximum)
Using Hurwicz criteria with 70% coefficient
For each machine
Machine A: 0.7(950) + 0.3(1,150) = 1,010
Machine B: 0.7(850) + 0.3(1,350) = 1,000
Machine C: 0.7(700) + 0.3(1,300) = 880
Weighted average =
= 0.7(best payoff) + (1 – 0.7)(worst payoff)
Decision: to select machine C based on this criterion
(it has the lowest weighted average costs)
DECISIONS
B 3
Boston University MET AD715 © Dr. Zlatev, 2019
Using equally likely criteria
For each machine
Machine A: (950 + 1,050 + 1,150)/3 = 1,050
Machine B: (850 + 1,100 + 1,350)/3 = 1,100
Machine C: (700 + 1,000 + 1,300)/3 = 1,000
25
Q/A: Costs Minimization - An Example DECISIONS
10,000 COPIES
PER MONTH
20,000 COPIES
PER MONTH
30,000 COPIES
PER MONTH
Machine A 950 1,050 1,150
Machine B 850 1,100 1,350
Machine C 700 1,000 1,300
Decision: to select machine C based on this criterion
(it has the lowest average costs)
B 3
Boston University MET AD715 © Dr. Zlatev, 2019
Using EMV Criterion
USAGE PROBABILITY
10,000 0.40
20,000 0.30
30,000 0.30
Q/A: Costs Minimization - An Example DECISIONS
Assumptions for probability
for the three states of nature
(based on past records)
10,000
COPIES PER
MONTH
20,000
COPIES PER
MONTH
30,000
COPIES PER
MONTH
EMV
Machine A 950 1,050 1,150 1,040
Machine B 850 1,100 1,350 1,075
Machine C 700 1,000 1,300 970
With perfect information 700 1,000 1,150 925
Probability 0.4 0.3 0.3
TABLE 3.14
Expected Monetary Values and Expected Value with Perfect
Information
Decision: to select machine C based
on this criterion (it has the
lowest EMV)
26
B 3
Boston University MET AD715 © Dr. Zlatev, 2019
Using EVPI & Expected
Opportunity Loss Criterion
Q/A: Costs Minimization - An Example DECISIONS
Criterion
10,000
COPIES PER
MONTH
20,000
COPIES PER
MONTH
30,000
COPIES PER
MONTH
EMV
Machine A 950 1,050 1,150 1,040
Machine B 850 1,100 1,350 1,075
Machine C 700 1,000 1,300 970
With perfect information 700 1,000 1,150 925
Probability 0.4 0.3 0.3
TABLE 3.14
Expected Monetary Values and Expected Value with Perfect
Information
EVwPI = $925
Best EMV without perfect information= $970
EVPI = 970 – 925 = $45
Decision: to select machine C based
on the minimax regret
criterion (it has the
minimum of the maximum)
10,000
COPIES PER
MONTH
20,000
COPIES PER
MONTH
30,000
COPIES PER
MONTH MAXIMUM EOL
Machine A 250 50 0 250 115
Machine B 150 100 200 200 150
Machine C 0 0 150 150 45
Probability 0.4 0.3 0.3
TABLE 3.15 – Opportunity Loss Table Decision: to select
machine C based
on the EOL criterion (it has
the lowest expected
opportunity loss)
27
B 3
Boston University MET AD715 © Dr. Zlatev, 2019
Decision Trees
Any problem that can be presented in a decision table can be
graphically represented in a decision tree
– Most beneficial when a sequence of decisions must be made
– All decision trees contain decision points/nodes and state-of-
nature points/nodes
– At decision nodes one of several alternatives may be chosen
– At state-of-nature nodes one state of nature will occur
28
1. Define the problem
2. Structure or draw the decision tree
3. Assign probabilities to the states of nature
4. Estimate payoffs for each possible combination of
alternatives and states of nature
5. Solve the problem by computing expected monetary
values (EMVs) for each state of nature node
Five Steps of Decision Tree Analysis
B 4
Boston University MET AD715 © Dr. Zlatev, 2019
Structure of Decision Trees
• Trees start from left to right
• Trees represent decisions and outcomes in
sequential order
• Squares represent decision nodes
• Circles represent states of nature nodes
• Lines or branches connect the decisions nodes
and the states of nature
Decision Trees
29
B 4
Boston University MET AD715 © Dr. Zlatev, 2019
Thompson’s Decision Tree
Favorable Market
Unfavorable Market
Favorable Market
Unfavorable Market
1
Construct
Small Plant
2
FIGURE 3.2
A Decision Node
A State-of-Nature Node
Decision Trees
30
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
Construct a large plant 200,000 –180,000
Construct a small plant 100,000 –20,000
Do nothing 0 0
Decision Table (Payoff Table) with Conditional Values
Business Running Case:
Thompson Lumber Company
B 4
Boston University MET AD715 © Dr. Zlatev, 2019
Favorable Market
Unfavorable Market
Favorable Market
Unfavorable Market
1
Construct
Small Plant
2
Alternative with best
EMV is selected
FIGURE 3.3
EMV for Node 1
= $10,000
= (0.5)($200,000) + (0.5)(–$180,000)
EMV for Node 2
= $40,000
= (0.5)($100,000)
+ (0.5)(–$20,000)
Payoffs
$200,000
–$180,000
$100,000
–$20,000
$0
(0.5)
(0.5)
(0.5)
(0.5)
31
Thompson’s Decision Tree
Decision Trees
Business Running Case:
Thompson Lumber Company
B 4
Boston University MET AD715 © Dr. Zlatev, 2019
Thompson’s Complex Decision Tree
First Decision
Point
Second Decision
Point
Favorable Market (0.78)
Unfavorable Market (0.22)
Favorable Market (0.78)
Unfavorable Market (0.22)
Favorable Market (0.27)
Unfavorable Market (0.73)
Favorable Market (0.27)
Unfavorable Market (0.73)
Favorable Market (0.50)
Unfavorable Market (0.50)
Favorable Market (0.50)
Unfavorable Market (0.50)
Small
Plant
No Plant
6
7
Small
Plant
No Plant
2
3
Small
Plant
No Plant
4
5
1
Payoffs
–$190,000
$190,000
$90,000
–$30,000
–$10,000
–$180,000
$200,000
$100,000
–$20,000
$0
–$190,000
$190,000
$90,000
–$30,000
–$10,000
FIGURE 3.4
32
Decision Trees
Business Running Case: Thompson Lumber Company
Thompson’s Complex
Decision Tree
B 4
Boston University MET AD715 © Dr. Zlatev, 2019
1. Given favorable survey results
EMV(node 2) = EMV(large plant | positive survey)
= (0.78)($190,000) + (0.22)(– $190,000) = $106,400
EMV(node 3) = EMV(small plant | positive survey)
= (0.78)($90,000) + (0.22)(– $30,000) = $63,600
EMV for no plant = – $10,000
33
Decision Trees
Business Running Case: Thompson Lumber Company
2. Given negative survey results EMV(node 4) = EMV(large
plant | negative survey)
= (0.27)($190,000) + (0.73)(– $190,000) = – $87,400
EMV(node 5) = EMV(small plant | negative survey)
= (0.27)($90,000) + (0.73)(– $30,000) = $2,400
EMV for no plant = – $10,000
Thompson’s Complex
Decision Tree
B 4
Boston University MET AD715 © Dr. Zlatev, 2019
3. Expected value of the market survey EMV(node 1) =
EMV(conduct survey)
= (0.45)($106,400) + (0.55)($2,400)
= $47,880 + $1,320 = $49,200
4. Expected value no market survey EMV(node 6) = EMV(large
plant)
= (0.50)($200,000) + (0.50)(– $180,000) = $10,000
EMV(node 7) = EMV(small plant)
= (0.50)($100,000) + (0.50)(– $20,000) = $40,000
EMV for no plant = $0
The best choice is to seek marketing information
Decision Trees Thompson’s Complex
Decision Tree
34
Business Running Case: Thompson Lumber Company
B 4
Boston University MET AD715 © Dr. Zlatev, 2019
FIGURE 3.5 First Decision
Point
Second Decision
Point
Favorable Market (0.78)
Unfavorable Market (0.22)
Favorable Market (0.78)
Unfavorable Market (0.22)
Favorable Market (0.27)
Unfavorable Market (0.73)
Favorable Market (0.27)
Unfavorable Market (0.73)
Favorable Market (0.50)
Unfavorable Market (0.50)
Favorable Market (0.50)
Unfavorable Market (0.50)
Small
Plant
No Plant
6
7
Small
Plant
No Plant
2
3
Small
Plant
No Plant
4
5
1
Payoffs
–$190,000
$190,000
$90,000
–$30,000
–$10,000
–$180,000
$200,000
$100,000
–$20,000
$0
–$190,000
$190,000
$90,000
–$30,000
–$10,000
$
4
0
,0
0
0
$
2
,4
0
0
$
1
0
6
,4
0
0
$
4
9
,2
0
0
$106,400
$63,600
–$87,400
$2,400
$10,000
$40,000
Decision Trees Thompson’s Complex
Decision Tree
35
Business Running Case: Thompson Lumber Company
B 4
Boston University MET AD715 © Dr. Zlatev, 2019
Expected Value of Sample Information
Thompson wants to know the actual value of doing the survey
= (EV with SI + cost) – (EV without SI)
EVSI = ($49,200 + $10,000) – $40,000 = $19,200
EVSI = –
Expected value
with sample
information
Expected value of best
decision without sample
information
Decision Trees
36
Business Running Case: Thompson Lumber Company
B 4
Boston University MET AD715 © Dr. Zlatev, 2019
Efficiency of Sample Information
• Possibly many types of sample information available
• Different sources can be evaluated
Efficiency of sample information =
EVSI
EVPI
100%
Efficiency of sample information =
19,200
60,000
100% = 32%
Market survey is only 32% as efficient
as perfect information
Decision Trees
Business Running Case: Thompson Lumber Company
37
B 4
Boston University MET AD715 © Dr. Zlatev, 2019
Sensitivity Analysis • How sensitive are the decisions to
changes in the probabilities?
• How sensitive is our decision to the probability of a favorable
survey result?
• If the probability of a favorable result (p = .45) where to
change, would we
make the same decision?
• How much could it change before we would make a different
decision?
Decision Trees
p = probability of a favorable survey result
(1 – p) = probability of a negative survey result
EMV(node 1) = ($106,400)p +($2,400)(1 – p)
= $104,000p + $2,400
Business Running Case: Thompson Lumber Company
We are indifferent when the EMV of node 1 is the
same as the EMV of not conducting the survey
$104,000p + $2,400 = $40,000
$104,000p = $37,600
p = $37,600/$104,000 = 0.36
DECISION:
If p < 0.36, do not conduct the survey
If p > 0.36, conduct the survey
38
B 4
Boston University MET AD715 © Dr. Zlatev, 2019
39
Q/A: Using Software for Payoff Table and Decision Tree
Problems
Other Decision Tree Software (A Short List):
Tutorial ‘Decision Trees in TreePlan’
>>> v-labs (Excel 2016 Add-In ‘TreePlan’)
ASSIGNMENT 2
Task 2-4: Apply TreePlan
B 4
1. Excel Decision Tree Add-Ins
• Risk Solver Pro & Analytic Solver Pro v2016 by
FrontlineSolvers, www.solver.com
• Monte Carlo Risk Simulation, Decision Tree and Statistical
Excel Analysis Add-In by Lumenaut, www.lumenaut.com
• Decision Tree Suite by Palisade, www.palisade.com
• TreePlan by TreePlan Software, www.treeplan.com
2. Top Decision Tree Analysis Software Products 2016
(ranked by Capterra, www.capterra.com ; Filter Results: 1000+
number of users):
• pcFinancials by Performance Canvas
Financials, http://www.performancecanvas.com
• Analytica by Lumina Decision Systems,
http://www.lumina.com/
• 1000Minds (Multi-Criteria Decision-Making) by
1000minds: www.1000minds.com
• Blaze Advisor by Fico, www.fico.com
• D-Sight Collaborative Decision-Making platform by D-Sight,
http://www.d-sight.com
• Decision Lens by Decision Lens, www.decisionlens.com
• Decision Support Software by Logicnets, www.logicnets.com
• DPL 8 Direct by Syncopation, www.syncopation.com
• Spotfire by Tibco, www.tibco.com
• VisiRule by Logic Programming Associates, www.lpa.co.uk
Boston University MET AD715 © Dr. Zlatev, 2019
http://www.solver.com/
http://www.lumenaut.com/
http://www.palisade.com/
http://www.treeplan.com/
http://www.capterra.com/
http://www.performancecanvas.com/
http://www.lumina.com/
http://www.1000minds.com/
http://www.fico.com/
http://www.d-sight.com/
http://www.decisionlens.com/
http://www.logicnets.com/
http://www.syncopation.com/
http://www.tibco.com/
http://www.lpa.co.uk/
Discussion W6: Quantitative Analysis and Managerial Decisions
in an OrganizationC
Boston University MET AD715 © Dr. Zlatev, 2019 39
With the help of one or several of the recommended tutorials for
Week 6, discuss your experience and plans for applying
analytical methods in your Assignment 2 or in your current (or
targeted) profession.
Recommended discussion topics (covered in Lecture 06):
Decision making under certainty and uncertainty
Decision making under risk
Decision trees
Using software for payoff table and decision tree problems
Assignment 2: Prep-Plan
40
D
Boston University MET AD715 © Dr. Zlatev, 2019
In-Class Exercise: Task 2-1
In-Class Exercise: Task 2-2
Assignment 2: Prep-Plan
41
D
Boston University MET AD715 © Dr. Zlatev, 2019
In-Class Exercise: Task 2-3
In-Class Exercise: Task 2-4
42Boston University MET AD715 © Dr. Zlatev, 2019
Individual Exercise W6:
Working with the Tutorial for AD715 “Decision Trees in
TreePlan”
F
Targeted Outcomes:
1. Learn how to access BU MET VLAB
2. Review the Tutorial for AD15 “Decision Trees in
TreePlan”
Bb course website >>> Content >>> Tutorials
1. Review the script “Decision Trees in TreePlan”
2. Go to the VLAB, open Excel 2016, and repeat the
steps from the script (task 3)
In this course, students will be using Microsoft Excel software
applications for
Windows. As part of the tuition, all BU students can use this
software free of charge.
Click here for directions to get free access to Microsoft Excel
applications from
MET’s Virtual Labs: http://www.bu.edu/metit/pc-labs/virtual-
labs/
You will not be able to download the software using this option,
but you will be given
access to it for use during the course.
If you are first-time VLAB user, please synchronize your BU
account with the BU
Active Directory by following the recommended
procedures:
https://weblogin.bu.edu/accounts/create?_hostname=ad;_conffil
e=kpw
From the existing two VLAB connection modes, I am
recommending to select
Horizon Client: http://www.bu.edu/metit/vlabs-client/
The process of accessing and working within the VLABs is
demonstrated and
explained with the help of Video Tutorials (one for Windows,
and the other for MAC
users).
Attention: Files saved on the desktop or local drive of the
virtual lab will be deleted
after you log off. Hence, before logging off, you must save your
work on an external
source, such as Google Drive, Shared Folder, USB drive, or
email the files to
yourself. Instructions how to save files in the MET VLABs are
accessible from here:
http://www.bu.edu/metit/vlabs-client/
To Get Help, call (617) 358-5401 or send a message to
[email protected] . Please
indicate that you have a VLAB issue and include your course
number.
http://www.bu.edu/metit/pc-labs/virtual-labs/
https://weblogin.bu.edu/accounts/create?_hostname=ad;_conffil
e=kpw
http://www.bu.edu/metit/vlabs-client/
http://www.bu.edu/metit/vlabs-client/
mailto:[email protected]
A2 TextAssignment 2: Case Problem "Real Estate Development:
Select a New Project"Problem DescriptionA real estate company
is considering the development of one of the following three
possible projects: (1) an apartment building; (2) an office
building; (3) a warehouse. The amount of payoff (profit) that
could be earned by selling the estate depends on the economic
conditions, specified as: optimistic, realistic and pessimistic.
The estimated payoffs and probabilities under optimistic,
realistic and pessimistic conditions are shown as
follows:AlternativesStates of NatureOptimistic
ConditionsRealistic ConditionsPessimistic ConditionsApartment
BuildingABCOffice
BuildingDEFWarehouseGHIProbabilityxyzIn preparation for a
final decision, the company is considering the hiring of a
business analyst. If the company hires the analyst, the decision
regarding which project to develop will not be made until the
analyst presents a survey. However, the analyst is requesting an
upfront payment for the survey in the amount of Z. The
probabilities of the survey results to be positive or negative are
i and k. Summary tables, in case the company hires a business
analyst:Fee for SurveyZProbability of survey results
positiveiProbability of survey results negativek(1) If the survey
results are positive:AlternativesStates of NatureOptimistic
ConditionsRealistic ConditionsPessimistic ConditionsApartment
BuildingA - ZB - ZC - ZOffice BuildingD - ZE - ZF -
ZWarehouseG - ZH - ZI - ZProbabilitydef(2) If the survey
results are negative: AlternativesStates of NatureOptimistic
ConditionsRealistic ConditionsPessimistic ConditionsApartment
BuildingA - ZB - ZC - ZOffice BuildingD - ZE - ZF -
ZWarehouseG - ZH - ZI - ZProbabilityghnAssignment 2:
Starting ConditionsEach student will receive from the instructor
an excel file with a different dataset for payoffs (A to I) and
probabilities (x,y,z,i,k,d,e,f,g,h,n). You have to prepare and
submit a managerial report where you should answer the
question: Which one of the development projects should be
selected? And based on your estimates, should the company hire
the business analyst?Grading Points
Per:TasksAssignment#Content per Tasks10Task 2-0Students
should structure and present their Assignment 2 in the form of a
Managerial Report. The expected length of the main body (tasks
2-1 to 2-4) is up to 3 pages APA format, excluding cover page,
table of content, executive summary (task 2-5), and appendices
(screenshots of the Payoff Table, EMV Table, Sensitivity
Analysis Diagram, TreePlan Diagram of the Decision Tree).
Submission requirements: Managerial Report (word file), and
excel file with completed worksheets (iii) to (vi).1Task 2-
1Prepare payoff tables and develop a decision tree for this
problem (without probabilities and EMVs).2Task 2-2Given the
probability of all three economic conditions and using expected
monetary values (EMVs), calculate EMVs for each node and
answer the questions: (1) What's the EMV for not hiring a
business analyst and the EMV for hiring a business analyst? (2)
What is your recommendation: to hire or not to hire a business
analyst?2Task 2-3Use sensitivity analysis to define the
probability range with respect to the survey results which might
affect the decision to hire or not to hire a business analyst, draw
the sensitivity chart, and find the probability for their cross
point. 2Task 2-4Apply a software tool for the construction of a
decision tree with payoffs, probabilities, and EMVs. The
recommended tool is TreePlan: a Microsoft Excel Add-Ins (it is
preinstalled on all V-PCs of the MET V-LABs)2Task 2-
5Prepare an executive summary1List of Worksheets in the Excel
File (it should be used as a reference for different tasks of the
managerial report)(i)A2 Text(ii) Payoff Table -
Template(iii)Payoff Table -
Solution
and a sketch of a decision tree (without probability and EMVs)
--> Needed for Task 2-1(iv) EMV Calculation: use EMV as a
decision criterion for each decision nodes and states of nature
nodes, calculate the EMV for each node, and recommend
whether to hire/not to hire a business analyst --> Needed for
Task 2-2(v)Sensitivity Analysis Diagram: compute the
probability of survey results and define the range of probability
values that the real estate company would hire or not hire a
business analyst (including the probability of the cross point) --
> Needed for Task 2-3(vi)TreePlan Diagram of the Decision
Tree: use BU MET V-LAB for Excel Add-In TreePlan -->
Needed for Task 2-4
Payoff Table Template1. If the company does not hire a
business analyst:AlternativesStates of NatureEMVOptimistic
ConditionsRealistic ConditionsPessimistic ConditionsApartment
BuildingABCOffice
BuildingDEFWarehouseGHIProbabilityxyz2. If the company
hires a business analyst:Fee for SurveyZ2.1 If the analysis
report results positive:AlternativesStates of
NatureEMVOptimistic ConditionsRealistic
ConditionsPessimistic ConditionsApartment BuildingOffice
BuildingWarehouseProbabilitydef2.2 If the analysis report
results negative:AlternativesStates of NatureEMVOptimistic
ConditionsRealistic ConditionsPessimistic ConditionsApartment
BuildingOffice BuildingWarehouseProbabilityghn3. Final

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CJ 316 Research Design Explains Hypothesis, Variables, and Methods

  • 1. CJ 316 – Research Methods in Criminal Justice Component #3 – Research Design/Conclusion Due by midnight on Saturday, February 24, 2018 Here you will explain the design for your proposed research. There are 3 elements to this section. 1. Hypothesis- after your literature review and problem statement you should have a clear thesis question that you are intending to answer. This should be your first sentence under this section backed up by a few supporting details that illustrates this claim. a. Example: Community orientated polices has been a major contributor for decreasing crime in inner cities. This fact has been cited throughout the literature over the years and has been seen as an effective strategy (Please add more details, this is just an example). b. Side note: You should have around 5 sentences, one stating your hypothesis/ thesis question, and the other sentences should involve supporting details about your hypothesis.
  • 2. 2. Operationalization- Please discuss the variables that you will be using in your study. Each study should contain a dependent and independent variable. In addition if you chose to use a theory to explain your thesis question then please explain why your chose that theory. a. Example: crime rate depends on community policing practices. The crime rate is the dependent variable and community policing is the independent variable. b. In addition, please include any issues of Validity, Reliability, or Ethics that pertain to your operationalizing. Each of these elements should be broken off into separate paragraphs. 3. Research design/ Data and Methods- please describe your proposed research design. This should include: • The units of analysis • Sampling frame • Sampling procedure • Sample size • Methods of collection Example:
  • 3. With the evolution of the criminal justice system and its continued reliance on technology, the electronic monitoring system is a safer and more effective way to keep track of criminals and reduce the recidivism of the probationers. With probation officers under increasing caseloads and having to keep track of more and more probationers, the people on probation are followed less and have less supervision while on probation. This gives the probationers the opportunity to break their rules with a less likely chance that the overworked officer will catch them. The ankle electronic monitoring system helps the officer keep track of more cases easier and track the probationers more closely. There are a few variables that are part of the electronic monitoring research. The independent variable of the research is the electronic monitoring devices and the dependent variable is the reduction of recidivism. The reduction of recidivism directly relates to the use of the ankle monitoring device. With the ankle monitor, it convinces the probationer to stick to his clean ways because the probation officer will be notified of the user’s actions. Without the electronic monitoring device the people on probation could be tempted to break their rules because the officer is overworked and sees
  • 4. them less. There are a few threats to the internal validity of this research. The first threat is history, unknown external events such as unexpected visits from old friends who are against the probation rules, this would cause them to break their probation and go back to jail. Another threat is instrumentation, the constant upgrade of ankle monitoring devices and the wide variety available to the probation officers can cause a reliability issue in the tracking of the probationers. A third threat is the selection biases; this is a problem because there is a higher likelihood that rich, white people will be selected for the use of the monitoring system. These people are less likely to recidivate due to their social status. There is construct validity threats as well. With this research it has to be sure that the ankle monitoring devices are actually the things that are reducing recidivism. There could be other things that could cause a reduction in recidivism, such as a group of individuals that made a mistake once, or an over active probation officer could keep track of the probationers so well that they have no chance to break their probation.
  • 5. Reliability can become an issue in this research. When researching you want to make sure that the results that are produced can yield the same result if the experiment is done over and over in different areas. When gathering information on whether the electronic ankle monitoring devices actually affect the recidivism of probationers the data needs to be reliable. The way to avoid the reliability issues in this experiment is to use interrater reliability. This way the results could be compared to other results gathered by other researchers to see if the data is reliable. Also, the test- retest method could be applied to make sure that the data gathered is reliable and accurate. The research being done dose have some ethical considerations to be dealt with. First, since it is a research project it would have to be cleared by the Institutional Review Board. They would make sure that there were no issues with the project. Some issues would be that the people being studied would be considered special populations and thus would require informed consent before starting the study. Another ethical problem that could occur is asking them about what they do on probation and trying to get the
  • 6. information from them without tricking or deceiving them. If the subjects are deceived then the data will not be reliable. In the data and methods section of the research design, the units of analysis would be individuals. The thing that is being studied are probationers, and they are people that are the same. The sampling procedure would be a disproportionate stratified sampling. This is the procedure for this research because not everyone is on probation, so it is not something common or a representative of the population. The people for the research have to be chosen from select cases where the people are on probation. The sample size of this research proposal would hopefully be bigger than smaller. Other research on this topic has had over fifty thousand people in their research. The one that is proposed would have about ten thousand participants in it. This is smaller than most of the other sample sizes so there would be less spurious data. But, it will have enough participants that the data will not be skewed in one way or another. With the methods of collection, the data would be collected through a mostly qualitative survey. This form of collection would be used because trying to discover whether
  • 7. the electronic ankle monitoring device actually influences people not to break their probation and actually decrease recidivism wouldn’t require numerical data. A longitudinal study would also be conducted during this study; a survey would be conducted just as the people got onto probation and when they received the ankle monitoring system. Then another survey would be presented to the subjects at the end of their probation period to see the results. There are some consequences to using this type of sample. Using a smaller sample size can sometimes be more accurate but has a tendency to more easily be skewed by outliers; it can also have a higher sampling error. A larger sample size on the other hand tends to average out the outliers and creates a larger picture that dose not really show the real data. Using a cross sectional study gives a real in depth view of the subjects during one point in time, but times always change so the data produced can quickly become obsolete. The longitudinal study covers the subjects over a longer period of time so it does not become old as quickly but does not go into as much depth as the other one dose. Lastly, using an experiment can cause unexpected problem among the subjects, such as the Stanford
  • 8. prison experiment where the subjects ended up suffering mental problems, causing the experiment to end quickly. A control on the other hand can produce results that are false. Placebos can trick people into thinking that they are actually feeling the results the real drug or treatment were supposed to produce. For the surveys given to the participants, it would be broken up into two different surveys. The first survey would be given at the start of their probation. It would ask on whether they had the electronic ankle monitor as part of their probation, how long their probation is and other questions along those lines. The second survey would be sent to the house of the person on probation and ask whether they felt it influenced them to not break probation, if they thought about breaking their probation, and whether they finished their probation without breaking any of the rules. Assistants and sending the surveys with a return envelope and postage will be the methods of handing out and collecting the surveys for this research. The positives of this process are that the subjects don’t have to gather at a certain place to take the survey and it is easier for
  • 9. them. But, at the same time this does not make the survey seem important and they could not fill it out. Also the people on probation could lie on the survey skewing the results. This format was chosen due to its easy style to answer for the participants and would show whether the electronic ankle monitoring devices actually have an influence on the recidivism of the users. The intended results from this research project would show that the use of electronic ankle monitoring devices used in probation actually reduces recidivism and makes the probation officers job easier. The device convinces the wearer that if they were to try and run away from their sentence or to go into areas that are off limits, the probation officer would quickly learn of it and they would break their rules of probation and head back to jail. With this success of reduced recidivism, the monitoring device should be more widely used than the amount it is now. It could help cut back crimes and pull back the prison population which is stressing our corrections area. The thought of someone watching them during their probation causes the subjects to change their habits for the better, so that by the time they are free people their bad habits have been changed to ones that won’t send them back to prison.
  • 10. Conclusion Please explain your intended results and the significance for developing this study. Sheet1AlternativesOptimistic ConditionsRealistic ConditionsPessimistic ConditionsApartment Building420000290000-90000Office Building240000110000- 200000Warehouse310000190000- 60000Probability0.250.650.1Fee for Survey12000Probability of survey results positive0.52Probability of survey results negative0.48If the analysis report results positiveOptimistic ConditionsRealistic ConditionsPessimistic Conditionsprobability0.520.370.11If the analysis report results negativeOptimistic ConditionsRealistic ConditionsPessimistic Conditionsprobability0.150.270.58 CASE PROBLEM ‘BICYCLE SHOP’ 1
  • 11. Assignment 2: Case Problem – Bicycle Shop Tom Grady Boston University AD715 Quantitative and Qualitative Decision-Making Richard Maltzman, PMP 11 MARCH 2016 CASE PROBLEM ‘BICYCLE SHOP’ 2
  • 12. Table of Contents Executive Summary ............................................................................................... .................. 3 The Bicycle Shop Case Problem ............................................................................................. 4 Payoff Table and Decision Tree Analysis .......................................................................... 4 Should Jerry Conduct and Use Marketing Research? ..................................................... 6 Sensitivity Analysis ............................................................................................... ............... 7 Conclusion .................................................................................. ............. ............................. 7 References ............................................................................................... .................................. 8 APPENDIX A ............................................................................................... ............................ 9 APPENDIX B ............................................................................................... .......................... 10
  • 13. CASE PROBLEM ‘BICYCLE SHOP’ 3 Executive Summary This managerial report aims to analyze Jerry Smith’s problem as to whether he should start a bicycle shop business either by opening a small shop, a large shop or no shop at all. Further analysis was done on whether he should engage his old marketing professor to conduct a marketing research study before starting his new business venture with a fee of $5,000. As such, payoff table, decision tree analysis and sensitivity analysis were used in analyzing Jerry’s problem and coming up with a decision on which alternative to be carried out. The result from the analysis in this managerial report indicates that Jerry should engage his old marketing professor to conduct a market research study with the fee of $5,000 with the condition that the probability of a favorable market research
  • 14. is more than 0.3 as shown in the sensitivity analysis. If the result of the market research study is favorable, Jerry should open a large shop as the expected monetary value (EMV) is $45,000 and if the research result is not favorable, Jerry should not open any shop at all as it has the best EMV of negative $5,000. CASE PROBLEM ‘BICYCLE SHOP’ 4 The Bicycle Shop Case Problem Jerry Smith had been contemplating on whether to start a new business venture by opening a bicycle shop in his hometown as he had found the right building at the perfect location to operate his business. The profit from the new business venture will depend on the size of the shop and whether there is a market for Jerry’s product. As such, Jerry has to make
  • 15. a few key decisions which are listed below before he could move forward. (1) Jerry has an alternative to either open a small shop, a big shop or no shop at all; and (2) Jerry could engage his old marketing professor to conduct a marketing research study with a fee of $5,000 before deciding the alternative stated in (1) above. Payoff Table and Decision Tree Analysis As Render et al. (2015) mentioned, a good decision is a decision that is based on logic, considers all available data and possible alternatives as well as applying quantitative approach. In order to make the best decision, Jerry has done some analysis on the profitability of the bicycle shop. He determined that there are only two possible outcomes – the market for bicycles could be favorable or it could be unfavorable, both the outcomes have a 0.5 probability. Jerry thinks that a large bicycle shop will earn $60,000 in a favorable market or loses $40,000 if the market is unfavorable. A small bicycle shop will result in a $30,000
  • 16. profit in a favorable market and a loss of $10,000 in an unfavorable market. Not opening a shop would result in $0 profit/loss in either market. The payoff table for Jerry’s conditional values is shown in table 1. Alternatives State of Nature Favorable Market ($) Unfavorable Market ($) Small Shop 30,000 -10,000 Large Shop 60,000 -40,000 No Shop 0 0 Probability 0.5 0.5 Table 1: Payoff Table with Conditional Values for the Bicycle Shop CASE PROBLEM ‘BICYCLE SHOP’ 5 Buckley and Dudley (1999) stated that in some cases where decisions have to be made, certain alternative choices could be clear. However, the consequences of these choices may not be readily apparent. As such, one possible tool that
  • 17. could be use in such a situation is the decision tree analysis whereby the payoff table could be graphically illustrated. Figure 1 shows the payoffs and probabilities for Jerry’s decision situation. Figure 1: Bicycle Shop’s Decision Tree The most popular method of making decision under risk where a decision is made in which several possible states of nature occurs and its possibilities are known is by selecting the alternative with the highest expected monetary value (EMV) (Render et al. 2015). As reflected in the decision tree in Figure 1, both the small shop and large shop has the same highest EMV of $10,000 whereas the EMV for no shop is $0. The calculations are as follow: EMV (small shop) = ($30,000)(0.5) + (-$10,000)(0.5) = $10,000 EMV (large shop) = ($60,000)(0.5) + (-$40,000)(0.5) = $10,000 EMV (no shop) = ($0)(0.5) + ($0)(0.5) = $0 Jerry’s initial analysis on the payoff for the alternatives and probability for the market
  • 18. conditions yielded the same EMV for both small shop and large shop which is $10,000. If 0.5 TreePlan.com Favorable Market $30,000 Small Shop $30,000 $10,000 0.5 Unfavorable Market -$10,000 -$10,000 0.5 Favorable Market $60,000 1 Large Shop $60,000 $10,000 $10,000 0.5 Unfavorable Market -$40,000 -$40,000
  • 19. No Shop $0 $0 1 2 CASE PROBLEM ‘BICYCLE SHOP’ 6 Jerry uses the information from the marketing research conducted by his old marketing professor with a fee of $5,000, the expanded decision tree is as shown in Figure 2 in Appendix A. Examining the decision tree in Figure 2, it is apparent that the best EMV is to conduct the market research with a value of $25,000 as compared to an EMV of $10,000 if market research was not conducted. So the best choice would be to conduct a market research. If the market research result is favorable, Jerry should open a large shop as indicated with an EMV of $45,000. However, if the research result is negative, Jerry should
  • 20. not open any shop at all as it has the best EMV of negative $5,000. Should Jerry Conduct and Use Marketing Research? As reflected in the decision tree in Figure 2, the best choice is to conduct a marketing research study. If Jerry were to engage his old marketing professor to conduct the marketing research study, it could change his situation from one of decision making under risk to one of decision making under certainty (Render et al. 2015). However, before engaging his old professor, Jerry should calculate the maximum that he would pay for that information using the expected value of perfect information (EVPI). The calculation is as follows, EVPI = Expected Value with Perfect Information (EVwPI) – Best EMV = [(best payoff in favorable market)(probability of favorable market) + (best payoff in unfavorable market)(probability of unfavorable market)] - Best EMV = [($60,000)(0.5) + ($0)(0.5)] - $10,000 = $20,000
  • 21. Therefore, the maximum amount that Jerry should pay for the perfect information is $20,000. Thus, the rate of $5,000 for the service that Jerry’s professor is charging to conduct a market research study is reasonable and Jerry should take the opportunity to carry out and use the marketing research. CASE PROBLEM ‘BICYCLE SHOP’ 7 Sensitivity Analysis Render et al. (2015) states that “sensitivity analysis investigates how our decision might change given a change in the problem data”. As such, we could use the sensitivity analysis to evaluate the impact that a change in the probability value of a favorable marketing research would have on the decision facing Jerry since he is unsure that the 0.6 probability of a favorable marketing research result is correct. In order to compute the sensitivity of the data, let ‘p’ be the probability of the favorable market research results and ‘1 – p’ is the probability
  • 22. for the unfavorable results. The equation for EMV of conducting the market research which is node 1 is as follows, EMV (node 1) = ($45,000)p + (-$5,000) (1 – p) = $50,000p – $5,000 Jerry will maintain indifferent with his decision to conduct the market research when the EMV for node 1 (conducting market research) is the same as the EMV of not conducting a market research with a value of $10,000. The indifference point is calculated as follows, $50,000p – $5,000 = $10,000 p = $15,000 / $50,000 = 0.3 By referring to the sensitivity analysis, it indicates that the probability of the favorable market research has to be less than 0.3 (as shown in point 1 in the graph of the EMV values in Figure 3 – Appendix B), in order for Jerry to change his decision to not conduct a market research. Conclusion With the above analysis, Jerry can finally decide to proceed with engaging his old
  • 23. marketing professor to conduct a market research study with a fee of $5,000 as long as the probability of the favorable market research is more than 0.3. If the result of the study is favorable, than Jerry should open a large shop. However, if the research result is negative, Jerry should not open any shop at all. CASE PROBLEM ‘BICYCLE SHOP’ 8 References Buckley, J. &. (1999). How Gerber Used a Decision Tree in Strategic Decision-Making. Graziadio Business Review, 2(3). Retrieved from https://gbr.pepperdine.edu/2010/08/how-gerber-used-a-decision- tree-in-strategic- decision-making/ Render, Stair, Hanna & Hale (2015). Quantitative Analysis for Management, 12 Edition. Pearson Education. Chapter 3: Decision Analysis, pages 65 - 95
  • 24. CASE PROBLEM ‘BICYCLE SHOP’ 9 APPENDIX A Figure 2: Bicycle Shop’s Decision Tree with Market Research 0.9 TreePlan.com Favorable Market $25,000 Small Shop $25,000 $21,000 0.1 Unfavorable Market -$15,000 -$15,000 0.6 0.9 Favorable Market $55,000 2 Large Shop $55,000 $45,000
  • 25. $45,000 0.1 Unfavorable Market -$45,000 -$45,000 No Shop -$5,000 -$5,000 0.12 $25,000 Favorable Market $25,000 Small Shop $25,000 -$10,200 0.88 Unfavorable Market -$15,000 -$15,000 0.4 0.12 Favorable Market $55,000
  • 26. 3 Large Shop $55,000 -$5,000 -$33,000 0.88 Unfavorable Market -$45,000 -$45,000 1 $25,000 No Shop -$5,000 -$5,000 0.5 Favorable Market $30,000 Small Shop $30,000 $10,000 0.5 Unfavorable Market -$10,000
  • 27. -$10,000 0.5 Favorable Market $60,000 1 Large Shop $60,000 $10,000 $10,000 0.5 Unfavorable Market -$40,000 -$40,000 No Shop $0 $0 Favorable Survey Result Unfavorable Survey Result Conduct
  • 28. Market Research Do Not Conduct Market Research 1 2 3 4 5 6 7 CASE PROBLEM ‘BICYCLE SHOP’ 10 APPENDIX B Figure 3: Sensitivity Analysis for the Probability of Favorable Market Research for the Bicycle Shop
  • 30. A LU E (E M V ) PROBABILITY OF FAVORABLE MARKET RESEARCH (P) SENSITIVITY ANALYSIS - BICYCLE SHOP Conduct Market Research Do Not Conduct Market Research point 1 0.3 Week 5: Summary Week 6, Lecture 6: Decision Analysis and Support in Organizations Bb Discussion W6: Quantitative Analysis and Decision Making in an Organization Preparation for Assignment 2 (Due Monday Oct-28 by 11:59pm) – Q&A Individual Exercise: Working with the Tutorial for AD715
  • 31. “Decision Trees in TreePlan” AD 715: Quantitative and Qualitative Decision-Making Week 6, Class 6 (10/8/2019) Boston University MET AD715 © Dr. Zlatev, 2019 B C D 1 A AGENDA F B Boston University MET AD715 © Dr. Zlatev, 2019 2 Week 6 C D Decision making and decision analysis – an introduction Decision making under certainty and uncertainty
  • 32. - an example decision tree problems 1 3 4 2 F The Six Steps in Decision Making: Decision Analysis Prospective 1. Clearly define the problem at hand 2. List the possible alternatives 3. Identify the possible outcomes or states of nature 4. List the payoff (typically profit) of each combination of alternatives and outcomes
  • 33. 5. Select one of the mathematical decision theory models 6. Apply the model and make your decision Step 1: Recognize the Need of a Decision Step 2: Generate Alternative Step 3: Assess Alternative Step 4: Choose Among Alternatives Step 5: Implement the Chosen Alternative Step 6: Learn from Feedback Decision Making Process
  • 34. The Steps in the Managerial Decision Making Process Decision Making and Decision Analysis – An Introduction 4 B 1 Boston University MET AD715 © Dr. Zlatev, 2019 Demonstration of the Decision Making Process as a Step-By-Step Analytical Approach Step 3 – Identify possible outcomes or states of nature • The market could be favorable or unfavorable Step 5 – Select the decision model • Depends on the environment and amount of risk and uncertainty Decision Making and Decision Analysis – An Introduction Business Running Case: Thompson Lumber Company Step 1 – Define the problem • Consider expanding by manufacturing and marketing a new
  • 35. product – backyard storage sheds Step 2 – List possible alternatives • Construct a large new plant • Construct a small new plant • Do not develop the new product line Step 4 – List the payoffs • Identify conditional values for the profits for large plant, small plant, and no development for the two possible market conditions Step 6 – Apply the model to the data 5 B 1 Boston University MET AD715 © Dr. Zlatev, 2019 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE
  • 36. MARKET ($) Construct a large plant 200,000 –180,000 Construct a small plant 100,000 –20,000 Do nothing 0 0 Decision Making and Decision Analysis – An Introduction Business Running Case: Thompson Lumber Company Step 3 – Identify possible outcomes or states of nature • The market could be favorable or unfavorable Step 2 – List possible alternatives • Construct a large new plant • Construct a small new plant • Do not develop the new product line States of Nature: Outcomes over which the decision makers has little or no control Decision Table (Payoff Table) with Conditional Values
  • 37. The easiest way to present the combination of decision alternatives, possible states of nature, and conditional values for each one of the possible decision alternatives and states of nature is called decision table or payoff table. 6 B 1 Boston University MET AD715 © Dr. Zlatev, 2019 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) Construct a large plant 200,000 –180,000 Construct a small plant 100,000 –20,000 Do nothing 0 0 Decision Table (Payoff Table) with Conditional Values
  • 38. Decision Making and Decision Analysis – An Introduction Business Running Case: Thompson Lumber Company Conditional Values: Possible combination of alternatives and outcomes, also called payoffs. Payoffs can be based on money or any appropriate means of measuring benefits. Step 4 – List the payoffs • Identify conditional values for the profits for large plant, small plant, and no development for the two possible market conditions Net profit of $200,000 is a conditional value because receiving the money is conditional upon both building a large factory and having a good (favorable) market Net loss of $180,000 is a conditional value because receiving the money is conditional upon both building a large factory and having a unfavorable market 7 B 1
  • 39. Boston University MET AD715 © Dr. Zlatev, 2019 Types of Decision-Making Environments • Decision making under certainty – The decision maker knows with certainty the consequences of every alternative or decision choice • Decision making under uncertainty – The decision maker does not know the probabilities of the various outcomes • Decision making under risk – The decision maker knows the probabilities of the various outcomes Decision Making and Decision Analysis – An Introduction 8 B 1 Boston University MET AD715 © Dr. Zlatev, 2019 Decision Making Under Certainty 9
  • 40. Example: You have $10,000 to invest for a one year period Existing alternatives to invest in two equally secure and guaranteed investments: Consequences (Return after 1 year in interest) • Alternative #1 is to open a saving account paying 4% interest $400 • Alternative #2 is to invest in a government Treasury bond paying 6% interest $600 Decision Choice: Select Alternative #2 ($600 > $400) The decision makers know with certainty the consequence of every alternative or decision choice B 2 Boston University MET AD715 © Dr. Zlatev, 2019 Decision Making Under Uncertainty Criteria for making decisions under uncertainty 1. Maximax (optimistic) 2. Maximin (pessimistic) 3. Criterion of realism (Hurwicz)
  • 41. 4. Equally likely (Laplace) 5. Minimax regret 10 B 2 Boston University MET AD715 © Dr. Zlatev, 2019 Optimistic Used to find the alternative that maximizes the maximum payoff – maximax criterion – Locate the maximum payoff for each alternative – Select the alternative with the maximum number STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) MAXIMUM IN A ROW ($) Construct a large plant
  • 42. 200,000 –180,000 200,000 Construct a small plant 100,000 –20,000 100,000 Do nothing 0 0 0 Maximax Decision Maximax 11 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) MINIMUM IN A ROW ($) Construct a large plant 200,000 –180,000 -180,000 Construct a small plant
  • 43. 100,000 –20,000 -20,000 Do nothing 0 0 0 Maximin Business Running Case: Thompson Lumber Company Maximin Decision Used to find the alternative that maximizes the minimum payoff – maximin criterion – Locate the minimum payoff for each alternative – Select the alternative with the maximum number Pessimistic Decision Making Under Uncer B 2 Boston University MET AD715 © Dr. Zlatev, 2019 Criterion of Realism (Hurwicz) Often called weighted average – Compromise between optimism and pessimism – Select a coefficient of realism ɑ, with 0 ≤ a ≤ 1
  • 44. a = 1 is perfectly optimistic a = 0 is perfectly pessimistic – Compute the weighted averages for each alternative – Select the alternative with the highest value – 12 nt alternative using ɑ = 0.8 (0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000 (0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) CRITERION OF REALISM (a = 0.8) $
  • 45. Construct a large plant 200,000 –180,000 124,000 Construct a small plant 100,000 –20,000 76,000 Do nothing 0 0 0 Criterion of Realism Decision Realism Business Running Case: Thompson Lumber Company Decision Making Decision B 2 Boston University MET AD715 © Dr. Zlatev, 2019 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) ROW
  • 46. AVERAGE ($) Construct a large plant 200,000 –180,000 10,000 Construct a small plant 100,000 –20,000 40,000 Do nothing 0 0 0 Equally Likely (Laplace) Considers all the payoffs for each alternative – Find the average payoff for each alternative – Select the alternative with the highest average Equally Likely Decision Equally likely 13 Decision Making Under Uncertainty Business Running Case: Thompson Lumber Company Boston University MET AD715 © Dr. Zlatev, 2019
  • 47. Minimax Regret fference between the optimal profit and actual payoff for a decision 1. Create an opportunity loss table by determining the opportunity loss from not choosing the best alternative 2. Calculate opportunity loss by subtracting each payoff in the column from the best payoff in the column 3. Find the maximum opportunity loss for each alternative and pick the alternative with the minimum number 14 Decision Making Under Uncertainty STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) Construct a large plant 200,000 - 200,000 0 – (–180,000) Construct a
  • 48. small plant 200,000 - 100,000 0 – (–20,000) Do nothing 200,000 - 0 0 - 0 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) Construct a large plant 0 180,000 Construct a small plant 100,000 20,000 Do nothing 200,000 0 Business Running Case: Thompson Lumber Company Determining Opportunity Losses Opportunity Loss Table STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($)
  • 49. UNFAVORABLE MARKET ($) MAXIMUM IN A ROW ($) Construct a large plant 0 180,000 180,000 Construct a small plant 100,000 20,000 100,000 Do nothing 200,000 0 200,000 Minimax Decision Using Opportunity Loss Minimax (Opportunity Loss) B 2 Boston University MET AD715 © Dr. Zlatev, 2019 Decision Making Under Risk
  • 50. Expected Monetary Value (EMV) When there are several possible states of nature and the probabilities associated with each possible state are known – Most popular method – choose the alternative with the highest expected monetary value (EMV) EMV(alternative) = X iP(X i )å where Xi = payoff for the alternative in state of nature i P(Xi) =probability of achieving payoff Xi (i.e., probability of state of nature i) ∑ = summation symbol 15 Expanding the equation EMV (alternative i) = (payoff of first state of nature) x (probability of first state of nature) + (payoff of second state of nature) x (probability of second state of nature) + … + (payoff of last state of nature) x (probability of last state of nature) Boston University MET AD715 © Dr. Zlatev, 2019
  • 51. • Each market outcome has a probability of occurrence of 0.50 • Which alternative would give the highest EMV? EMV (large plant) = ($200,000)(0.5) + (–$180,000)(0.5) = $10,000 EMV (small plant) = ($100,000)(0.5) + (–$20,000)(0.5) = $40,000 EMV (do nothing) = ($0)(0.5) + ($0)(0.5) = $0 Business Running Case: Thompson Lumber Company (EMV) STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) EMV ($) Construct a large plant 200,000 –180,000 10,000 Construct a small plant
  • 52. 100,000 –20,000 40,000 Do nothing 0 0 0 Probabilities 0.5 0.5 Decision Table with Probabilities and EMVs Best EMV Decision Making Under Risk 16 EMVB 3 Boston University MET AD715 © Dr. Zlatev, 2019 Expected Value of Perfect Information (EVPI) EVPI places an upper bound on what you should pay for additional information EVwPI is the long run average return if we have perfect information before a decision is made EVwPI = ∑(best payoff in state of nature i) (probability of state of nature i) Decision Making Under Risk Expanded EVwPI becomes EVwPI = (best payoff for first state of nature)
  • 53. x (probability of first state of nature) + (best payoff for second state of nature) x (probability of second state of nature) + … + (best payoff for last state of nature) x (probability of last state of nature) EVPI = EVwPI – Best EMV and 17 Boston University MET AD715 © Dr. Zlatev, 2019 • Scientific Marketing, Inc. offers analysis that will provide certainty about market conditions (favorable) • Additional information will cost $65,000 Business Running Case: Thompson Lumber Company (EVPI) STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) EMV ($) Construct a large plant
  • 54. 200,000 –180,000 10,000 Construct a small plant 100,000 –20,000 40,000 Do nothing 0 0 0 Probabilities 0.5 0.5 With Perfect Information 200,000 0 100,000 Decision Table with Perfect Information Best EVwPI Best EMV The maximum EMV without additional information is $40,000 EVwPI = $200,000 x 0.5 + $0 x 0.5 = $100,000 where $200,000 is best payoff for first state of nature $0 is the best payoff for second state of nature EVPI = EVwPI – Best EMV = $100,000 - $40,000 = $60,000 Therefore, the maximum Thompson should pay for the additional information is $60,000 SOLUTION: Thompson should not pay $65,000 for this information Should Thompson Lumber
  • 55. purchase the information? Decision Making Under Risk 18 Boston University MET AD715 © Dr. Zlatev, 2019 Expected Opportunity Loss Expected opportunity loss (EOL) is the cost of not picking the best solution – Construct an opportunity loss table – For each alternative, multiply the opportunity loss by the probability of that loss for each possible outcome and add these together – Minimum EOL will always result in the same decision as maximum EMV – Minimum EOL will always equal EVPI 19 Decision Making Under Risk Business Running Case: Thompson Lumber Company EOL (large plant) = (0.50)($0) + (0.50)($180,000) = $90,000
  • 56. EOL (small plant) = (0.50)($100,000) + (0.50)($20,000) = $60,000 EOL (do nothing) = (0.50)($200,000) + (0.50)($0) = $100,000 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) EOL ($) Construct a large plant 0 180,000 90,000 Construct a small plant 100,000 20,000 60,000 Do nothing 200,000 0 100,000 Opportunity Loss Table Probabilities 0.5 0.5 Best EOL
  • 57. EOL Table Opportunity Loss) B 3 Boston University MET AD715 © Dr. Zlatev, 2019 EMV & Sensitivity Analysis EMV(large plant) = $200,000P – $180,000)(1 – P) = $200,000P – $180,000 + $180,000P = $380,000P – $180,000 If P = 1 then EMV = $380,000x1 - $180,000 = $200,000 If P = 0 then EMV = $380,000x0 - $180,000 = -$180,000 EMV(small plant) = $100,000P – $20,000)(1 – P) = $100,000P – $20,000 + $20,000P = $120,000P – $20,000 If P = 1 then EMV = $120,000x1 - $20,000 = $100,000 If P = 0 then EMV = $120,000x0 - $20,000 = -$20,000 EMV(do nothing) = $0P + 0(1 – P) = $0
  • 58. 20 $300,000 $200,000 $100,000 0 –$100,000 –$200,000 EMV Values EMV (large plant) EMV (small plant) EMV (do nothing) Point 1 Point 2 .167 .615 1 Values of P Business Running Case: Thompson Lumber Company B 3
  • 59. Boston University MET AD715 © Dr. Zlatev, 2019 Probabilities P (1-P) EMV & Sensitivity Analysis EMV(large plant) = $200,000P – $180,000)(1 – P) = $200,000P – $180,000 + $180,000P = $380,000P – $180,000 EMV(small plant) = $100,000P – $20,000)(1 – P) = $100,000P – $20,000 + $20,000P = $120,000P – $20,000 EMV(do nothing) = $0P + 0(1 – P) = $0 21 D $300,000 $200,000 $100,000 0
  • 60. –$100,000 –$200,000 EMV Values EMV (large plant) EMV (small plant) EMV (do nothing) Point 1 Point 2 .167 .615 1 Values of P Point 1: EMV(do nothing) = EMV(small plant) Point 2: EMV(small plant) = EMV(large plant) 0 = $120,000P - $20,000 20,000 P = ------------- = 0.167 120,000 $120,000P - $20,000 = $380,000P - $180,000 160,000 P = ------------- = 0.615
  • 61. 260,000 Business Running Case: Thompson Lumber Company B 3 Boston University MET AD715 © Dr. Zlatev, 2019 EMV & Sensitivity Analysis 22 $300,000 $200,000 $100,000 0 –$100,000 –$200,000 EMV Values EMV (large plant) EMV (small plant)
  • 62. EMV (do nothing) Point 1 Point 2 .167 .615 1 Values of P Business Running Case: Thompson Lumber Company BEST ALTERNATIVE RANGE OF P VALUES Do nothing Less than 0.167 Construct a small plant 0.167 – 0.615 Construct a large plant Greater than 0.615 CONCLUSIONS: B 3 Boston University MET AD715 © Dr. Zlatev, 2019 Problem (Text, p.p.75 - 77): A department will be signing three year lease for a new copy machine and three different machines are being considered
  • 63. • For each of the machines, there is a monthly fee (incl. monthly fee & charge per each copy) • The department has estimated that the number of copies/Mo could be 10,000 or 20,000 or 30,000 • The monthly cost for each machine based on the offers and the three levels of activities is shown in the table below Which machine should be selected? 10,000 COPIES PER MONTH 20,000 COPIES PER MONTH 30,000 COPIES PER MONTH Machine A 950 1,050 1,150 Machine B 850 1,100 1,350 Machine C 700 1,000 1,300 TABLE 3.12 – Payoff Table 23 Q/A: Costs Minimization - An ExampleB 3 Boston University MET AD715 © Dr. Zlatev, 2019
  • 64. 10,000 COPIES PER MONTH 20,000 COPIES PER MONTH 30,000 COPIES PER MONTH BEST PAYOFF (MINIMUM) WORST PAYOFF (MAXIMUM) Machine A 950 1,050 1,150 950 1,150 Machine B 850 1,100 1,350 850 1,350 Machine C 700 1,000 1,300 700 1,300 TABLE 3.13 – Best and Worst Payoffs 24 Q/A: Costs Minimization - An Example
  • 65. Using Best Payoff (Minimum) vs Worst Payoff (Maximum) Using Hurwicz criteria with 70% coefficient For each machine Machine A: 0.7(950) + 0.3(1,150) = 1,010 Machine B: 0.7(850) + 0.3(1,350) = 1,000 Machine C: 0.7(700) + 0.3(1,300) = 880 Weighted average = = 0.7(best payoff) + (1 – 0.7)(worst payoff) Decision: to select machine C based on this criterion (it has the lowest weighted average costs) DECISIONS B 3 Boston University MET AD715 © Dr. Zlatev, 2019 Using equally likely criteria For each machine Machine A: (950 + 1,050 + 1,150)/3 = 1,050 Machine B: (850 + 1,100 + 1,350)/3 = 1,100
  • 66. Machine C: (700 + 1,000 + 1,300)/3 = 1,000 25 Q/A: Costs Minimization - An Example DECISIONS 10,000 COPIES PER MONTH 20,000 COPIES PER MONTH 30,000 COPIES PER MONTH Machine A 950 1,050 1,150 Machine B 850 1,100 1,350 Machine C 700 1,000 1,300 Decision: to select machine C based on this criterion (it has the lowest average costs) B 3 Boston University MET AD715 © Dr. Zlatev, 2019 Using EMV Criterion USAGE PROBABILITY 10,000 0.40
  • 67. 20,000 0.30 30,000 0.30 Q/A: Costs Minimization - An Example DECISIONS Assumptions for probability for the three states of nature (based on past records) 10,000 COPIES PER MONTH 20,000 COPIES PER MONTH 30,000 COPIES PER MONTH EMV Machine A 950 1,050 1,150 1,040 Machine B 850 1,100 1,350 1,075 Machine C 700 1,000 1,300 970 With perfect information 700 1,000 1,150 925
  • 68. Probability 0.4 0.3 0.3 TABLE 3.14 Expected Monetary Values and Expected Value with Perfect Information Decision: to select machine C based on this criterion (it has the lowest EMV) 26 B 3 Boston University MET AD715 © Dr. Zlatev, 2019 Using EVPI & Expected Opportunity Loss Criterion Q/A: Costs Minimization - An Example DECISIONS Criterion 10,000 COPIES PER MONTH 20,000 COPIES PER MONTH 30,000
  • 69. COPIES PER MONTH EMV Machine A 950 1,050 1,150 1,040 Machine B 850 1,100 1,350 1,075 Machine C 700 1,000 1,300 970 With perfect information 700 1,000 1,150 925 Probability 0.4 0.3 0.3 TABLE 3.14 Expected Monetary Values and Expected Value with Perfect Information EVwPI = $925 Best EMV without perfect information= $970 EVPI = 970 – 925 = $45 Decision: to select machine C based on the minimax regret criterion (it has the minimum of the maximum) 10,000 COPIES PER MONTH 20,000
  • 70. COPIES PER MONTH 30,000 COPIES PER MONTH MAXIMUM EOL Machine A 250 50 0 250 115 Machine B 150 100 200 200 150 Machine C 0 0 150 150 45 Probability 0.4 0.3 0.3 TABLE 3.15 – Opportunity Loss Table Decision: to select machine C based on the EOL criterion (it has the lowest expected opportunity loss) 27 B 3 Boston University MET AD715 © Dr. Zlatev, 2019 Decision Trees Any problem that can be presented in a decision table can be graphically represented in a decision tree
  • 71. – Most beneficial when a sequence of decisions must be made – All decision trees contain decision points/nodes and state-of- nature points/nodes – At decision nodes one of several alternatives may be chosen – At state-of-nature nodes one state of nature will occur 28 1. Define the problem 2. Structure or draw the decision tree 3. Assign probabilities to the states of nature 4. Estimate payoffs for each possible combination of alternatives and states of nature 5. Solve the problem by computing expected monetary values (EMVs) for each state of nature node Five Steps of Decision Tree Analysis B 4 Boston University MET AD715 © Dr. Zlatev, 2019 Structure of Decision Trees • Trees start from left to right • Trees represent decisions and outcomes in
  • 72. sequential order • Squares represent decision nodes • Circles represent states of nature nodes • Lines or branches connect the decisions nodes and the states of nature Decision Trees 29 B 4 Boston University MET AD715 © Dr. Zlatev, 2019 Thompson’s Decision Tree Favorable Market Unfavorable Market Favorable Market Unfavorable Market 1 Construct Small Plant 2
  • 73. FIGURE 3.2 A Decision Node A State-of-Nature Node Decision Trees 30 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) Construct a large plant 200,000 –180,000 Construct a small plant 100,000 –20,000 Do nothing 0 0 Decision Table (Payoff Table) with Conditional Values Business Running Case: Thompson Lumber Company B 4 Boston University MET AD715 © Dr. Zlatev, 2019
  • 74. Favorable Market Unfavorable Market Favorable Market Unfavorable Market 1 Construct Small Plant 2 Alternative with best EMV is selected FIGURE 3.3 EMV for Node 1 = $10,000 = (0.5)($200,000) + (0.5)(–$180,000) EMV for Node 2 = $40,000 = (0.5)($100,000) + (0.5)(–$20,000) Payoffs $200,000 –$180,000
  • 75. $100,000 –$20,000 $0 (0.5) (0.5) (0.5) (0.5) 31 Thompson’s Decision Tree Decision Trees Business Running Case: Thompson Lumber Company B 4 Boston University MET AD715 © Dr. Zlatev, 2019 Thompson’s Complex Decision Tree First Decision Point Second Decision
  • 76. Point Favorable Market (0.78) Unfavorable Market (0.22) Favorable Market (0.78) Unfavorable Market (0.22) Favorable Market (0.27) Unfavorable Market (0.73) Favorable Market (0.27) Unfavorable Market (0.73) Favorable Market (0.50) Unfavorable Market (0.50) Favorable Market (0.50) Unfavorable Market (0.50) Small Plant No Plant 6 7 Small
  • 78. $100,000 –$20,000 $0 –$190,000 $190,000 $90,000 –$30,000 –$10,000 FIGURE 3.4 32 Decision Trees Business Running Case: Thompson Lumber Company Thompson’s Complex Decision Tree B 4 Boston University MET AD715 © Dr. Zlatev, 2019 1. Given favorable survey results EMV(node 2) = EMV(large plant | positive survey)
  • 79. = (0.78)($190,000) + (0.22)(– $190,000) = $106,400 EMV(node 3) = EMV(small plant | positive survey) = (0.78)($90,000) + (0.22)(– $30,000) = $63,600 EMV for no plant = – $10,000 33 Decision Trees Business Running Case: Thompson Lumber Company 2. Given negative survey results EMV(node 4) = EMV(large plant | negative survey) = (0.27)($190,000) + (0.73)(– $190,000) = – $87,400 EMV(node 5) = EMV(small plant | negative survey) = (0.27)($90,000) + (0.73)(– $30,000) = $2,400 EMV for no plant = – $10,000 Thompson’s Complex Decision Tree B 4 Boston University MET AD715 © Dr. Zlatev, 2019 3. Expected value of the market survey EMV(node 1) = EMV(conduct survey)
  • 80. = (0.45)($106,400) + (0.55)($2,400) = $47,880 + $1,320 = $49,200 4. Expected value no market survey EMV(node 6) = EMV(large plant) = (0.50)($200,000) + (0.50)(– $180,000) = $10,000 EMV(node 7) = EMV(small plant) = (0.50)($100,000) + (0.50)(– $20,000) = $40,000 EMV for no plant = $0 The best choice is to seek marketing information Decision Trees Thompson’s Complex Decision Tree 34 Business Running Case: Thompson Lumber Company B 4 Boston University MET AD715 © Dr. Zlatev, 2019 FIGURE 3.5 First Decision Point Second Decision Point Favorable Market (0.78)
  • 81. Unfavorable Market (0.22) Favorable Market (0.78) Unfavorable Market (0.22) Favorable Market (0.27) Unfavorable Market (0.73) Favorable Market (0.27) Unfavorable Market (0.73) Favorable Market (0.50) Unfavorable Market (0.50) Favorable Market (0.50) Unfavorable Market (0.50) Small Plant No Plant 6 7 Small Plant
  • 84. ,4 0 0 $ 4 9 ,2 0 0 $106,400 $63,600 –$87,400 $2,400 $10,000 $40,000 Decision Trees Thompson’s Complex Decision Tree 35 Business Running Case: Thompson Lumber Company B 4 Boston University MET AD715 © Dr. Zlatev, 2019
  • 85. Expected Value of Sample Information Thompson wants to know the actual value of doing the survey = (EV with SI + cost) – (EV without SI) EVSI = ($49,200 + $10,000) – $40,000 = $19,200 EVSI = – Expected value with sample information Expected value of best decision without sample information Decision Trees 36 Business Running Case: Thompson Lumber Company B 4 Boston University MET AD715 © Dr. Zlatev, 2019 Efficiency of Sample Information
  • 86. • Possibly many types of sample information available • Different sources can be evaluated Efficiency of sample information = EVSI EVPI 100% Efficiency of sample information = 19,200 60,000 100% = 32% Market survey is only 32% as efficient as perfect information Decision Trees Business Running Case: Thompson Lumber Company 37 B 4 Boston University MET AD715 © Dr. Zlatev, 2019 Sensitivity Analysis • How sensitive are the decisions to changes in the probabilities? • How sensitive is our decision to the probability of a favorable survey result?
  • 87. • If the probability of a favorable result (p = .45) where to change, would we make the same decision? • How much could it change before we would make a different decision? Decision Trees p = probability of a favorable survey result (1 – p) = probability of a negative survey result EMV(node 1) = ($106,400)p +($2,400)(1 – p) = $104,000p + $2,400 Business Running Case: Thompson Lumber Company We are indifferent when the EMV of node 1 is the same as the EMV of not conducting the survey $104,000p + $2,400 = $40,000 $104,000p = $37,600 p = $37,600/$104,000 = 0.36 DECISION: If p < 0.36, do not conduct the survey If p > 0.36, conduct the survey 38 B 4
  • 88. Boston University MET AD715 © Dr. Zlatev, 2019 39 Q/A: Using Software for Payoff Table and Decision Tree Problems Other Decision Tree Software (A Short List): Tutorial ‘Decision Trees in TreePlan’ >>> v-labs (Excel 2016 Add-In ‘TreePlan’) ASSIGNMENT 2 Task 2-4: Apply TreePlan B 4 1. Excel Decision Tree Add-Ins • Risk Solver Pro & Analytic Solver Pro v2016 by FrontlineSolvers, www.solver.com • Monte Carlo Risk Simulation, Decision Tree and Statistical Excel Analysis Add-In by Lumenaut, www.lumenaut.com • Decision Tree Suite by Palisade, www.palisade.com • TreePlan by TreePlan Software, www.treeplan.com 2. Top Decision Tree Analysis Software Products 2016 (ranked by Capterra, www.capterra.com ; Filter Results: 1000+ number of users): • pcFinancials by Performance Canvas Financials, http://www.performancecanvas.com
  • 89. • Analytica by Lumina Decision Systems, http://www.lumina.com/ • 1000Minds (Multi-Criteria Decision-Making) by 1000minds: www.1000minds.com • Blaze Advisor by Fico, www.fico.com • D-Sight Collaborative Decision-Making platform by D-Sight, http://www.d-sight.com • Decision Lens by Decision Lens, www.decisionlens.com • Decision Support Software by Logicnets, www.logicnets.com • DPL 8 Direct by Syncopation, www.syncopation.com • Spotfire by Tibco, www.tibco.com • VisiRule by Logic Programming Associates, www.lpa.co.uk Boston University MET AD715 © Dr. Zlatev, 2019 http://www.solver.com/ http://www.lumenaut.com/ http://www.palisade.com/ http://www.treeplan.com/ http://www.capterra.com/ http://www.performancecanvas.com/ http://www.lumina.com/ http://www.1000minds.com/ http://www.fico.com/ http://www.d-sight.com/ http://www.decisionlens.com/ http://www.logicnets.com/ http://www.syncopation.com/ http://www.tibco.com/ http://www.lpa.co.uk/
  • 90. Discussion W6: Quantitative Analysis and Managerial Decisions in an OrganizationC Boston University MET AD715 © Dr. Zlatev, 2019 39 With the help of one or several of the recommended tutorials for Week 6, discuss your experience and plans for applying analytical methods in your Assignment 2 or in your current (or targeted) profession. Recommended discussion topics (covered in Lecture 06): Decision making under certainty and uncertainty Decision making under risk Decision trees Using software for payoff table and decision tree problems Assignment 2: Prep-Plan 40 D Boston University MET AD715 © Dr. Zlatev, 2019 In-Class Exercise: Task 2-1 In-Class Exercise: Task 2-2
  • 91. Assignment 2: Prep-Plan 41 D Boston University MET AD715 © Dr. Zlatev, 2019 In-Class Exercise: Task 2-3 In-Class Exercise: Task 2-4 42Boston University MET AD715 © Dr. Zlatev, 2019 Individual Exercise W6: Working with the Tutorial for AD715 “Decision Trees in TreePlan” F Targeted Outcomes: 1. Learn how to access BU MET VLAB 2. Review the Tutorial for AD15 “Decision Trees in TreePlan” Bb course website >>> Content >>> Tutorials 1. Review the script “Decision Trees in TreePlan” 2. Go to the VLAB, open Excel 2016, and repeat the steps from the script (task 3)
  • 92. In this course, students will be using Microsoft Excel software applications for Windows. As part of the tuition, all BU students can use this software free of charge. Click here for directions to get free access to Microsoft Excel applications from MET’s Virtual Labs: http://www.bu.edu/metit/pc-labs/virtual- labs/ You will not be able to download the software using this option, but you will be given access to it for use during the course. If you are first-time VLAB user, please synchronize your BU account with the BU Active Directory by following the recommended procedures: https://weblogin.bu.edu/accounts/create?_hostname=ad;_conffil e=kpw From the existing two VLAB connection modes, I am recommending to select Horizon Client: http://www.bu.edu/metit/vlabs-client/ The process of accessing and working within the VLABs is demonstrated and explained with the help of Video Tutorials (one for Windows, and the other for MAC
  • 93. users). Attention: Files saved on the desktop or local drive of the virtual lab will be deleted after you log off. Hence, before logging off, you must save your work on an external source, such as Google Drive, Shared Folder, USB drive, or email the files to yourself. Instructions how to save files in the MET VLABs are accessible from here: http://www.bu.edu/metit/vlabs-client/ To Get Help, call (617) 358-5401 or send a message to [email protected] . Please indicate that you have a VLAB issue and include your course number. http://www.bu.edu/metit/pc-labs/virtual-labs/ https://weblogin.bu.edu/accounts/create?_hostname=ad;_conffil e=kpw http://www.bu.edu/metit/vlabs-client/ http://www.bu.edu/metit/vlabs-client/ mailto:[email protected] A2 TextAssignment 2: Case Problem "Real Estate Development: Select a New Project"Problem DescriptionA real estate company is considering the development of one of the following three possible projects: (1) an apartment building; (2) an office building; (3) a warehouse. The amount of payoff (profit) that could be earned by selling the estate depends on the economic
  • 94. conditions, specified as: optimistic, realistic and pessimistic. The estimated payoffs and probabilities under optimistic, realistic and pessimistic conditions are shown as follows:AlternativesStates of NatureOptimistic ConditionsRealistic ConditionsPessimistic ConditionsApartment BuildingABCOffice BuildingDEFWarehouseGHIProbabilityxyzIn preparation for a final decision, the company is considering the hiring of a business analyst. If the company hires the analyst, the decision regarding which project to develop will not be made until the analyst presents a survey. However, the analyst is requesting an upfront payment for the survey in the amount of Z. The probabilities of the survey results to be positive or negative are i and k. Summary tables, in case the company hires a business analyst:Fee for SurveyZProbability of survey results positiveiProbability of survey results negativek(1) If the survey results are positive:AlternativesStates of NatureOptimistic ConditionsRealistic ConditionsPessimistic ConditionsApartment BuildingA - ZB - ZC - ZOffice BuildingD - ZE - ZF - ZWarehouseG - ZH - ZI - ZProbabilitydef(2) If the survey results are negative: AlternativesStates of NatureOptimistic ConditionsRealistic ConditionsPessimistic ConditionsApartment BuildingA - ZB - ZC - ZOffice BuildingD - ZE - ZF - ZWarehouseG - ZH - ZI - ZProbabilityghnAssignment 2: Starting ConditionsEach student will receive from the instructor an excel file with a different dataset for payoffs (A to I) and probabilities (x,y,z,i,k,d,e,f,g,h,n). You have to prepare and submit a managerial report where you should answer the question: Which one of the development projects should be selected? And based on your estimates, should the company hire the business analyst?Grading Points Per:TasksAssignment#Content per Tasks10Task 2-0Students should structure and present their Assignment 2 in the form of a Managerial Report. The expected length of the main body (tasks 2-1 to 2-4) is up to 3 pages APA format, excluding cover page, table of content, executive summary (task 2-5), and appendices
  • 95. (screenshots of the Payoff Table, EMV Table, Sensitivity Analysis Diagram, TreePlan Diagram of the Decision Tree). Submission requirements: Managerial Report (word file), and excel file with completed worksheets (iii) to (vi).1Task 2- 1Prepare payoff tables and develop a decision tree for this problem (without probabilities and EMVs).2Task 2-2Given the probability of all three economic conditions and using expected monetary values (EMVs), calculate EMVs for each node and answer the questions: (1) What's the EMV for not hiring a business analyst and the EMV for hiring a business analyst? (2) What is your recommendation: to hire or not to hire a business analyst?2Task 2-3Use sensitivity analysis to define the probability range with respect to the survey results which might affect the decision to hire or not to hire a business analyst, draw the sensitivity chart, and find the probability for their cross point. 2Task 2-4Apply a software tool for the construction of a decision tree with payoffs, probabilities, and EMVs. The recommended tool is TreePlan: a Microsoft Excel Add-Ins (it is preinstalled on all V-PCs of the MET V-LABs)2Task 2- 5Prepare an executive summary1List of Worksheets in the Excel File (it should be used as a reference for different tasks of the managerial report)(i)A2 Text(ii) Payoff Table - Template(iii)Payoff Table - Solution and a sketch of a decision tree (without probability and EMVs) --> Needed for Task 2-1(iv) EMV Calculation: use EMV as a decision criterion for each decision nodes and states of nature nodes, calculate the EMV for each node, and recommend whether to hire/not to hire a business analyst --> Needed for
  • 96. Task 2-2(v)Sensitivity Analysis Diagram: compute the probability of survey results and define the range of probability values that the real estate company would hire or not hire a business analyst (including the probability of the cross point) -- > Needed for Task 2-3(vi)TreePlan Diagram of the Decision Tree: use BU MET V-LAB for Excel Add-In TreePlan --> Needed for Task 2-4 Payoff Table Template1. If the company does not hire a business analyst:AlternativesStates of NatureEMVOptimistic ConditionsRealistic ConditionsPessimistic ConditionsApartment BuildingABCOffice BuildingDEFWarehouseGHIProbabilityxyz2. If the company hires a business analyst:Fee for SurveyZ2.1 If the analysis report results positive:AlternativesStates of NatureEMVOptimistic ConditionsRealistic ConditionsPessimistic ConditionsApartment BuildingOffice BuildingWarehouseProbabilitydef2.2 If the analysis report results negative:AlternativesStates of NatureEMVOptimistic ConditionsRealistic ConditionsPessimistic ConditionsApartment BuildingOffice BuildingWarehouseProbabilityghn3. Final