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Defense Resources Management InstituteNaval Postgraduate School
Monterey, California
Analytical Decision Making for Financial
Managers
How do you make decisions?
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Analysis
The process of breaking a complex topic or problem into smaller parts to gain a better understanding of it
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Robert McNamara (1961)
• “Major decisions should be made by choices among explicit, balanced, feasible alternatives”
• “The Secretary should have an active analytic staff to provide him with relevant data and unbiased perspectives”
• “Open and explicit analysis, available to all parties, must form the basis for major decisions”
4
Decision maker
New problem (never encountered)
SOLUTION
Analyst
Experienceand
judgment
Decision Maker and Analyst
5
Why Do Analysis?
• Analysis can be difficult, time consuming, and expensive
• But analysis creates
Answers that are accessible to critical examination
Answers that can be retraced by others
Answers that account for different factors and elements
• And it leads to better decisions
6
Elements of Analysis
• Goals: What the decision maker is trying to achieve
• Objectives: Outcomes that you want to occur to achieve a goal
• Alternatives: Choices available to achieve goals
• Models: Tools for predicting and evaluating the consequences of choosing an alternative
• Preferences: Rules for ranking the alternatives (best to worst)
7
Formulation (conceptual
phase)
Define issues of concern
Clarify objective
Scope problem
Search (research
phase)
Develop alternatives
Look for data
Identify alternatives
Build mental models
Evaluation (analytic phase)
Build mathematical
models
Use models to predict
consequences
Interpretation (judgmental
phase)
Compare alternatives
based on model
predictions
Derive conclusions
Indicate courses of
action
Process of Analysis
8
Process and Elements of Analysis
9
Formulation (conceptual
phase)
Search (research
phase)
Evaluation (analytic phase)
Interpretation (judgmental
phase)
Goal
Objective
Alternatives
Data
ModelModel output
How well are we doing on our ?
Preferences
Formulation Phase
• Focus on the right problem
• Do not jump immediately to solving the problem
• Think about
Goal(s)
Objective(s)
Scope
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Work on the Right Decision Problem
• Ask yourself why there is a problem
• Ask what triggered the decision
• Focus on the problem not the symptoms
• Be creative about defining the problem
• Turn problems into opportunities
What can you gain from the situation?
What are the opportunities here?
11
Goal
• Examples
Achieve 95% availability
Eliminate IED attacks12
• Desired end state, what are you ultimately trying to achieve
• Binary condition: either you achieve the goal or you don’t
Objective
• Outcomes that will help you to achieve a goal
• Directionally oriented--usually maximize or minimize
• Examples:
Maximize number of IEDs detected
Minimize IED production
Maximize reliability of radar
Maximize effectiveness
13
Identifying Objectives: First Steps
• Start with strategic objectives: review planning and strategy documents
• Identify appropriate stakeholders and involve them in the processDecision makersSuperiors or commanding officersOther leadersOperators or customersCommunity leadersGovernment agenciesLegislative bodies
14
Generating Possible Objectives
• Expansive generation of objectives (pruning and structuring comes later)
• Solicit others’ ideas but avoid group work initially
• Brainstorming: solicit objectives from stakeholders without evaluating them
You may or may not want stakeholders in a room together
Try to focus on objectives not positions or alternatives
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Some Questions to Generate Objectives
• What is your goal?
• Why is there a decision to be made?
• If you had no limitations or constraints, what would your objectives be?
• What is your ideal outcome of the decision, and what makes it so ideal?
• What is your nightmare scenario and what makes it so bad?
• What consequences would be unacceptable?
16
Discovering Your Goal(s)
The way things are The way things
should be
COMPARE
Needs
Goals
Objectives
Descriptive
scenario
Prescriptive
scenario
17
Military Healthcare Example
Healthcare for military veterans has been provided by military hospitals. A recent study found that civilian hospitals generally have more advanced medical technology and better trained physicians than military hospitals. Additionally, an increase in the number of veterans has led to longer wait times for some services at military hospitals. The director of veterans affairs is considering a plan under which the Ministry of Defense would pay for veterans to receive services at civilian hospitals.
What should be the goal for the director of veterans affairs when considering whether to adopt the new plan?
18
Cyber Security Example
The Army’s chief technology officer is concerned about the increasing number of cyber attacks against the Army’s computer network. He is unsure whether these attacks are coming from individual hackers who want to cause mischief or from the country’s primary rival for power in the region. Although the vast majority of cyber attacks are unsuccessful at cracking the Army’s firewall, some attacks have gotten through the firewall although even these attacks have been discovered quickly and thwarted thus far.
What should be the goal of the chief technology officer when considering different cyber security alternatives?
19
Military Healthcare Example
What objectives support the primary goal in the military healthcare example?
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Scope
Extent or range of viewpoint or outlook of analysis
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Scoping in Scoping out
Narrowing the problem Broadening the problem
Considering one specific decision
Considering other related decisions
More easily tackled definition
Comprehensive definition
Military Healthcare Example
• Scoping out the problem
How to measure quality of care?
What to do with military doctors employed by veterans affairs? Current military hospitals?
Will decision impact current force structure of the military?
• Scoping in the problem: Assume quality of care is equal under either alternative and select lowest-cost alternative
• Changing scope: Understand what the problems are in the current structure and trying to fix those problems 22
What Does This Mean?
Analysis can help you solve a problem and make a better decision, but only if you are working on the right problem
• Define the scope that you should be considering
• Think about broadening the scope
• Define goals and objectives to correspond with the scope
23
Formulation (conceptual
phase)
Define issues of concern
Clarify objective
Scope problem
Search (research
phase)
Develop alternatives
Look for data
Identify alternatives
Build mental models
Evaluation (analytic phase)
Build mathematical
models
Use models to predict
consequences
Interpretation (judgmental
phase)
Compare alternatives
based on model
predictions
Derive conclusions
Indicate courses of
action
Process of Analysis
24
Search Phase
• Asking questionsWhat are the alternatives?What data do we need?What are the important elements and relationships
of this decision?
• Designing alternativesIdentify all courses of action available to youSelect an appropriate set of possible alternatives to
examine• Too few may not find the best one• Too many may reduce quality of analysis
25
Decision Elements
Should be identified in formulation and search phases
26
PREFERENCESFUTURE
CONDITIONS
OUTCOMES PAYOFFALTERNATIVES
Result ValueCourses of action
Outcome Vs. Payoff
• Outcome: Result or consequence that can occur based on the alternative and future condition
• PayoffHow the decision maker “feels”
about the outcome
Based on the decision maker’s preferences
• Outcome and payoff can be the same thing (example: money)
27
Mental Models
• Graphically depict decision elements using shapes and arrows
28
OUTCOMES PAYOFFALTERNATIVES
Future Conditions Preferences
Bioterrorism
Treatments Detection Development
Transmission
Sanitation
Natural
Diseases
Infection
Control
Healthy
Soldiers
Hospital
Care
29
Hints for Mental Maps
• Begin simple and then make it more complex if necessary
• Do not specify each alternative
Decision node captures several alternatives
• Only include elements that impact your decision or goal/objective
30
Nuclear Weapons Program Example
31
Future nuclear defense
Direct security threats
Regional nuclear
environment
National security
Domestic support
Interdiction strategy
Political and economic
environment
International standing
Political leader
Nuclear weapons program
Adapted from D.J. Caswell and M.E. Paté-Cornell, 2011, “Probabilistic analysis of a country’s program to acquire nuclear weapons,” Military Operations Research 16(1): 5-20.
Decision
Outcome
Importance of Mental Maps
• Structure the problem
Identify outcomes, future conditions, decisions
Examine relationships between variables
• Provide framework for multiple decision makers
32
Why Structure Problems?
We impose structure (like mental mappings) on decision problems to
• Gain insight into the problem
• Specify what we do and don’t “control”
• Better understand uncertainty
• Facilitate quantitative analysis
33
Formulation (conceptual
phase)
Define issues of concern
Clarify objective
Scope problem
Search (research
phase)
Develop alternatives
Look for data
Identify alternatives
Build mental models
Evaluation (analytic phase)
Build mathematical
models
Use models to predict
consequences
Interpretation (judgmental
phase)
Compare alternatives
based on model
predictions
Derive conclusions
Indicate courses of
action
Process of Analysis
34
Evaluation Phase
35
All models
Mental models
Symbolic models
Physical models
Mathematical models
Verbal models
Amount of money
available is budget minus
expenses
M = B - X
• Model: simplified version of reality
• Mathematical models to
Predict consequences
Evaluate decisions
Select alternatives
Mathematical Model Components
1. VariablesRepresent things that change, either with our choice, or because they are inherently unknown or uncertain
2. RelationsRepresent the connections between variables
3. ParametersRepresent the assumptions and information available from data
36
𝑥 𝑦
𝑧
+
≤
=
𝑔 = 9.8 𝑚 𝑠2
• Mathematical models can be classified by their representational formAlgebraic
Tabular
Graphical 13
7
𝑥
𝑦
Mathematical Models
37
𝑦 = 1 + 2𝑥
𝒙 𝒚
1 3
2 5
3 7
Mathematical Models
• Mathematical models can be classified by their treatment of uncertainty
Deterministic
Probabilistic
• Mathematical models can be classified by their treatment of time
Static
Dynamic
38
Mathematical Models
• Mathematical models can be classified by their type of application
Optimization (prescriptive)
• Maximize or minimize an objective
• Subject to some constraints
• Calculate best alternative
Simulation (descriptive)
• What is the relationship between different variables?
• How often is an event likely to occur?
• Simulation models can also be used as inputs into an optimization model
39
Importance of Models
• Allow us to create an ordering over all the alternatives.
• Aid decision makers in ranking alternatives using something universally understood
40
BESTGOODO.K.BADREALLY BAD
5-9 15 21 34 42
A3A2 A6A1A5A4
Model Building Process
41
Can youmake themodel?
Makeassumptions
Is themodeluseful?
NoSimplify
Meaningfuloutput?
Yes
Test themodel
Yes
Identifythe
problem
NoSimplify
Implementthe model
YesMaintainthe model
No
Simplification and Assumption
• Most decision problems have uncertainty and change over time
• But these models are difficult to build and to solve
• Making assumptions and simplifying is necessary
42
Mathematical model• Probabilistic• Dynamic
Mathematical model• Deterministic?• Static?
Assumptions
• Decide which assumptions
Are necessary in order to build and solve a model
Make the model too simple to be useful
• Explain what assumptions are in the model
• Answer how the model output changes if assumptions change
• Incorporate enough detail so that
Results meet your needs
Model is consistent with available data
Model can be analyzed in the time available
43
Example: Renting a Car
• Goal: Select the cheapest rental car company
• Objective: Minimize total weekly costs
• Assumptions1. All cars of equal size and type;
equally efficient and effective
44
2. No alternatives accept awards programs or other incentives
3. Available insurance options all equal
4. Services equal across all alternatives
Car Rental Company Selection
Mental map
45
Rental company Weekly
rental rate
Mileage rate
Mileage cost
Miles driven
Weekly total cost
Car Rental Company Selection
Three Rental Car Alternatives
1. Hurts
• $70 per week plus $0.30 per mile driven
2. Avion
• $100 per week plus $0.80 per mile
• But first 200 miles per week are free
3. Bottomdollar
• $160 per week with unlimited free miles
46
Car Rental Company Selection
Algebraic model
Hurts = $70 + $.30(mileage)
Avion = if mileage <= 200 then cost=$100
else cost = $100 + $.8(mileage - 200)
Bottomdollar = $160
47
Car Rental Company Selection
Tabular model
48
Miles driven
50 100 200 300 375
Hurts 85 100 130 160 183
Avion 100 100 100 180 240
Bottomdollar 160 160 160 160 160
Weekly Auto Rental Cost
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$-
$50
$100
$150
$200
$250
$300
0 50 100 150 200 250 300 350 400
Miles Driven
Co
st
Hurts Avion Bottomdollar
Model Building
• Decision rule becomes clear - when to switch
• Reduces problem to its most important element - mileage
• Aids in understanding the influence of parametersWhat happens if the flat rate on Bottom Dollar
drops to $120?
What happens if the milage rate on Hurts is reduced to $0.60
50
Model Complexity
Complexity
Err
or
Oversimplification Measurement
Total
Optimal complexity depends on the decision context!
51
Model Complexity
• A model always simplifies reality.
• Incorporate enough detail so that:
Results meet your needs
Model is consistent with available data
Model can be analyzed in the time available
Mental maps help you define this boundary
52
“Everything should be made as simple as possible - but no
simpler”
Albert Einstein
1879-1959
53
Formulation (conceptual
phase)
Define issues of concern
Clarify objective
Scope problem
Search (research
phase)
Develop alternatives
Look for data
Identify alternatives
Build mental models
Evaluation (analytic phase)
Build mathematical
models
Use models to predict
consequences
Interpretation (judgmental
phase)
Compare alternatives
based on model
predictions
Derive conclusions
Indicate courses of
action
Process of Analysis
54
Formulation (conceptual
phase)
Search (research
phase)
Evaluation (analytic phase)
Interpretation (judgmental
phase)
Iteration
• Analysis and model building are iterative processes
• Returning to formulation and search phases may be beneficial
Redefine goals and objectives
Develop new alternatives
Change assumptions
55
Logistics
Minimize cost Collect
data
Identifyalternatives
Compareoutcomes
Test forsensitivity
Buildmodels
Predictconsequences
Evaluate &decide
Questionassumptions
Strategy
Minimizevulnerability
Strategic Air Command Air Base Study
56
Collectdata
Identifyalternatives
Predictconsequences
Buildmodels
Key Takeaways
• Before attempting to solve a problem
Think about your goals and objectives
Scope the problem so that it aligns with your goals
• Construct a mental map or use another brainstorming tool to identify key variables and decisions
• Don’t be afraid to go back and revisit assumptions and/or revise your model
57
?
TheAnalytical World
TheReal World
Outcome PayoffINTERACTIONof
DECISIONwith
ENVIRONMENT
VALUATIONof
OUTCOMEvia
PREFERENCES
Environment
“Market”“Operations”
CombatHumanitarian Relief
Peace Keeping
Decision(alternative)
DM Preferences
Analytical Processof
Decision Making
58
Our Modelof the
Real World
Outcome PayoffINTERACTIONof
DECISIONwith
ENVIRONMENT
VALUATIONof
OUTCOMEvia
PREFERENCES
Environment
Decision(alternative)
FUTURECONDITIONS
PreferenceGOAL
OBJECTIVE
59
Decision Environments
Certainty Uncertainty
Complete
information
Incomplete
information
60
“… as we know, there are known knowns;
there are things we know we know.
We also know there are known unknowns;
that is to say we know there are some
things we do not know.
But there are also unknown unknowns --
the ones we don't know we don't know …”
http://www.defenselink.mil/news/Feb2002/t02122002_t212sdv2.html
Secretary of Defense Donald H. Rumsfeld
61
Decision Environments
Certainty Uncertainty
You know:
• all the alternatives
• the one future condition
• all the payoffs
62
Decision Matrix Under Certainty
Future Condition
Alternative 1
Alternative 2
:
Alternative 3
63
Decision Environments
Certainty Uncertainty
Complete
information
Incomplete
information
You do not know one or more of:
• all the alternatives
• all the future conditions
• all the payoffs
• all the probabilities
of the future conditions
64
Decision Environments
Certainty Uncertainty
Complete
information
Incomplete
information
You know:
• all the alternatives
• all the future conditions
• all the payoffs
• all the probabilities
of the future conditions
65
Future
Condition 1
Future
Condition 2
• • • Future
Condition N
Alternative 1 Probability
Alternative 2 Outcome
Payoff
•
•
•
•
Alternative K • • •
Static Decisions
Decision Matrix
66
67
Probability
• A measure of the likelihood of the occurrence of a future event
• The quantification of uncertainty
474
240
158
65
3820
4 10.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
1.5 - 2.5 2.5 - 3.5 3.5 - 4.5 4.5 - 5.5 5.5 - 6.5 6.5 - 7.5 7.5 - 8.5 8.5 - 9.5
Histogram
Do
Nothing
New
Codes
New Codes
1 2 3 4 5 6 7 8F F F F F F F F
0
10
50
ImplementationCost
Earthquake Problem.474
.240
.065
.158
.038 .020.004 .001
.5
.4
.3
.2
.1
0
Re
lati
ve
Fre
qu
en
cy
1.5 7.56.55.54.53.52.5 9.58.5
& Retrofit
69
Do
Nothing
New
Codes
New Codes
& Retrofit
F1 F2 F3 F4 F5 F6 F7 F8
Earthquake Problem
0
10
50
25 25,000,0002,500,000250,00025,0002,500250
18 4,106
472
522
10651 58
74 32,778 262,154
3,214 23,780
2,097,162
178,029
250,000,000
16,777,226
1,334,889
.474
.240
.065
.158
.038 .020.004 .001
.5
.4
.3
.2
.1
0
Re
lati
ve
Fre
qu
en
cy
ImplementationCost
1.5 7.56.55.54.53.52.5 9.58.5
70
Do
Nothing
New
Codes
New Codes
& Retrofit
F1 F2 F3 F4 F5 F6 F7 F8
Earthquake Problem
0
10
50
25
18
51
.474
.240
.065
.158
.038 .020.004 .001
.5
.4
.3
.2
.1
0
Re
lati
ve
Fre
qu
en
cy
ImplementationCost
Decision Rule:
Most Likely
1.5 7.56.55.54.53.52.5 9.58.5
71
Earthquake Problem.474
.240
.065
.158
.038 .020.004 .001
.5
.4
.3
.2
.1
0
Re
lati
ve
Fre
qu
en
cy
Decision Rule:
Expected Value
Do
Nothing
New
Codes
New Codes
& Retrofit
32,030
2,730
411,592
1.5 7.56.55.54.53.52.5 9.58.5
72
Malaria Prevention
Mental Map
Payoff
Exposed
to Malaria?
Take
Malaria
Pills?
73
F1
Exposed to Malaria
F2
Not exposed to Malaria
Take Malaria Pills
Don’t Take Malaria Pills
Malaria Prevention
(Decision Matrix)
74
Dynamic Decisions
What happens when choice of an alternative changes the matrix ?
• when the likelihoods change ? • when the number of future
conditions change ?• when there is a sequence of
decisions ?
75
Tree Model
Decision node
Future condition node
NODES BRANCHES
76
Payoffs
Take
Malaria Pills
Malaria Prevention
(Decision Tree)
Don’t Take
Malaria Pills
Exposed
to Malaria
Not Exposed
to Malaria
Not Exposed
to Malaria
Exposed
to Malaria
77
• If you have been exposed to malaria, you
can take medications immediately after
exposure to prevent malaria
Lowers your chances of malaria
Why use a decision tree?(Sequential decisions)
78
Malaria Prevention
Mental Map
Payoff
Develop
Malaria?
Take
Malaria
Pills?
Exposed
to Malaria?
Take
Post-
Exposure
Pills?
79
Malaria Prevention
Take
Malaria Pills
Don’t Take
Malaria Pills
Exposed
to Malaria
Not Exposed
to Malaria
Not Exposed
to Malaria
Exposed
to Malaria
Take Post-
Exposure Pills
No Post-
Exposure Pills
Take Post-
Exposure Pills
No Post-
Exposure Pills
Malaria
No Malaria
Malaria
No Malaria
Malaria
No Malaria
Malaria
No Malaria
80
Which Alternative is Better?
A
C
B
$ Cost
Benefits
81
Which Alternative is Better?
A C B
$ Cost
Benefits
82
Which Alternative is Better?
AC
B
$ Cost
Benefits
83
Guidance(OMB Circular A-94)
“The goal is…to promote efficient resource allocation through well-informed decision-making by the
Federal Government.”
84
http://www.whitehouse.gov/omb/circulars_a094/
Decision Criteria
With UNLIMITED resources…if there is anypositive benefit, then no matter what it costs, make the investment in:
National Security;
Transportation;
Education;
Health & Safety Regulations
Posner & Adler (Eds) 2001 Cost-Benefit Analysis
85
Why Worry About Cost?
• Any course of action, any decision, will exact a cost
Cost is a measure of the consequences of our decision
• As long as resources are limited, cost will be a factor in our decision
86
Decision Criteria
• Equal BenefitsMinimize costs
• Equal CostsMaximize benefits
• Different Costs and BenefitsIf benefits can be monetized
• Net Present Value
If not…• Need to make tradeoffs!
87
Getting Started
• Identify feasible, mutually exclusive alternatives
• Define the planning horizon
• Develop cash flow profiles
• Specify the discount rate to be used
88
Planning Horizon
• The period of time over which the cash flows of alternatives are compared
Must be the same for each alternative
Must consider useful life of alternatives
• Common approaches
Least common multiple of lives
Shortest life
Standard horizon
89
90
Specifying the Interest Rate
Circular A-94 sec 8
Benefit-Cost Analysis
• Benefits and costs can be monetized
• Real 7% (marginal pretax rate of return on an average investment in the private sector)
– Market interest rates are nominal
Cost-Effectiveness Analysis
• Most DoD decisions fall in this category
• Treasury’s borrowing rates for comparable length of maturity
– Published Treasury rates are nominal
OMB Guidance
• Cost-Effectiveness is appropriate whenever it is unnecessary or impractical to consider the dollar value of the benefits.
• Analysis of alternative defense systems often falls in this category.
OMB Circular A-94, par. 5b
91
Cost-Effectiveness Analysis
• Benefits can not be quantified in monetary terms
Define effectiveness based on desired capabilities/characteristics
Measure capabilities of alternatives and assign a measure of effectiveness
• Identify "efficient frontier"
• Incremental analysis (tradeoffs)
effectiveness vs. cost
92
Risk is part of life
• Every decision in an uncertain world involves some degree of risk.
There is the risk that the cost will be higher than expected.
There is the risk that the benefit will be lower than expected.
93
ASSESSING RISK
• What can go wrong?
• What is the likelihood?
• What are the consequences?
• How do we feel about the consequences?
What do we mean by Cost Risk?
• What can go wrong?
The actual cost of a program exceeds the budget for that program (cost overrun)
• What is the probability of a cost overrun?
• What are the consequences of a cost overrun?
X
1 2 3123
68%
Normal DistributionProbabilities
X
1 2 3123
95%
Normal DistributionProbabilities
X
1 2 3123
99%
Normal DistributionProbabilities
Thinking about the budget
Funding at the 50% level means there is a 50% chance of cost overrun.
P(cost overrun)
= 9.63%
P(cost overrun)
= 97.76%
Comparing the Risk of Alternatives
Acceptable Risk?
Risk cannot be spoken of as acceptable or not in
isolation, but only in combination with the costs and
benefits that are attendant to that risk. Considered in
isolation, no risk is acceptable! A rational person
would not accept any risk at all except possibly in
return for the benefits that come along with it.
Even then, if a risk is acceptable on that basis, it is still
not acceptable if it is possible to obtain the same
benefit in another way with less risk.
Kaplan and Garrick, “On The Quantitative Definition of Risk”,
Risk Analysis, Vol. 1, No. 1, 1981
101
Risk Tradeoff
Risk
Cost
Acceptable
Risk
Required Budget
Too Risky
Proposed Budget
102
Risk
Cost
Risk Management
old
new
103
Risk
CostProposed Budget
Less Risk
new
Risk Management
104
Risk
Cost
Acceptable
Risk
Less Cost
new
Risk Management
105
Ultimately, policy makers must decide how much
the United States is willing to pay to lower the risks
associated with deploying forces abroad. But some
might argue that defense planners occasionally focus
on absolute requirements – the minimum number of
forces that they believe will meet DoD’s military
needs – without fully weighing the relative risks
and costs of alternative levels.
Moving U.S. Forces: Options for Strategic Mobility
Congressional Budget Office, Feb. 1997
106
Pitfalls in All Analysis
• Not enough time spent defining the
problem.
• Examining a restricted range of
alternatives.
• Too much time spent in the details of
the models.
107
Advantages of Analysis
• Answers are accessible to critical
examination
• Answers can be retraced by others
• Answers can be modified by others
108