1
Ethical Issues in a Health Assessment
Giovanna Skylar
Institutional Affiliation
HHA3002
Dr. Tilman
July 26th, 2022
2
Ethical Issues in a Health Assessment
Question 1
The reporting of a client's health status must abide by the disclosure policies and
procedures provided in the health and medical standards. After my client has tested positive, I
will report her health status to the state health departments. The information is supposed to help
public health officials monitor the state's health status. It is fundamental to report this
information as the federal and state funding for HIV services is often targeted to regions under
severe attacks by the epidemic (HIV.gov, 2017). The second party that should be notified of the
status is the new boyfriend in the waiting room, who should be notified under the client's
consent. The non-disclosure of this information will likely put the new boyfriend at risk of being
infected. As suggested by the HPCSA, for information to be disclosed, the potential for causing
harm to third parties must be high enough to surpass the patient's right to privacy. The
information should, however, be disclosed through the counseling process to make them
understand the importance of extending care to the patients.
Question 2
Confidentiality of the client data is essential in communication between the health worker
and the client. Confidentiality is especially useful in the process of counseling and treatment
services. Although health workers' professional ethics recommend adherence to patient
confidentiality, observing these guidelines strictly may risk the client's significant other and the
public. Therefore, I will use the counseling approach to help the client realize the dangers that
might find her significant others. The lack of disclosure by the client is based on the assumption
the information could cause her separation from her new relationship. However, previous studies
suggest that couple counseling schemes have successfully reduced the number of marriage
3
separations after the HIV status diagnosis (Dessalegn et al., 2019). The impact the infection can
cause on a partner would be severe, and it is necessary to create awareness on this matter. I will
take this approach because counseling may enable my client to provide individual consent for the
disclosure, thus avoiding the breach of confidentiality.
Question 3
The first action that must be taken to protect the confidentiality of the patient's
information is to prohibit sharing information without informed consent. Strict rules should be
implemented to help share information where there are exceptions (Liz Stokes, 2019). In this
case, exceptions should only be permitted when a person's life is endangered, in case there is a
legal requirement, or where the non-disclosure threatens the public. This information should also
be limited to relevant entities, such as the public health department.
Some policies that must be implemented should include informing the patient through
writing regarding the information to be released, the party to release the information, and the
individuals who will receive the information (Liz Stokes, 2019). The second action that can help
to protect patient data confidentiality is offering education to staff concerning potential areas of
misuse of patient information. The health centers should implement policies regarding the
improper use of information (Araújo et al., 2020). For example, the policies should address areas
such as personal electronic data devices, emails, and electronic transmission of data.
4
References
Araújo, W. J. S., Bragagnollo, G. R., Nascimento, K. C. D., Camargo, R. A. A. D., Tavares, C.
M., & Monteiro, E. M. L. M. (2020). Educational intervention on HIV/AIDS with elderly
individuals: a quasi-experimental study. Texto & Contexto-Enfermagem, 29.
Dessalegn, N. G., Hailemichael, R. G., Shewa-Amare, A., Sawleshwarkar, S., Lodebo, B.,
Amberbir, A., & Hillman, R. J. (2019). HIV Disclosure: HIV-positive status disclosure to
sexual partners among individuals receiving HIV care in Addis Ababa, Ethiopia. PloS
one, 14(2), e0211967.
Liz Stokes, J. D. (2019). ANA position statement: Nursing advocacy for LGBTQ+
populations. Online Journal of Issues in Nursing, 24(1), 1-6.
HIV.gov. (2017, August 31). Limits on Confidentiality. HIV.gov. https://www.hiv.gov/hivbasics/living-well-with-hiv/your-legal-rights/limits-on-confidentiality
1
Pre-Assessment
Giovanna Skylar
Walden University
HA3002
2
Pre-Assessment
Provision of the Code of Ethics for Nurses
Code of Ethics for Nurses provides an ethical framework to guide the decision-making in
ethical dilemmas. Besides, the code ensures nurses provide quality care through ethically guided
action that places the patient at the center of the care process. In this context, Provision 3 of the
code of ethics stipulates that nurse promotes, advocates for, and protects the patient's rights and
safety (American Nurses Association, 2019). In this provision, nurses are ethically obligated to
protect patient's privacy and confidentiality. In this regard, the nurse has the moral responsibility
to provide a safe and private environment to engage in conversation with the patient.
In the current case, the need-to-know basis would be appropriate to ensure quality care.
Studies by Stutterheim et al. (2014) revealed that explicit breaches of confidentiality and
carelessness were common violations of patient privacy and confidentiality for those diagnosed
with HIV. In part, eases of access to patient files, use of the nurse notes, and unnecessary referral
increased stigma and perception of poor quality. In this regard, the need to know will form the
basis of sharing the patient HIV status with other professionals. At the same time, documentation
and file storage will align with hospital standards of data protection and privacy policies.
Holistic Approach
Holistic approaches to the assessment of people with HIV should be longitudinal. In
particular, new complications and challenges tend to arise during the cause of the treatment. HIV
disclosure to the patient partner is vital in social support groups and has positive and negative
consequences. In part, disclosure can increase the risk of relationship dissolution, while on the
other hand, disclosure has the potential to increase social support and the subsequent adherence
to antiretroviral therapy (ART). Besides, the motivation to disclose among HIV patients is
3
related to various factors. Notably, when the patient considers the personal and interpersonal
gains for others, the likelihood of self-disclosure is high.
Thus, the narrative therapy approach offers a viable model for providing holistic care. In
particular, the narrative approach addresses the need to establish closeness, the fear of rejection,
and privacy concerns. In the narrative approach, the patient gains the ability to externalize the
problem rather than internalize the problems. In this case, the approach relies on the patient's
skills and the sense of purpose as a resource during difficult times. The patients' need is
addressed through the after-mentioned strategy, considering both the emotional aspects.
Alignment with the Code of Ethics
Research has consistently shown that the barrier to disclosing HIV is linked to the fear of
stigma. In essence, fear of discrimination, relationship dissolution, and intimate partner violence
are cited as the primary motive for withholding HIV serostatus (Xiao et al., 2015). Besides, the
legal mandate for self-disclosure further violates the patient's rights to privacy and increases
emotional distress. On the other hand, the perception of control over privacy issues and the
perception of interpersonal and personal gain is associated with a higher willingness to disclose
HIV status to partners and friends.
In this regard, the narrative approach aligns with ANA provision 3. In this case, the nurse
focuses on protecting the patient's right to privacy and confidentiality. In the narrative approach,
the patient needs and privacy concerns are fully addressed in that the potential of a breach of
confidentiality is limited (Obermeyer et al., 2011). Instead, patients leverage on own skills to
find the motivation to disclose while receiving emotional and social support from the health care
providers. Compared to mandatory reporting set by legal provisions, the narrative approach is
holistic. It addresses other underlying issues, such as adherence to ART and overcoming distress
4
due to violating individual privacy. Hence, rather than resorting to legal means, enabling the
patient to externalize the problem will increase the motivation to disclose the serostatus based on
the positive perception of support from the health care provider and total control over personal
privacy.
5
References
American Nurses Association. (2019). American nurses association code of ethics for nurses.
https://nursing.rutgers.edu/wp-content/uploads/2019/06/ANA-Code-of-Ethics-forNurses.pdf
Obermeyer, C. M., Baijal, P., & Pegurri, E. (2011). Facilitating HIV disclosure across diverse
settings: A review. American Journal of Public Health, 101(6), 1011–1023.
https://doi.org/10.2105/ajph.2010.300102
Stutterheim, S. E., Sicking, L., Brands, R., Baas, I., Roberts, H., van Brakel, W. H., Lechner, L.,
Kok, G., & Bos, A. E. R. (2014). Patient and provider perspectives on HIV and hivrelated stigma in dutch health care settings. AIDS Patient Care and STDs, 28(12), 652–
665. https://doi.org/10.1089/apc.2014.0226
Xiao, Z., Li, X., Qiao, S., Zhou, Y., Shen, Z., & Tang, Z. (2015). Using communication privacy
management theory to examine HIV disclosure to sexual partners/spouses among PLHIV
in guangxi. AIDS Care, 27(sup1), 73–82.
https://doi.org/10.1080/09540121.2015.1055229
STEPHEN G. POWELL
KENNETH R. BAKER
MANAGEMENT
SCIENCE
CHAPTER 8 POWERPOINT
NONLINEAR OPTIMIZATION
The Art of Modeling with Spreadsheets
Compatible with Analytic Solver Platform
FOURTH EDITION
OPTIMIZATION
• Find the best set of decisions for a particular measure of
performance
• Includes:
– The goal of finding the best set
– The algorithms (procedures) to accomplish this goal
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
2
EXCEL OPTIMIZATION SOFTWARE
• Solver
– Standard with Excel
• Analytic Solver Platform
– Comes with text – install off text CD
– More advanced than standard solver
– Is preferred tool throughout text
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
3
DECISION VARIABLES
• Levers used to improve performance
• Want to find the best values for the variables
• Finding these best values can be challenging
– Need Solver’s sophisticated software
– Still relatively easy to construct models beyond Solver’s
capabilities
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
4
SOLVER WINDOW
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
5
FORMULATION
• Decision variables
– What must be decided? Be explicit with units
• Objective function
– What measure compares decision variables?
– Use only one measure (as a “yardstick”) – put in target cell
• Constraints
– What restrictions limit our choice of decision variables?
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
6
CONSTRAINTS
• Left-hand-side (LHS)
– Usually a function
• Right-hand-side (RHS)
– Usually a number (i.e., a parameter)
• Three types of constraints
– LHS = RHS
– LHS = RHS
Chapter 8
(less-than [LT] constraint)
(Greater than [GT] constraint)
(Equality [EQ] constraint)
Copyright © 2013 John Wiley & Sons, Inc.
7
TYPES OF CONSTRAINTS
• LT constraints (LHSRHS)
– Commitments or thresholds
• EQ constraints (LHS=RHS)
– Material balance
– Define related variables consistently
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
8
LAYOUT
• Standard model template is advisable
• Enhances ability to communicate
– Provides common language
– Reinforces understanding how models shaped
• Improves ability to spot modeling errors
• Enables “scaling up” more easily
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
9
LAYOUT
• Organize worksheet in modules
– Decision variables, objective function, constraints
• Place decision variables in single row (or column)
• Use color or border highlighting
• Place objective in single highlighted cell
• Arrange constraints for visual comparison of LHS and RHS
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
10
SOLVER TIP: RANGES FOR DECISION VARIABLES
• Arrange worksheet with all decision variables in adjacent
cells
– Enables a single reference to their range
– Makes data entry efficient
– Reduces clutter in Solver interface
– Makes task pane description easier to interpret
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
11
INTERPRETING RESULTS
• Optimal values of decision variables
– Best course of action for the model
• Optimal value of objective function
– Best level of performance possible
• Constraint outcomes
– Constraint is tight or binding if LHS=RHS in LT or GT
constraint
– Throughout optimization, generally only some constraints
are binding
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
12
INTERPRETING RESULTS: OPTIMIZATION SOLUTION
• Tactical information
– Plan for decision variables
• Strategic information
– What factors could lead to better levels of performance?
– Binding constraints are economic factors that restrict the
value of the objective.
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
13
MODEL CLASSIFICATION AND THE NONLINEAR SOLVER
• Linear optimization or linear programming
– Objective and all constraints are linear functions of the
decision variables
• Nonlinear optimization or nonlinear programming
– Either objective or a constraint (or both) are nonlinear
functions of the decision variables
• Techniques for solving linear models are more powerful
– Use wherever possible
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
14
“HILL CLIMBING”
• Technique used by Solver for nonlinear optimization
• Called LSGRG (Large-Scale Generalized Reduced
Gradient) algorithm
• Hill climbing in a fog
– Try to follow steepest path going up
– After each step, or group of steps, again find steepest path
and follow it
– Stop if no path leads up
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
15
LOCAL AND GLOBAL OPTIMUM
• The highest peak is the global optimum.
– What we want to find
• Any peak higher than all points around it is a local
optimum.
– What the LSGRG algorithm locates
– Except in special circumstances, there is no way to
guarantee that a local optimum is the global optimum.
– If multiple local optima, then which is found depends on
starting point for decision variables – may want to run
Solver starting from multiple points
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
16
PROGRAMMING EXAMPLES
• Facility location
• Revenue maximization
– Maximize revenue in the presence of a demand curve
• Curve fitting
– Fit a function to observed data points
• Economic Order Quantity
– Trade-off ordering and carrying costs for inventory
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
17
SOLVER TIP: SOLUTIONS FROM THE LSGRG ALGORITHM
• When the GRG algorithm concludes with the convergence message,
“Solver has converged to the current solution, all constraints are
satisfied”, the algorithm should be rerun from the stopping point.
• This message may then reappear, in which case Solver should be
rerun once more.
• Eventually, the algorithm should conclude with the optimality
message, “Solver found a solution, all constraints and optimality
conditions are satisfied”, which signifies that it has found a local
optimum.
• To help determine whether the local optimum is also a global
optimum, Solver should be restarted at a different set of decision
variables and rerun.
• If several widely differing starting solutions lead to the same local
optimum, that is some evidence that the local optimum is likely to
be a global optimum, but in general there is no way to know for
sure.
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
18
SOLVER TIP: AVOID DISCONTINUOUS FUNCTIONS
• A number of functions familiar to experienced Excel
programmers should be avoided when using the
nonlinear solver.
• These include:
– Logical functions (e.g., IF or AND)
– Mathematical functions (e.g., ROUND or CEILING)
– Lookup and reference functions (e.g., CHOOSE or VLOOKUP)
– Statistical functions (e.g., RANK or COUNT).
• In general, avoid using any function that changes
discontinuously.
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
19
SENSITIVITY ANALYSIS FOR NONLINEAR PROGRAMS
• Tests our initial assumptions to see what impact they
have on our conclusions.
• Analysis of one or two variables can lead to optimal
values of those variables.
– E.g., using the Parametric Sensitivity tool.
• Solver tool for larger numbers of variables and
constraints
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
20
SOLVER TIP: WHAT KIND OF SENSITIVITY ANALYSIS?
• Easy to confuse parametric sensitivity with optimization
sensitivity, which answer different questions:
– Optimization sensitivity determines how the optimal
solution changes with a change in parameter.
– Parametric sensitivity answers how specific outputs change
with parameters.
• The Solver tool can answer questions about how specific
outputs change with a change in one or two parameters.
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
21
THE PORTFOLIO OPTIMIZATION MODEL
• The performance of a portfolio of stocks is measured in
terms of return and risk.
• When we create a portfolio of stocks, our goals are
usually to maximize the mean return and to minimize the
risk.
• Both goals cannot be met simultaneously, but we can use
optimization to explore the trade-offs involved.
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
22
*EXCEL MINI-LESSON: THE COVAR FUNCTION
• The COVAR function in Excel calculates the covariance
between two equal-sized sets of numbers representing
observations of two variables.
• The covariance measures the extent to which one
variable tends to rise or fall with increases and decreases
in the other variable.
– If the two variables rise and fall in unison, their covariance
is large and positive.
– If the two variables move in opposite directions, then their
covariance is negative.
– If the two variables move independently, then their
covariance is close to zero.
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
23
SUMMARY
• Optimization: Answers “What values of the decision
variables lead to the best possible value of the
objective?”
• Excel Solver: Collection of optimization procedures
– Nonlinear Solver is Solver’s default choice
• Steps: 1) formulating, 2) solving, and 3) interpreting
optimization problems.
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
24
SUMMARY
• These guidelines for model builders are the craft skills
typically exhibited by experts:
– Follow a standard form whenever possible.
– Enter cell references in the Solver windows; keep
numerical values in cells.
– Try out some feasible (and infeasible) possibilities as a way
of debugging the model and exploring the problem.
– Test intuition and suggest hypotheses before running
Solver.
Chapter 8
Copyright © 2013 John Wiley & Sons, Inc.
25
COPYRIGHT © 2013 JOHN WILEY & SONS, INC.
All rights reserved. Reproduction or translation of
this work beyond that permitted in section 117 of the 1976
United States Copyright Act without express permission of
the copyright owner is unlawful. Request for further
information should be addressed to the Permissions
Department, John Wiley & Sons, Inc. The purchaser may
make back-up copies for his/her own use only and not for
distribution or resale. The Publisher assumes no
responsibility for errors, omissions, or damages caused by
the use of these programs or from the use of the information
herein.
10 - 26
STEPHEN G. POWELL
KENNETH R. BAKER
MANAGEMENT
SCIENCE
CHAPTER 9 POWERPOINT
LINEAR OPTIMIZATION
The Art of Modeling with Spreadsheets
Compatible with Analytic Solver Platform
FOURTH EDITION
MODEL CLASSIFICATION
• Linear optimization or linear programming
– Objective and all constraints are linear functions of the
decision variables.
• Nonlinear optimization or nonlinear programming
– Either objective or a constraint (or both) are nonlinear
functions of the decision variables.
• Techniques for solving linear models are more powerful.
– Use wherever possible.
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
2
PROPERTIES OF LINEAR FUNCTIONS
• Term “linear” refers to a feature of the objective function
and the constraints.
• Linear function exhibits:
– Additivity
– Proportionality
– Divisibility
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
3
EXCEL MINI-LESSON: THE SUMPRODUCT FUNCTION
• The SUMPRODUCT function in Excel takes the pairwise
products of two sets of numbers and sums the products.
• SUMPRODUCT(Array1,Array2)
– Array1 references the first set of numbers.
– Array2 references the second set of numbers.
• The two arrays must have identical layouts and be the
same size.
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
4
THE SIMPLEX ALGORITHM FOR LINEAR OPTIMIZATION
• Exploits special properties of linearity to find optimal
solutions.
• Imagine the surface of a diamond which represents feasible
decision variables:
– Starts with a feasible set of decision variables that corresponds to a corner on a
diamond.
– Checks to see if a feasible neighboring corner point is better.
– If not, stops; otherwise moves to that better neighbor and return to step 2.
Guaranteed to converge
to the global optimal solution
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
5
LINEAR PROGRAMMING PROBLEMS
• Allocation models
– Maximize objective (e.g., profit) subject to LT constraints on capacity
• Covering models
– Minimize objective (e.g., cost) subject to GT constraints on required
coverage
• Blending models
– E.g., in determining product mix; mix materials with different
properties to find best blend
• Network models
– Describe patterns of flow in a connected system
– Covered in Chapter 10
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
6
SOLVER TIP: RESCALING THE MODEL
• Consider scaling parameters to appear in thousands or
millions
• Saves work in data entry – decreases errors
• Spreadsheet looks less crowded
• Helps with Solver algorithms
– Value of objective, constraints, and decision variables
should not differ from each other by more than a factor of
1000, at most 10,000.
• Can always display model output on separate sheet with
separate units
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
7
AUTOMATIC SCALING
• Use if scaling problems difficult to avoid
• Consider when:
– Solver claims no feasible solution when user is sure there
is one.
• Preferable for model-builder to do the scaling
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
8
SENSITIVITY ANALYSIS FOR LINEAR PROGRAMS
• A distinct pattern to the change in the optimal solution
when varying a coefficient in the objective function
• In some interval around the base case
– No change in optimal decisions
– Objective will change if decision variable is positive
• Outside this interval a different set of values is optimal
for decision variables
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
9
SOLVER TIP: OPTIMIZATION SENSITIVITY AND SHADOW
PRICES
• Break-even price where attractive to acquire more of a
scarce resource
• Improvement in objective function from a unit increase
(or decrease) in RHS of constraint
• In linear programs, constant for some range of changes
to RHS.
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
10
SENSITIVITY ANALYSIS
FOR BINDING CAPACITY CONSTRAINTS
• A distinct pattern in sensitivity tables when varying
availability of scare resource
• In some interval around the base case:
– Marginal value (shadow price) of capacity remains
constant
– Some variables change linearly with capacity
– Others remain the same
• Below this interval the value decreases and eventually
reaches zero.
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
11
PATTERNS IN LINEAR PROGRAMMING SOLUTIONS
• The optimal solution tells a “story” about a pattern of
economic priorities.
– Leads to more convincing explanations for solutions
– Can anticipate answers to “what-if” questions
– Provides a level of understanding that enhances decision
making
• After optimization, should always try to discern the
qualitative pattern in the solution.
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
12
CONSTRUCTING PATTERNS
• Decision variables
– Which are positive and which are zero?
• Constraints
– Which are binding and which are not?
• “Construct” the optimal solution from the given
parameters
– Determine one variable at a time
– Can be interpreted as a list of priorities which reveal the
economic forces at work
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
13
DEFINING PATTERNS
• Qualitative description
• Pattern should be complete and unambiguous
– Leads to full solution
– Always leads to same solution
• Ask where shadow prices come from
– Should be able to trace the incremental changes to derive
shadow price of constraint
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
14
*DATA ENVELOPMENT ANALYSIS
• DEA is a linear programming application aimed at
evaluating the efficiencies of similar organizational
departments or decision-making units (DMUs).
• DMUs are characterized in terms of inputs and outputs,
not in terms of operating details.
• A DMU is considered efficient if it gets the most output
from its inputs.
• The purpose of DEA is to identify inefficient DMUs when
there are multiple outputs and multiple inputs.
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
15
EXCEL MINI-LESSON: THE INDEX FUNCTION
• The INDEX function finds a value in a rectangular array
according to the row number and column number of its
location.
• The basic form of the function, as we use it for DEA
models, is the following:
– INDEX(Array, Row, Column)
• Array references a rectangular array.
• Row specifies a row number in the array.
• Column specifies a column number in the array. If Array
has just one column, then this argument can be omitted.
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
16
SUMMARY
• Linear programming represents the most widely used
optimization technique in practice.
• The special features of a linear program are a linear
objective function and linear constraints.
• Linearity in the optimization model allows us to apply the
simplex method as a solution procedure, which in turn
guarantees finding a global optimum whenever an
optimum of any kind exists.
• Therefore, when we have a choice, we are better off with
a linear formulation of a problem than with a nonlinear
formulation.
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
17
SUMMARY
• While optimization is a powerful technique, we should
not assume that a solution that is optimal for a model is
also optimal for the real world.
• Often, the realities of the application will force changes
in the optimal solution determined by the model.
• One powerful method for making this translation is to
look for the pattern, or the economic priorities, in the
optimal solution.
• These economic priorities are often more valuable to
decision makers than the precise solution to a particular
instance of the model.
Chapter 9
Copyright © 2013 John Wiley & Sons, Inc.
18
COPYRIGHT © 2013 JOHN WILEY & SONS, INC.
All rights reserved. Reproduction or translation of
this work beyond that permitted in section 117 of the 1976
United States Copyright Act without express permission of
the copyright owner is unlawful. Request for further
information should be addressed to the Permissions
Department, John Wiley & Sons, Inc. The purchaser may
make back-up copies for his/her own use only and not for
distribution or resale. The Publisher assumes no
responsibility for errors, omissions, or damages caused by
the use of these programs or from the use of the information
herein.
11 - 19
STEPHEN G. POWELL
KENNETH R. BAKER
MANAGEMENT
SCIENCE
CHAPTER 10 POWERPOINT
NETWORK MODELS
The Art of Modeling with Spreadsheets
Compatible with Analytic Solver Platform
FOURTH EDITION
THE NETWORK MODEL
• Describes patterns of flow in a connected system, where
the flow might involve material, people, or funds
• System elements may be locations (e.g., cities,
warehouses, or assembly lines), or points in time.
• We construct diagrams to represent such systems with
elements are represented by nodes (circles). The paths of
flow are represented by arcs or arrows.
Chapter 10
Copyright © 2013 John Wiley & Sons, Inc.
2
THE TRANSPORTATION MODEL
• A very common supply chain involves the shipment of
goods from suppliers at one set of locations to customers
at another set of locations.
• The classic transportation model is characterized by a set
of supply sources (each with known capacities), a set of
demand locations (each with known requirements) and
the unit costs of transportation between supply-demand
pairs.
Chapter 10
Copyright © 2013 John Wiley & Sons, Inc.
3
TRANSPORTATION PROBLEM: MODEL FORMULATION
• The transportation model has two kinds of constraints:
– Less-than capacity constraints and
– Greater-than demand constraints
• If total capacity equals total demand, both capacity and
demand constraints are “=”.
• If capacity exceeds demand, the capacity constraints are
“”.
• If demand exceeds capacity, the capacity constraints are
“>” and the demand constraints are “ 1
• Project 2, or Project 5, or both, will be selected, thus
satisfying the requirement of at least one selection.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
14
RELATIONSHIP: AT MOST N PROJECTS MUST BE SELECTED
• y4 + y5 < 1
• Project 4, or Project 5, or neither, but not both will be
selected, thus satisfying the requirement of at most one
selection.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
15
RELATIONSHIP: EXACTLY K PROJECTS MUST BE SELECTED
• y4 + y5 = 1
• Exactly one of either Project 4 or Project 5 will be
selected, thus satisfying the requirement of exactly one
selection.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
16
RELATIONSHIP:
SOME PROJECTS HAVE CONTINGENCY RELATIONSHIPS
• y3 – y5 > 0
• If Project 5 is selected, then project 3 must be as well.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
17
LINKING CONSTRAINTS AND FIXED COSTS
• We commonly encounter situations in which activity
costs are composed of fixed costs and variable costs, with
only the variable costs being proportional to activity
level.
• With an integer programming model, we can also
integrate the fixed component of cost.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
18
LINKING CONSTRAINTS AND FIXED COSTS
• We separate the fixed and variable components of cost.
• In algebraic terms, we write cost as:
Cost = Fy + cx
where F represents the fixed cost, and c represents the
linear variable cost.
• The variables x and y are decision variables, where x is a
normal (continuous) variable, and y is a binary variable.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
19
LINKING CONSTRAINTS AND FIXED COSTS
• To achieve consistent linking of the two variables, we add
the following generic linking constraint to the model:
x < My
where the number M represents an upper bound on the
variable x.
• In other words, M is at least as large as any value we can
feasibly choose for x.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
20
LINKING CONSTRAINT: X < MY
• When y = 0 (and therefore no fixed cost is incurred), the righthand side becomes zero, and Solver interprets the constraint
as x = 0, these two constraints together force
x to be zero.
– Thus, when y = 0, it will be consistent to avoid the fixed cost.
• On the other hand, when y = 1, the right-hand side will be so
large that Solver does not need to restrict x at all, permitting
its value to be positive while we incur the fixed cost.
– Thus, when y = 1, it will be consistent to incur the fixed cost.
• Of course, because we are optimizing, Solver will never
produce a solution with the combination of y = 1 and x = 0,
because it would always be preferable to set y = 0.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
21
SOLVER TIP:
LOGICAL FUNCTIONS AND INTEGER PROGRAMMING
• Experienced Excel programmers might be tempted to use
the logical functions (IF, AND, OR, etc.) to express certain
relationships.
• Unfortunately, the linear solver does not always detect
the nonlinearity caused by the use of logical functions, so
it is important to remember never to use an IF function in
a model built for the linear solver.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
22
THRESHOLD LEVELS AND QUANTITY DISCOUNTS
• Threshold level requirement: a decision variable is
either at least as large as a specified minimum, or else it
is zero.
• The existence of a threshold level does not directly affect
the objective function of a model, and it can be
represented in the constraints with the help of binary
variables.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
23
THRESHOLD LEVELS
• Suppose we have a variable x that is subject to a
threshold requirement. Let m denote the minimum
feasible value of x if it is nonzero. Then we can capture
this structure in an integer programming model by
including the following pair of constraints:
x – my > 0
x – My < 0
where, as before, M is a large number that is greater
than or equal to any value x could feasibly take.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
24
*THE FACILITY LOCATION MODEL
• The transportation model (discussed in Chapter 10) is
typically used to find optimal shipping schedules in
supply chains and logistics systems.
• The applications of the model can be viewed as tactical
problems, in the sense that the time interval of interest is
usually short, say a week or a month.
• Over that time period, the supply capacities and
locations are unlikely to change at all, and the demands
can be predicted with reasonable precision.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
25
*THE FACILITY LOCATION MODEL
• Over a longer time frame, a strategic version of the
problem arises. In this setting, the decisions relate to the
selection of supply locations as well as the shipment
schedule.
• These decisions are strategic in the sense that, once
determined, they influence the system for a relatively
long time interval.
• The basic model for choosing supply locations is called
the facility location model.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
26
THE CAPACITATED PROBLEM
• Conceptually, we can think of this problem as having two
stages.
• In the first stage, decisions must be made about how
many warehouses to open and where they should be.
• Then, once we know where the warehouses are, we can
construct a transportation model to optimize the actual
shipments.
• The costs at stake are also of two types: fixed costs
associated with keeping a warehouse open and variable
transportation costs associated with shipments from the
open warehouses.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
27
THE UNCAPACITATED PROBLEM
• Once we see how to solve the facility location problem
with capacities given, it is not difficult to adapt the model
to the uncapacitated case.
• Obviously, we could choose a virtual capacity for each
warehouse that is as large as total demand, so that
capacity would never interfere with the optimization.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
28
THE ASSORTMENT MODEL
• The facility location model, with or without capacity
constraints, clearly has direct application to the design of
supply chains and the choice of locations from a discrete
set of alternatives.
• But the model can actually be used in other types of
problems because it captures the essential trade-off
between fixed costs and variable costs.
• An example from the field of Marketing is the
assortment problem, which asks which items in a
product line should be carried, when customers are
willing to substitute.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
29
SUMMARY
• Integer programming problems are optimization
problems in which at least one of the variables is
required to be an integer.
• Solver’s solutions to linear integer programs are reliable:
a global optimal solution always occurs as long as the
Integer Tolerance parameter has been set to zero.
• Binary variables can represent all-or-nothing decisions
that allow only accept/reject alternatives.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
30
SUMMARY
• Binary variables can also be instrumental in capturing
complicated logic in linear form so that we can harness
the linear solver to find solutions.
• Binary variables make it possible to accommodate
problem information on:
– Contingency conditions between projects
– Mutual exclusivity among projects
– Linking constraints for consistency
– Threshold constraints for minimum activity levels
• With the capability of formulating these kinds of
relationships in optimization problems, our modeling
abilities expand well beyond the basic capabilities of the
linear and nonlinear solvers.
Chapter 11
Copyright © 2013 John Wiley & Sons, Inc.
31
COPYRIGHT © 2013 JOHN WILEY & SONS, INC.
All rights reserved. Reproduction or translation of
this work beyond that permitted in section 117 of the 1976
United States Copyright Act without express permission
of the copyright owner is unlawful. Request for further
information should be addressed to the Permissions
Department, John Wiley & Sons, Inc. The purchaser may
make back-up copies for his/her own use only and not for
distribution or resale. The Publisher assumes no
responsibility for errors, omissions, or damages caused by
the use of these programs or from the use of the
information herein.
13 - 32
STEPHEN G. POWELL
KENNETH R. BAKER
MANAGEMENT
SCIENCE
CHAPTER 12 POWERPOINT
NON-SMOOTH MODELS
The Art of Modeling with Spreadsheets
Compatible with Analytic Solver Platform
FOURTH EDITION
INTRODUCTION
• Evolutionary solver is a Solver algorithm that can be
effective on models that cannot be optimized in any
other way.
• The evolutionary solver is particularly suited to models
containing nonsmooth objective functions.
• Because the evolutionary solver makes virtually no
assumptions about the nature of the objective function,
it is not able to identify an optimal solution.
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
2
INTRODUCTION (CONT’D)
• This method conducts a systematic search with random
elements, comparing the solutions encountered along
the way and retaining the better ones.
• The best solution it finds may not be optimal, although it
may be a very good solution.
• This type of procedure is called a heuristic procedure,
meaning that it is a systematic procedure for identifying
good solutions, but not guaranteed optimal solutions.
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
3
FEATURES OF THE EVOLUTIONARY SOLVER
• The evolutionary solver is designed to mimic the process of
biological evolution in certain ways.
• The algorithm proceeds through a series of stages, which are
analogous to generations in a biological population. In each
generation the approach considers not a single solution, but a
population of perhaps 25 or 50 solutions.
• New members are introduced to this population through a
process that mimics mating in that offspring solutions
combine the traits of their parent solutions.
• Occasional mutations occur in the form of offspring solutions
with some random characteristics that do not come from their
parents.
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
4
FEATURES OF THE EVOLUTIONARY SOLVER (CONT’D)
• The ‘‘fitness’’ of each member of the population is
determined by the value of its objective function.
• Members of the population that are less fit (have a relatively
worse value of the objective function) are removed from the
population by a process that mimics natural selection.
• This process of selection propels the population toward better
levels of fitness (better values of the objective function).
• The procedure stops when there is evidence that the
population is no longer improving (or if one of the userdesignated stopping conditions is met).
• When it stops, the procedure displays the bes tmember of the
final population as the solution.
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
5
THE ENGINE TAB FOR THE EVOLUTIONARY SOLVER
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
6
THE ADVERTISING BUDGET PROBLEM
• The decision variables in this problem are the quarterly
expenditures on advertising.
• The objective function is nonlinear but smooth, since
there are diminishing returns to advertising
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
7
ADVERTISING BUDGET MODEL WITH UNIT COST TABLE
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
8
OPTIMAL ALLOCATION FROM THE NONLINEAR SOLVER
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
9
OPTIMAL ALLOCATION FROM THE EVOLUTIONARY SOLVER
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
10
RESULTS OF USING EVOLUTIONARY SOLVER
• The evolutionary solver finds a solution with a profit of $87,541,
which is 63 percent higher than the base case and 25 percent
higher than the solution found by the nonlinear solver.
• The advertising expenditures in this solution focus on the fourth
quarter.
• Repeated runs of Scatter Search fail to improve on this solution
significantly, so we can accept it as optimal or nearly so.
• This example demonstrates that even a modest alteration to one
function in a model (here, the product’s cost) can fundamentally
change the approach required for optimization.
• The lesson for model building: recognize that the choice of Excel
functions may affect the most suitable optimization algorithms to
use and the results that can be achieved.
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
11
THE CAPITAL BUDGETING PROBLEM
• Although the evolutionary solver can work with
constraints, it is less efficient when constraints are
present, and performance tends to deteriorate as the
number of constraints increases.
• Rather than imposing an explicit constraint, we add a
term to the objective function that penalizes the solution
for violations of a constraint.
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
12
WORKSHEET FOR THE MODIFIED MARR CORPORATION EXAMPLE
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
13
RESULTS OF RUNNING EVOLUTIONARY SOLVER ON THIS
MODEL
• A solution of $35 million, which is better than the optimum in the base
case.
• If the previous run stopped because of convergence, we should expand
the population size.
• If it stopped because improvement was impossible, then the Max time
without Improvement parameter should be increased or the Tolerance
parameter should be reduced to zero.
• If this stopping condition persists, then it is a good idea to start the search
with a different set of decision variables.
• If we simply run into the time limit, then the maximum time parameter
should be increased to 60 seconds (and beyond, if we have the time).
• It appears that an objective function of $35 million is the best we can
achieve.
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
14
SUMMARY
• The evolutionary solver contains an algorithm that complements
the nonlinear solver, the linear solver, and the integer solver.
• Evolutionary solver can often find good, near-optimal solutions to
very difficult problems, and it may be the only effective procedure
when there is a nonsmooth objective function.
• The evolutionary solver works with a set of specialized parameters.
• Practice and experience using the evolutionary solver are the key
ingredients in effective parameter selection.
• We usually reserve the use of the evolutionary solver for only the
most difficult problems, when the other solvers would fail or when
we cannot build a suitable model with a smooth objective function.
Chapter 12
Copyright © 2013 John Wiley & Sons, Inc.
15
COPYRIGHT © 2013 JOHN WILEY & SONS, INC.
All rights reserved. Reproduction or translation of this
work beyond that permitted in section 117 of the 1976
United States Copyright Act without express permission of
the copyright owner is unlawful. Request for further
information should be addressed to the Permissions
Department, John Wiley & Sons, Inc. The purchaser may
make back-up copies for his/her own use only and not for
distribution or resale. The Publisher assumes no
responsibility for errors, omissions, or damages caused by
the use of these programs or from the use of the information
herein.
14 - 16
STEPHEN G. POWELL
KENNETH R. BAKER
MANAGEMENT
SCIENCE
CHAPTER 13 POWERPOINT
DECISION ANALYSIS
The Art of Modeling with Spreadsheets
Compatible with Analytic Solver Platform
FOURTH EDITION
INTRODUCTION
• Many business problems contain uncertain elements
that are impossible to ignore without losing the essence
of the situation.
• In this chapter, we introduce some basic methods for
analyzing decisions affected by uncertainty.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
2
UNCERTAIN PARAMETERS
• Now, we broaden our viewpoint to include uncertain inputs—
parameter values subject to uncertainty.
• Uncertain parameters become known only after a decision is made.
• When a parameter is uncertain, we treat it as if it could take on two
or more values, depending on influences beyond our control.
• These influences are called states of nature, or more simply, states.
• In many instances, we can list the possible states, and for each one,
the corresponding value of the parameter.
• Finally, we can assign probabilities to each of the states so that the
parameter outcomes form a probability distribution.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
3
PAYOFF TABLES AND DECISION CRITERIA
• For each action-state combination, the entry in the table
is a measure of the economic result.
• Typically, the payoffs are measured in monetary terms,
but they need not be profit figures.
• They could be costs or revenues in other applications, so
we use the more general term payoff.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
4
BENCHMARK CRITERIA
• The Maximax payoff criterion seeks the largest of the
maximum payoffs among the actions.
• The maximin payoff criterion seeks the largest of the
minimum payoffs among the actions.
• The minimax regret criterion seeks the smallest of the
maximum regrets among the actions.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
5
INCORPORATING PROBABILITIES
• We can immediately translate this information into
probability distributions for the payoffs corresponding to
each of the potential actions.
• We use the notation EP to represent an expected payoff
(e.g., an expected profit).
• Note that the expected payoff calculation ignores no
information: all outcomes and probabilities are
incorporated into the result.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
6
USING TREES TO MODEL DECISIONS
• A probability tree depicts one or more random factors
• The node from which the branches emanate is called a
chance node, and each branch represents one of the
possible states that could occur.
• Each state, therefore, is a possible resolution of the
uncertainty represented by the chance node.
• Eventually, we’ll specify probabilities for each of the
states and create a probability distribution to describe
uncertainty at the chance node.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
7
SIMPLE PROBABILITY TREE
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
8
THREE CHANCE NODES IN TELEGRAPHIC FORM
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
9
DECISION TREES
• Decision-tree models offer a visual tool that can
represent the key elements in a model for decision
making under uncertainty and help organize those
elements by distinguishing between decisions
(controllable variables) and random events
(uncontrollable variables).
• In a decision tree, we describe the choices and
uncertainties facing a single decision-making agent.
• This usually means a single decision maker, but it could
also mean a decision-making group or a company.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
10
REPRESENTING DECISIONS
• In a decision tree, we represent decisions as square
nodes (boxes), and for each decision, the alternative
choices are represented as branches emanating from the
decision node.
• These are potential actions that are available to the
decision maker.
• In addition, for each uncertain event, the possible
alternative states are represented as branches emanating
from a chance node, labeled with their respective
probabilities.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
11
ANALYZING THE DECISION TREE
• Whereas we build the tree left to right, to reflect the
temporal sequence in which a decision is followed by a
chance event, we evaluate the tree in the reverse
direction.
• At each chance node, we can calculate the expected
payoff represented by the probability distribution at the
node.
• This value becomes associated with the corresponding
action branch of the decision node.
• Then, at the decision node, we calculate the largest
expected payoff to determine the best action.
• This process of making the calculations is usually referred
to as rolling back the tree.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
12
DECISION TREES: RISK PROFILES
• The distribution associated with a particular action is
called its risk profile.
• The risk profile shows all the possible economic
outcomes and provides the probability of each: It is a
probability distribution for the principal output of the
model.
• This form reinforces the notion that, when some of the
input parameters are described in probabilistic terms, we
should examine the outputs in probabilistic terms.
• After we determine the optimal decision, we can use a
probability model to describe the profit outcome.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
13
DECISION TREES FOR A SERIES OF DECISIONS
• Decision trees are especially useful in situations where there
are multiple sources of uncertainty and a sequence of
decisions to make.
• For example, suppose that we are introducing a new product
and that the first decision determines which channel to use
during test-marketing.
• When this decision is implemented, and we make an initial
commitment to a marketing channel, we can begin to develop
estimates of demand based on our test.
• At the end of the test period, we might reconsider our
channel choice, and we may decide to switch to another
channel.
• Then, in the full-scale introduction, we attain a level of profit
that depends, at least in part, on the channel we chose
initially.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
14
EXAMPLE
• In the following example, we have depicted (in
telegraphic form) a situation in which we choose our
channel initially, observe the test market, reconsider our
choice of a channel, and finally observe the demand
during full-scale introduction.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
15
DECISION TREE WITH SEQUENTIAL DECISIONS
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
16
PRINCIPLES FOR BUILDING
AND ANALYZING DECISION TREES
1.
2.
3.
4.
5.
6.
7.
Determine the essential decisions and uncertainties.
Place the decisions and uncertainties in the appropriate temporal
sequence.
Start the tree with a decision node representing the first
decision.
Select a representative (but not necessarily exhaustive) number
of possible choices for the decision node.
For each choice, draw a chance node representing the first
uncertain event that follows the initial decision.
Select a representative (but not necessarily exhaustive) number
of possible states for the chance node.
Continue to expand the tree with additional decision nodes and
chance nodes until the overall outcome can be evaluated.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
17
ROLLBACK PROCEDURE FOR ANALYZING TREES
1.
2.
3.
4.
5.
6.
7.
Start from the last set of nodes—those leading to the ends of the
paths.
For each chance node, calculate the expected payoff as a
probability-weighted average of the values corresponding to its
branches.
Replace each chance node by its expected value.
For each decision node, find the best expected value (maximum
benefit or minimum cost) among the choices corresponding to its
branches.
Replace each decision node by the best value, and note which
choice is best.
Continue evaluating chance nodes and decision nodes, backward
in sequence, until the optimal outcome at the first node is
determined.
Construct its risk profile.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
18
THE COST OF UNCERTAINTY
• An action must be chosen before learning how an
uncertain event will unfold.
• The situation would be much more manageable if we
could learn about the uncertain event first and then
choose an action.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
19
IMPERFECT VS. PERFECT INFORMATION
• When we have to make a decision before uncertainty is
resolved, we are operating with imperfect information
(uncertain knowledge) about the state of nature.
• When we can make a decision after uncertainty is
resolved, we can respond to perfect information about
the state of nature.
• Our probability assessments of event outcomes remain
unchanged, and we are still dealing with expected values.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
20
EXPECTED VALUE OF PERFECT INFORMATION (EVPI)
• The expected payoff with perfect information must
always be at least as good as the expected payoff from
following the optimal policy in the original problem, and
it will usually be better.
• The EVPI measures the difference, or the gain due to
perfect information.
• The calculation of EVPI can also be represented with a
tree structure, where we reverse the sequence of
decision and chance event in the tree diagram, just as we
did in the calculations.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
21
DECISION TREE FOR THE EVPI CALCULATION
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
22
USING DECISION TREE SOFTWARE
• It is often difficult to create a layout for the calculations
that is tailored to the features of a particular example.
• For that reason, it makes sense to take advantage of
software that has been designed expressly for
representing decision trees in Excel.
• Decision Tree is a tool contained in Analytic Solver
Platform for constructing and analyzing decision tree.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
23
DECISION TREE MENU
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
24
DEFAULT INITIAL TREE PRODUCED BY DECISION TREE
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
25
DETAILS FOR THE FIRST DECISION NODE
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
26
EXPANDED INITIAL TREE DIAGRAM
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
27
NODE WINDOW FOR THE FIRST EVENT NODE
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
28
FIRST EVENT NODE PRODUCED BY DECISION TREE
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
29
EXPANDED DIAGRAM WITH SECOND EVENT NODE COPIED
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
30
FULL DIAGRAM
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
31
SENSITIVITY ANALYSIS WITH TREEPLAN
• A decision-tree analysis retains the properties of a
spreadsheet.
• The worksheet produced by Decision Tree contains
inputs, formulas, and outputs, just as in any welldesigned model.
• Thus, we can perform sensitivity analyses in the usual
ways.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
32
SENSITIVITY ANALYSIS FOR THE EXAMPLE MODEL
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
33
MINIMIZING EXPECTED COSTS WITH DECISION TREE
• We could just as easily apply Decision Tree to a problem
involving the criterion of expected costs by treating all
costs as negative profits and finding the maximum
expected profit.
• However, Decision Tree can accommodate costs in a
more direct fashion and simply minimize expected cost.
• To do so, we enter the task pane on the Model tab, select
the root node (Decision Tree) in the main window, and in
the table below, find the Decision Node parameter and
use its pull-down menu to switch from Maximize to
Minimize.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
34
LOCATION OF THE MAXIMIZATION SETTING ON THE TASK PANE
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
35
*MAXIMIZING EXPECTED UTILITY WITH DECISION TREE
• What if we wish to incorporate some aversion to risk in our decision
making?
• Suppose that we could evaluate payoffs in some risk-adjusted
manner—that is, with a measure that combines notions of monetary
value along with the risk of an undesired outcome.
• To contrast this measure with the measure of pure dollars unadjusted
for risk, we’ll adopt the name utils for this new scale.
• With this scale available, the decision maker can compute the value of
a particular action in utils and select as the optimal decision the action
with the largest such value.
• The value of an action, measured in utils, incorporates both outcomes
and probabilities, just as expected value does, but it also acknowledges
risk.
• We say that a decision maker who is behaving in this way seeks to
maximize expected utility.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
36
EXPONENTIAL UTILITY FUNCTION
•
Although there are many ways of converting dollars to
utils, one straightforward method uses an exponential
utility function:
U = a – b exp (–D/R)
where D is the value of the outcome in dollars; U is the
utility value, or the value of an outcome in utils; and a,
b, and R represent parameters of the utility function.
Parameters a and b are essentially scaling parameters; R
influences the shape of the curve and is known as the
risk tolerance.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
37
ANALYSIS WITH UTILITIES
• To carry out the analysis, we use this function to convert
each monetary outcome from dollars to utils, and then
we determine the action that achieves the maximum
expected utility.
• Although Decision Tree allows the flexibility of setting
three different parameters, we usually advise setting
a = b = 1.
• This choice ensures that the function passes through the
origin, so that our remaining task is finding a value of R
that captures the decision maker’s preferences.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
38
GRAPH OF UTILITY FUNCTION FOR THE EXAMPLE
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
39
USING TREE PLAN WITH EXPONENTIAL UTILITY FUNCTION
• In Decision Tree, it is necessary to specify the three
parameters in the exponential utility function.
• These three values must be entered in the task pane on
the Model tab, along with designating the value for
Certainty Equivalents to be the Exponential Utility
Function.
• After the user designates the use of Exponential Utility
Function, Decision Tree displays additional calculations in
columns B, F, and J. Immediately below the monetary
payoffs the display shows the same figures converted to
utils.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
40
MODIFICATION OF THE EXAMPLE MODEL FOR EXPONENTIAL UTILITIES
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
41
SUMMARY
• A decision tree is a specialized model for recognizing the role of
uncertainties in a decision-making situation.
• Trees help us distinguish between decisions and random events, and more
importantly, they help us sort out the sequence in which they occur.
• Probability trees provide us with an opportunity to consider the possible
states in a random environment when there are several sources of
uncertainty, and they become components of decision trees.
• The key elements of decision trees are decisions and chance events. A
decision is the selection of a particular action from a given list of
possibilities.
• A chance event gives rise to a set of possible states, and each action-state
pair results in an economic payoff.
• In the simplest cases, these relationships can be displayed in a payoff
table, but in complex situations, a decision tree tends to be a more flexible
way to represent the relationships and consequences of decisions made
under uncertainty.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
42
SUMMARY (CONT’D)
• The choice of a criterion is a critical step in solving a decision problem
when uncertainty is involved.
• There are benchmark criteria for optimistic and pessimistic decision
making, but these are somewhat extreme criteria. They ignore some
available information, including probabilities, in order to simplify the task
of choosing a decision.
• The more common approach is to use probability assessments and then to
take the criterion to be maximizing the expected payoff, which in the
business context translates into maximizing expected profit or minimizing
expected cost.
• Using the rollback procedure, we can identify those decisions that
optimize the expected value of our criterion. Furthermore, we can
produce information in the form of a probability distribution to help
assess the risk associated with any decision in the tree.
• Decision Tree is a straightforward spreadsheet program that assists in the
structuring of decision trees and in the calculations required for a
quantitative analysis.
Chapter 13
Copyright © 2013 John Wiley & Sons, Inc.
43
COPYRIGHT © 2013 JOHN WILEY & SONS, INC.
All rights reserved. Reproduction or translation of
this work beyond that permitted in section 117 of the 1976
United States Copyright Act without express permission of
the copyright owner is unlawful. Request for further
information should be addressed to the Permissions
Department, John Wiley & Sons, Inc. The purchaser may
make back-up copies for his/her own use only and not for
distribution or resale. The Publisher assumes no
responsibility for errors, omissions, or damages caused by
the use of these programs or from the use of the information
herein.
STEPHEN G. POWELL
KENNETH R. BAKER
MANAGEMENT
SCIENCE
CHAPTER 1 POWERPOINT
INTRODUCTION
The Art of Modeling with Spreadsheets
Compatible with Analytic Solver Platform
FOURTH EDITION
WHAT IS MODELING?
• Creating a simplified version of reality
– Maps
• Working with this version to understand or control some
aspect of the world
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
2
TYPES OF MODELS
• Mental
• Visual
• Physical
• Mathematical
– Algebra
– Calculus
– Spreadsheets
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
3
WHY STUDY MODELING?
• Models generate insight which leads to better decisions.
• Modeling improves thinking skills:
– Break problems down into components
– Make assumptions explicit
• Modeling improves quantitative skills:
– Ballpark estimation, number sense, sensitivity analysis
• Modeling is widely used by business analysts:
– Finance, marketing, operations
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
4
MODELS IN BUSINESS: TYPES
• One time decision models (usually built by the decision
maker)
– Will be the primary focus in this text
• Decision support models
• Embedded models
– A computer makes the decision without the user being
explicitly aware
• Models used in business education
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
5
BENEFITS OF BUSINESS MODELS
• Modeling allows us to make inexpensive errors.
• Allows exploration of the impossible
• Improves business intuition
• Provides timely information
• Reduces costs
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
6
ROLE OF SPREADSHEETS
• Principal vehicle for modeling in business
• Mathematics at an accessible level
– Versus calculus, algebra
• Correspond nicely to accounting statements
• “The Swiss Army knife of business analysis”
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
7
SPREADSHEETS:
“THE SWISS ARMY KNIFE OF BUSINESS ANALYSIS”
• Prior to the 1980s, modeling was performed only by
specialists using demanding software on expensive
hardware.
– Spreadsheets changed all this in the 1990s
• The “second best” way to do many kinds of analysis
– Many specialized decision tools exist (e.g., simulation
software, optimization software, etc.).
• The best way to do most modeling
– An effective modeler should know its limitations and when
to call in specialists.
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
8
RISKS OF SPREADSHEET USE
• Spreadsheets contain internal errors, and more errors are
introduced as these spreadsheets are used and modified.
• A sampling of errors with serious ramifications:
– Sorting a spreadsheet improperly
– Careless naming of spreadsheet files
– Copy-and-paste error in a spreadsheet
– Erroneous numerical input in a spreadsheet
– Numbers entered as text in a spreadsheet
– Shifting a spreadsheet so the wrong numbers appear in
the wrong columns
– Incorrect references in a spreadsheet formula
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
9
WHY ARE ERRORS SO COMMON?
• Traditional computer programming is carried out largely
by trained professionals.
• It uses elaborate and formalized development methods.
• Very few corporations (and even fewer individuals)
employ even the most basic design and inspection
procedures.
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
10
CHALLENGES FOR SPREADSHEET USERS
• End-user spreadsheets frequently have bugs.
• End-users are overconfident about the quality of their
spreadsheets.
• Development process is inefficient
• Most productive methods for generating insights not
employed
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
11
END USER INEFFICIENCIES
• Lack of planning causes extensive rework
• No prototyping; too much complexity too soon
• Users rarely spend time debugging
• Users rarely seek review
• Do not use Excel’s best tools for clearest insights (even
advanced users)
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
12
BASIC KNOWLEDGE FOR SPREADSHEET MODELING
• Basic algebra
– e.g., quadratic, exponential, logarithmic functions
• Simple logic
– e.g., IF statements or MAX functions
• Basic probability
– e.g., distributions and sampling
• Basic familiarity with Excel
– e.g., entering and formatting text, using functions
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
13
REAL WORLD
PROBLEM
STATEMENT
MODEL WORLD
FORMULATION
ASSUMPTIONS
and
MODEL
STRUCTURES
ANALYSIS
SOLUTION
INTERPRETATION
— translation
— communication
RESULTS
and
CONCLUSIONS
THE REAL WORLD AND THE MODEL WORLD
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
14
MODEL FORMULATION
• Decisions
– Possible choices or actions to take
• Outcomes
– Consequences of the decisions
• Structure
– Logic that links elements of the model together
• Data
– Numerical assumptions in model
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
15
FIVE ASPECTS OF MODELING ACTIVITY
• Problem context
– Situation from which modeler’s problem arises
• Model structure
– Building the model
• Model realization
– Fitting model to available data and calculating results
• Model assessment
– Evaluating model’s correctness, feasibility, and acceptability
• Model implementation
– Working with client to derive value from the model
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
16
HABITS OF EXPERT MODELERS
• Experts:
– Frequently switched among the five aspects of modeling
– Spent 60% of activity time on model structure with
frequent switches between model structure and model
assessment.
– Used model structure as the organizing principle around
which the related activities were arrayed
• Conclusion: Craft skills are as essential as technical skills
in effective modeling.
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
17
RANKING OF MODELING SKILLS
• Creativity, sensitivity to client needs, persistence
• Communication, teamwork skills, etc.
• Technical expertise
• Knowledge of the industry or problem-type
• Above ranking confirms the importance of craft skills
alongside technical skills in modeling.
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
18
BEHAVIORS THAT LIMIT MODELING EFFECTIVENESS
• Over-reliance on given numerical data
• Taking shortcuts to an answer
• Insufficient use of abstract variables and relationships
• Ineffective self-regulation
• Overuse of brainstorming relative to structured problem
solving
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
19
ORGANIZATION OF TEXT
• Spreadsheet engineering
– How to design build, test and perform analysis with a
spreadsheet model
• Modeling craft
– Effective abstraction, model debugging, and translating
models into managerial insights
• Data analysis
– Exploring datasets and basic techniques for classification,
prediction
• Management science
– Optimization
– Simulation
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
20
SUMMARY OF TEXT PHILOSOPHY
• Modeling is a necessary skill for every business analyst.
• Spreadsheets are the modeling platform of choice.
• Basic spreadsheet modeling skills are an essential
foundation.
• End-user modeling is cost-effective.
• Craft skills are essential to the effective modeler.
• Analysts can learn the required modeling skills.
• Management science/statistics are important advanced
tools.
Chapter 1
Copyright © 2013 John Wiley & Sons, Inc.
21
COPYRIGHT © 2013 JOHN WILEY & SONS, INC.
All rights reserved. Reproduction or
translation of this work beyond that permitted in
section 117 of the 1976 United States Copyright Act
without express permission of the copyright owner is
unlawful. Request for further information should be
addressed to the Permissions Department, John Wiley
& Sons, Inc. The purchaser may make back-up copies
for his/her own use only and not for distribution or
resale. The Publisher assumes no responsibility for
errors, omissions, or damages caused by the use of
these programs or from the use of the information
herein.
STEPHEN G. POWELL
KENNETH R. BAKER
MANAGEMENT
SCIENCE
CHAPTER 2 POWERPOINT
MODELING IN A PROBLEM-SOLVING FRAMEWORK
The Art of Modeling with Spreadsheets
Compatible with Analytic Solver Platform
FOURTH EDITION
MODELERS’ ROLES IN THE PROBLEM-SOLVING PROCESS
• End user
– Identifies problems, develops model, uses model, and
implements results
– Often the modeler
• Team member
– Communication skills critical
– Whole team must understand model and assumptions
• Independent consultant
– Model is for a client
– Model must be consistent with client’s goals
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
2
KEY TERMS: “PROBLEM” VERSUS A “MESS”
• A problem is a well-defined situation that is capable of
resolution.
• A mess is a morass of unsettling symptoms, causes, data,
pressures, shortfalls, opportunities, etc.
• Identifying a problem in the mess is the first step in the
creative problem solving process.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
3
PROBLEM STATEMENTS
• A statement in the form “In what ways might…?”
– Focuses on defining the problem to be solved
– Example: “In what ways might we increase revenues to
keep pace with costs?”
• Solutions will differ based on the problem statement, so:
– Pay close attention to the problem definition.
– Take any problem definition as tentative.
– Prepare to alter the definition if evidence suggests a
different statement would be more effective.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
4
CHARACTERISTICS OF WELL-STRUCTURED PROBLEMS
• The objectives of the analysis are clear.
• The assumptions that must be made are obvious.
• All the necessary data are readily available.
• The logical structure behind the analysis is well
understood.
• Example: Algebra problems are typically well- structured
problems.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
5
ILL-STRUCTURED PROBLEMS
• Objectives, assumptions, data, and structure of the
problem are all unclear.
• Examples:
– Should the Red Cross institute a policy of paying for blood
donations?
– Should Boeing’s next major commercial airliner be a small
supersonic jet or a slower jumbo jet?
– Should an advertiser spend more money on the creative
aspects of an ad campaign or on the delivery of the ad?
– How much should a mid-career executive save out of
current income toward retirement?
• Require exploration more than solutions.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
6
EXPLORATION
• With an inquiring mind and a spirit of discovery,
exploration involves:
– formulating hypotheses
– making assumptions
– building simple models
– deriving tentative conclusions
• It often reveals aspects of the problem that are not
obvious at first glance.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
7
DIVERGENT AND CONVERGENT THINKING
• Divergent thinking
– Thinking in different directions
– Searching for a variety of answers to questions that may
have many right answers
– Brainstorming
• Convergent thinking
– Directed toward achieving a goal or single solution
– Involves trying to find the one best answer
– Emphasis shifts from idea generation to evaluation
• Decision makers need to be clear as to which they use at
a given time, and balance the two.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
8
THE SIX-STAGE PROBLEM-SOLVING PROCESS
1. Exploring the mess
Divergent phase
Search the mess for problems and opportunities.
Convergent phase
Accept a challenge and undertake systematic efforts to respond to it.
2. Searching for information
Divergent phase
Gather data, impressions, feelings, observations; examine the situation from many
different viewpoints.
Convergent phase
Identify the most important information.
3. Identifying a problem
Divergent phase
Generate many different potential problem statements.
Convergent phase
Choose a working problem statement.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
9
THE SIX-STAGE PROBLEM-SOLVING PROCESS (CONT’D)
4. Searching for solutions
Divergent phase
Develop many different alternatives and possibilities for solutions.
Convergent phase
Select one or a few ideas that seem most promising.
5. Evaluating solutions
Divergent phase
Formulate criteria for reviewing and evaluating ideas.
Convergent phase
Select the most important criteria; use them to evaluate, strengthen, and refine ideas.
6. Implementing a solution
Divergent phase
Consider possible sources of assistance and resistance to proposed solution. Identify
implementation steps and required resources.
Convergent phase
Prepare the most promising solution for implementation.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
10
EXAMPLE: INVIVO DIAGNOSTICS
• A $300M pharmaceutical company built on the strength
of a single product that accounts for over 75% of
revenues.
• In 18 months, the patent for this product will expire.
• The CEO wants to explore ways to plug the expected
$100-$200M revenue gap as revenues from this product
decline.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
11
1. EXPLORING THE MESS
• What problems or opportunities do we face?
• Where is there a gap between the current situation and
the desired one?
• What are the stated and unstated goals?
• This stage is complete when we have:
– A description of the situation
– Identified (not gathered) key facts and data
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
12
2. SEARCHING FOR INFORMATION
• What are the symptoms and causes?
• What measures of effectiveness seem appropriate?
• What actions are available?
• This stage is complete when we have:
– Found and organized relevant data
– Made initial hypotheses about problem causes and
solutions
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
13
3. IDENTIFYING A PROBLEM
• Which is the most important problem?
• Is this problem like others we have dealt with?
• What are the consequences of a broad versus narrow
problem statement?
• This stage is complete when we have produced a working
problem statement.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
14
4. SEARCHING FOR SOLUTIONS
• What decisions are open to us?
• What solutions have been tried in similar situations?
• How are the various candidate solutions linked to
outcomes of interest?
• This stage is complete when we have produced a list of
potential solutions.
– Perhaps also a list of advantages and disadvantages
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
15
5. EVALUATING SOLUTIONS
• How does this solution impact each of the criteria?
• What factors within our control could improve the
outcomes?
• What factors outside our control could alter the
outcomes?
• This stage is complete when we have produced a
recommended course of action along with justification.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
16
6. IMPLEMENTING A SOLUTION
• What are the barriers to successful implementation?
• Where will there be support and motivation, or
resistance and conflict?
• Are the resources available for successful
implementation?
• This stage is complete when we have produced an
implementation plan and begun execution.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
17
MENTAL MODELS (INFORMAL MODELING)
• Help us to relate cause and effect
– But often in a simplified, incomplete way
• Help us determine what is feasible
– But may be limited by personal experiences
• Are influenced by our preferences for certain outcomes
• Are useful but can be limiting
• Problem solvers construct quick, informal mental models
at many different points in the process.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
18
FORMAL MODELS
• Provide the same kind of information as mental models
– Link causes to effects, aid in evaluating solutions
• Require a set of potential solutions and criteria to
compare solutions to be identified
• More costly and time consuming to build than mental
models
• Make assumptions, logic, and preferences explicit and
open to debate
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
19
INFLUENCE CHARTS
• A simple diagram to show outputs and how they are
calculated from inputs
• Tool of choice for complex, unstructured problems
• Identifies main elements of a model
• Delineates the boundaries of a model
• Recommended for early stages of any problem
formulation task
• Flexible, support frequent revision
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
20
BUILDING AN INFLUENCE CHART
• Built from right to left
• Conventions on types of variables
– Outputs – hexagons
– Decisions – boxes
– Inputs – triangles
– Other variables – circles
– Random variables – double circles
– See Figure 2.3
Figure 2.3
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
21
INFLUENCE CHART PRINCIPLES
• Start with outcome measure
• Decompose outcome measure into independent
variables that directly determine it
• Repeat decomposition for each variable in turn
• Identify input data and decisions as they arise
• Ensure each variable appears only once
• Highlight special types of elements with consistent
symbols
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
22
EXAMPLE 1: A PRICING DECISION
• “Determine the price we should set for our product so as
to generate the highest possible profit this coming year.”
• See Figures 2.2a – 2.2f
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
23
EXAMPLE 1: A PRICING DECISION
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
24
EXAMPLE 1: A PRICING DECISION
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
25
EXAMPLE 1: A PRICING DECISION
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
26
EXAMPLE 2: THE SS KUNIANG1
• In the early 1980s, New England Electric System (NEES)
was deciding how much to bid for the salvage rights to a
grounded ship, the SS Kuniang. If the bid were successful,
the ship could be repaired and outfitted to haul coal for
the company’s power-generation stations. But the value
of doing so depended on the outcome of a U.S. Coast
Guard judgment about the salvage value of the ship.
• See Figure 2.6
1D. E. Bell, “Bidding for the S.S. Kuniang,” Interfaces 14 (1984): 17–23.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
27
EXAMPLE 3: AUTOMOBILE LEASING
• The primary challenge for companies offering a closedend lease is to select the residual value of the vehicle.
• See Figure 2.7
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
28
INFLUENCE CHARTS WRAP-UP
• The goal is to develop a problem structure—not to solve
the problem.
• There is no one correct chart.
• Charts ignore all available numerical data.
• Charts rely on modeling assumptions that should be
recorded as made.
Chapter 2
Copyright © 2013 John Wiley & Sons, Inc.
29
CRAFT SKILLS FOR MODELING
• Successful modelers draw on both techni...
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