COMPLEX PROBLEMS
CLASS 2
I THINK, THEREFORE I SOLVE
Lessons from Analytical Methods
Analytical Disciplines

Math, Physics, Operations Research,
Economics, Finance, …
» Utilize modeling techniques and tools (math,
logic, abstraction) for well-structured problems
» Overlap in procedures used
» Borrowing methods for ill-structured problems
Solving a “Word Problem”

Problem:
» In the U.S., temperature is typically reported in degrees Fahrenheit where
boiling point of water is 212 and freezing point is 32. Most other countries
and scientific endeavors use degrees Celsius where the boiling point is 100
and freezing point is 0. If the temperature in Rome is 7 degrees Celsius,
what is it in Fahrenheit?

Steps?
»
»
»
»
Goal: Need to find conversion formula (C to F); plug in 7C
Relevant information: 32F=0C; 212F=100C
Illustration: Draw graph depicting Celsius on x-axis, F on y-axis
Math concepts (words to equations): linear relationship so y=mx+b; use known
points (0,32), (100, 212); “b” or “y-intercept” = 32F; slope = (y2-y1)/(x2-x1) or
(212-180)/(100-0) = 1.8; F = 32 + 1.8*C; 7C = 44.6F.
Generalizing Steps in
Analytical Problem Solving

Basics
» Explicitly identify (write out) objective
» Simplify (Abstract)
– Eliminate extraneous-incidental information
– Explicitly identify key information (objective; variables, values, …)
» Organize Key Information
– Mathematical representation, equation, table, illustration, lists, …
» Perform appropriate math/logical operations

If problem with multiple solutions
» Assign probabilities or weights to each possible outcome
» Calculate expected value or weighted value of each outcome
» Compare values
A Business Example For a (Relatively) WellStructured Problem

Executive management must determine the best location for a new unit of a
multinational company. Return on Investment and how well the new unit will fit
organizationally should be the most important factors with the ability to attract and
retain a suitable workforce a secondary consideration. The Capital Investments
Committee has determined a short list of possible cities that includes Bangkok,
Chicago, Sydney, Singapore, and Shanghai. Their ROI estimates for each city (in
order) are 12%, 12%, 10%, 15%, 25%. Human Resources has assigned staff
retention rate scores and organization fit scores on a scale from 1-10 (10 best) for
each city. For staff these are 10, 8, 6, 4, 2 and for fit these are 2, 6, 10, 2, 4. The
Travel Office has also calculated the following travel multipliers using Chicago as
the base of 1.0. These multipliers are 2.0, 1.0, 1.8, 1.8, 2.2.
Thinking about the problem

What are the “well-structured” aspects?

What are the “fuzzy” aspects making it just
“relatively” well-structured?
A Possible Solution
ROI
Weights
Staff
Organizational
Retention
Fit
(0.4)
(0.2)
(0.4)
5
5
4
6
10
10
8
6
4
2
2
6
10
2
4
Total
(1.0)
Alternatives
Bangkok
Chicago
Sydney
Singapore
Shanghai
4.8
6.0
6.8
4.0
6.0
Notes on Solution
1. The criteria used here are ROI, Staff retention and Organizational fit. Your criteria would
reflect your values for this decision (this is a not-so-well structured part of problem)
2. Weights reflect the relative importance assigned to each of the criteria. This is another value
judgement.
3. The scores assigned to the alternatives for each of the criteria should use the same range. In
the above example, we have used a score out of 10 for each criterion. This required
converting the ROI estimates. A simple ranking of alternatives on each criterion could
have been used.
4. The weighted total is the sum of the alternative scores X the weights. For example,
Bangkok’s total is given by the following calculation.
*Weighted Total = (5)(0.4) + (10)(0.2) + (2)(0.4) = 2 + 2 + 0.8 = 4.8
Potential Problems

The “fuzzy” parts of the problem
»
»
»
»
Inappropriate limits on alternatives
Weights/Probabilities are rarely known or known with precision
Values (preferences) behind weights may be unclear or in conflict
Data quality
Analytical Techniques for Solving Harder
Problems (including ill-structured)
Analogy
 Solve in Parts
 Backward-Forward
 Transformation into Known Problem
 Solve for Simplified Case -- Generalize

Problem-Solving by Analogy

General example
» X+Y

Y+X
Business Example
» Managers have opened a store in Bowling
Green, KY and use it as a template for store in
Jackson, TN
Solving by Parts

General Example
» Integration by parts

Business Example
» Large construction project such as Channel Tunnel -determine sequence of tasks (land; tunnel; rail; rail cars;
ports of entry)…
Backward-Forward (if needed)
 General
Example
» Detective working backward from evidence to criminal as well
as from interviews of criminal to evidence
» Proving right triangle XYZ with area z2/4 has 2 equal sides
» Backward: Solution means x=y; so (x-y)=0; so (x-y)2 = 0; so x2-2xy-y2
» Forward: area = xy/2 = z2/4; x2+y2= z2 (Pythagorean); so xy/2=(x2+y2)/4; x2-2xy-y2 =0;
» Business Example
» Strategic Games -- looking ahead to rival’s best options
– Stage 1: Company1 Innovate/Not Innovate
– Stage 2: Company 2 Response: Aggressive, Moderate, Mild
– Company 1 looks ahead to Stage 2 decisions for company 2 best on company 2
best action; trim decision tree
Transform into Known Problem

General Example
» Stats: Male height is normally distributed with mean of 70” and
s.d. of 2”, what is the probability of male > 74” -- transform into
standardized units (mean = 0, sd =1) and use standard normal
distribution
» Differential Equations

Business Example
» Contemplating a contract regarding several contingencies based
on performance or exogenous conditions -- transform into
option pricing model using information or guesses about
distribution of relevant contingent variables
Solve for Simplified Case &
Generalize

General Example
» Celsius-Fahrenheit example: solve for two
points on line; extrapolate (generalize) to any
points

Business Example
» Method for resolving inter-unit disputes
developed for two units, expanded to entire
company
Additional Pitfalls in Analytical
Methods for Ill-Structured Problems
 Analytical
(Cognitive) Biases
» Limited capacities confronting complex worlds
» Not always clear how we are really thinking
– mental shortcuts
– limited introspective abilities rendering perceived
analysis as little more than “rationalization”
» It is not easy to change how we think
– preconceptions; self-serving
Examples of Cognitive Biases
Strong Priors or
Anchoring
Bias
Relying almost exclusively prior
beliefs about the relationship between
variables; not updating beliefs in the
face of new or contradictory evidence
A manager believes that firms
that moving quickly always wins
will keep doing so even when the
firm is not doing well
Analogy
Bias
Using an example gained from one
situation to apply to another situation
that appears similar but overstating and
understating differences
Companies that diversify into
new markets often assume that
the policies-strategies that
worked in one setting will work
in another
Representative
Bias
Assuming that a result from a small
sample is representative of a larger
group or time period
An investor who made a 200%
return between 1995-2000
invests expecting this to hold into
the future
Mean Bias
or Stereotyping
Assuming that the average result holds
for a specific individual case
Control Bias
Overconfidence in one's ability to
control outcomes
Thinking that market influences
can be ignored with no
Cognitive Biases (con’t)
Framing Bias
Making different decisions or giving
different answers when the same
problem or question is stated
differently
Choosing decision with a 95%
chance of success; rejecting one
with a 5% chance of failure.
Escalation Bias
Continuing with an action when it is
rational to stop.
Companies competing in bidding
for an acquisition target will
sometimes bid well beyond the
rational value of that target
Attribution Bias
Improperly understanding factors
contributing to your own or others
decisions or outcomes (especially in
self-serving ways)
We’re successful because of
strong management; We’re
failing because of a poor market
Availability
Bias
Making judgments based on how easily
you can think of information that is
relevant to the judgment
Confirmation
Bias
Valuing information that supports
belief & rejecting contrary
Critical Lessons

Analytical Thinking is Powerful
»
»
»
»

clarifying objectives
simplifying
identifying & converting key information
using logical/organizational tools
“Tricks” of Solving Hard Analytical Problems
» Analogy; Break into Parts; Backward-Forward;
Transformation; Generalizing from Special Case

Analytical Biases are Also Powerful
» Self-Awareness Critical
Mini-Assignment

Come to class with
» a workplace example of a problem solvable
with analytical methods
» a workplace example of a cognitive bias