COMPLEX PROBLEMS CLASS 2

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COMPLEX PROBLEMSCLASS 2

• I THINK, THEREFORE I SOLVE
• Lessons from Analytical Methods

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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

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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 32F0C 212F100C
• Illustration Draw graph depicting Celsius on
  x-axis, F on y-axis
• Math concepts (words to equations) linear
  relationship so ymxb 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 1.8C 7C 44.6F.

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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

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A Business Example For a (Relatively)
Well-Structured 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.

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Thinking about the problem

• What are the well-structured aspects?
• What are the fuzzy aspects making it just
  relatively well-structured?

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A Possible Solution

• Staff Organizational
  ROI
  Retention Fit Total
  
• Weights (0.4)
  (0.2) (0.4) (1.0)
• Alternatives
• Bangkok 5 10 2
  4.8
• Chicago 5 8 6 6.0
• Sydney 4 6 10 6.8
• Singapore 6 4 2 4.0
• Shanghai 10 2 4
  6.0

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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,
  Bangkoks total is given by the following
  calculation.
• Weighted Total (5)(0.4) (10)(0.2)
  (2)(0.4) 2 2 0.8 4.8

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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

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Analytical Techniques for Solving Harder Problems
(including ill-structured)

• Analogy
• Solve in Parts
• Backward-Forward
• Transformation into Known Problem
• Solve for Simplified Case -- Generalize

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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

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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)

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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 xy so (x-y)0 so
  (x-y)2 0 so x2-2xy-y2
• Forward area xy/2 z2/4 x2y2 z2
  (Pythagorean) so xy/2(x2y2)/4 x2-2xy-y2 0
• Business Example
• Strategic Games -- looking ahead to rivals 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

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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 gt 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

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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

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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

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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 detrimental effects
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Cognitive Biases (cont)
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) Were successful because of strong management Were 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
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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

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Mini-Assignment

• Come to class with
• a workplace example of a problem solvable with
  analytical methods
• a workplace example of a cognitive bias