Decision Analysis

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Decision Analysis

• How to make decisions when faced with uncertain
  or imperfect information.
• Definitions
• States of Nature - future events not under the
  decision makers control
• Alternatives - different courses of action
  intended to solve a problem
• Criteria - factors that are important to the
  decision maker and influenced by the alternatives
• Decision making under uncertainty non
  probabilistic
• Cant quantify probabilities associated with
  states of nature
• Helps us understand our own attitudes and
  preferences toward risk.
• Decision making under risk - probabilistic
• Involve probabilistic information about the
  likelihood of states of nature.

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Non probabilistic methods Decision making
under uncertainty

• Decision options given alternate states of nature
  without any probabilities (nonprobabilistic
  approach - avoiding the process of quantifying
  probabilities).
• Four simple approaches
• Laplace - treat each state equally likely, hence
  select the decision with the best average (the
  best average is either the lowest average, e.g.
  cost, waiting time, etc., or the highest average,
  e.q., for profit, revenue, etc.)
• Maximax (or Minimin) - optimist (aggressive
  decision maker)
• Maximin (or Minimax) - pessimist (conservative
  decision maker)
• Minimax Regret - minimize the maximum opportunity
  loss
• Note that this approach works for both
  maximization and minimization problems the same
  way. (hint no negative regret figures).

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Example
Excel time
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Probabilistic methods -Decision making under risk

• States of nature are now assigned probabilities.
• P(Sj) or pj likelihood of state j
• Expected (monetary) value decision rule (EMV)
• Select the decision with the highest expected
  monetary value
• Expected regret or expected opportunity loss
  (EOL)
• Results the same decision as EMV (functionally
  equivalent)
• Expected value of perfect information (EVPI)
• For each state, determine the best decision, and
  using the best decisions for each state,
  calculate EMV"
• minus
• previously selected best decision via EMV.
• Decision trees

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Multistage Decision Making

• Many problems involve a series of decisions
• Multistage decisions can be analyzed using
  decision trees
• COMTECT Example
• Submit a proposal or not
• If awarded the grant which technology to use
• Sketch the decision tree first
• Then use TreePlan.xla add-in
• Excel time

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COM-TECH

• The Occupational Safety and Health Administration
  ( OSHA) has recently announced that it will award
  an 85,000 research grant to the person or
  company submitting the best proposal for using
  wireless communications technology to enhance
  safety in the coal- mining industry. Steve
  Hinton, the owner of COM- TECH, a small
  communications research firm located just outside
  of Raleigh, North Carolina, is considering
  whether or not to apply for this grant. Steve
  estimates that he would spend approximately
  5,000 preparing his grant proposal and that he
  has about a 50- 50 chance of actually receiving
  the grant. If he is awarded the grant, he then
  would need to decide whether to use microwave,
  cellular, or infrared communications technology.
  He has some experience in all three areas, but
  would need to acquire some new equipment
  depending on which technology is used. The cost
  of the equipment needed for each technology is
  summarized as
• Microwave 4,000 Cellular 5,000 and
  Infrared 4,000.
• In addition to the equipment costs, Steve knows
  that he will spend money in re-search and
  development ( R D) to carry out the research
  proposal, but he does not know exactly what the
  R D costs will be. For simplicity, Steve
  estimates the following best- case and worst-
  case R D costs associated with using each
  technology, and he assigns probabilities to each
  outcome based on his degree of expertise in each
  area.
• Steve needs to synthesize all the factors in this
  problem to decide whether or not to submit a
  grant proposal to OSHA.

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Another Decision Tree Example

• Dean Kuroff started a business of rehabbing old
  homes. He recently purchased a circa-1800
  Victorian mansion and converted it into a
  three-family residence. Recently, one of his
  tenants complained that the refrigerator was not
  working properly. As Dean's cash flow was not
  extensive, he was not excited about purchasing a
  new refrigerator. He is considering two other
  options purchase a used refrigerator or repair
  the current unit. He can purchase a new one for
  400, and it will easily last three years. If he
  repairs the current one, he estimates a repair
  cost of 150, but he also believes that there is
  only a 30 percent chance that it will last a full
  three years and he will end up purchasing a new
  one anyway. If he buys a used refrigerator for
  200, he estimates that there is a .6 probability
  that it will last at least three years. If it
  breaks down, he will still have the option of
  repairing it for 150 or buying a new one.
• Develop a decision tree for this situation and
  determine Dean's optimal strategy.  

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Multiple criteria decision making

• Decision problems often involve two or more
  sometimes conflicting criterion or objectives
• There is no single best/optimal solution
• Only exception is that if a decision alternative
  is rated the best for all criteria, which will
  make it a trivial toy problem!)
• Analytical Hierarchy Process (AHP) developed by
  Dr. Thomas Saaty
• A structured approach for determining the scores
  and weights in a multi-criteria scoring model
• Based on pairwise comparisons between the
  decision alternatives on each of the criteria, as
  well as pairwise comparisons between the criteria
  to determine their relative importance
• Develop rankings from pairwise comparison
  matrices

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Scale for pairwise comparisons in AHP
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An AHP example

• A.C.S. and his lovely wife D.R.C. are shopping
  for a sports car. They have four principal
  decision criteria price, reliability,
  performance, and style. They have narrowed their
  search to three cars (1) 2001 BMW Z3 (27K), (2)
  2003 Mazda Miata (24K), and (3) 2001 Honda S
  2000 (26K).
• In class, we will
• Step 1 Breakdown the problem
• Top level Buy a sports car.
• Major criteria price, reliability, performance
  and style
• Decision alternatives Z3, Miata, S2000
• Step 2 Decision maker(s) develop comparison
  matrices (this is us!)
• Step 3 Develop a comparison matrix for criteria
• Step 4 Compute relative priorities via a
  normalization process.
• sum column-wise, divide elements in that column
  with the sums.
• calculate avg. (score) for each row --gt relative
  priorities per row
• Compute consistency ratios for each matrix (are
  we consistent?)
• Step 5 Using the relative priorities for each
  criterion calculate the weighted average for
  each decision alternative. The car they will buy
  is

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Problems

• The chef recommends the following food for your
  thoughts
• 7, 8, 30 31
• The End

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ANALYTICS READING LIST

• Supercrunchers, Ian Ayers
• Moneyball The Art of Winning an Unfair Game,
  Michael M. Lewis
• Revenue Management, Robert H. Cross
• The Future of Pricing, E. Andrew Boyd
• Competing on Analytics, Thomas H. Davenport and
  Jeanne G. Harris
• Analytics at Work, Thomas H. Davenport and Jeanne
  G. Harris