BA 555 Practical Business Analysis

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BA 555 Practical Business Analysis
Agenda

• Decision Analysis
• PrecisionTree

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Decision-making under Certainty

• Decision-making under certainty entails the
  selection of a course of action when we know the
  results that each alternative action will yield.
  
• This type of decision problems can be solved by
  linear/integer programming technique.
• Example A company produces two different auto
  parts A and B. Part A (B) requires 2 (2) hours
  of grinding and 2 (4) hours of finishing. The
  company has two grinders and three finishers,
  each of which works 40 hours per week. Each Part
  A (B) brings a profit of 3 (4). How many items
  of each part should be manufactured per week?

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Decision-making under Uncertainty

• Decision-making under uncertainty entails the
  selection of a course of action when we do not
  know with certainty the results that each
  alternative action will yield.
• This type of decision problems can be solved by
  statistical techniques along with good judgment
  and experience.
• Example 1 (p.105). McCovery Development Co. has
  purchased land in Texas, on the shore of the Gulf
  of Mexico, and is attempting to determine the
  size of the condominium complex it should build.
  Three sizes are being considered small, medium,
  and large. Management also contemplates three
  possible levels of demand low, medium, and high,
  each equally probable. (1). If the demand is
  high, McCovey will make 900K if they build the
  large complex, 600K if they build the medium
  complex, and 400K if they build the small
  complex. (2). If the demand is medium, McCovey
  will make 300K if they build the large complex,
  600K if they build the medium complex, and 400K
  if they build the small complex. (3). If the
  demand is low, McCovery will lose 300K if they
  build the large complex, will make 100K if they
  build the medium complex, and will make 400K if
  they build the small complex. What is the
  optimal strategy of the company?

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Elements of a Decision Analysis (p.106)

• Alternative/Action An alternative (or action)
  is a course of action intended to solve a
  problem.
• Build a small size of condominium complex
• Build a medium size of condominium complex
• Build a large size of condominium complex
• State of Nature and Probabilities The
  uncontrollable future events that affect the
  payoff associated with a decision alternative.
• Low demand (1/3)
• Medium demand (1/3)
• High demand (1/3)
• Payoff The outcome measure, such as profit or
  cost. Each combination of a decision alternative
  and a state of nature has an associated payoff.
• If the demand is high, McCovey will make 900K if
  they build the large complex.
• If the demand is low, McCovery will lose 300K if
  they build the large complex.
• Payoff Matrix A tabular representation of the
  payoffs for a decision problem. The rows of the
  matrix correspond to the decision alternatives,
  and the columns of the matrix correspond to the
  possible states of nature.

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Decision Rules for Single-Stage Decision Problems

• The Maximax Decision Rule
• The Maximin Decision Rule
• The Minimax Regret Decision Rule
• The Expected Monetary Value Decision Rule
• The Expected Regret Decision Rule

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The Maximax Decision Rule
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The Maximin Decision Rule
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The Minimax Regret Decision Rule

• Regret Matrix a table summarizes the possible
  opportunity losses that could result from each
  decision alternative under each state of nature.
  Each entry in the regret matrix shows the
  difference between the maximum payoff that can
  occur under a given state of nature and the
  payoff that would be realized from each
  alternative under the same state of nature.

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The EMV Decision Rule

• Expected Monetary Value (EMV) the weighted
  average of the payoffs, with weights given by the
  probabilities of the different states of nature.
  This rule selects the decision alternative with
  the largest expected monetary value.

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The Expected Opportunity Loss Decision Rule
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Decision Tree Using the EMV Rule

• Decision Tree is a graphical representation of
  the decision problem that shows the sequential
  nature of the decision-making process.
• In a decision tree,
• decisions are denoted by boxes.
• random (uncertain) outcomes are denoted by
  circles.

Read the tree from left to right

• Solve the tree
• from right to left
• At a box, choose the branch
• with the best EMV.
• At a chance node (circle),
• computer the EMV.

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Solving Multi-Stage Decision Problems Decision
Tree

• Oilco must determine whether or not to drill for
  oil in the South China Sea. It costs 1M and if
  oil is found the value is estimated to be 6M.
  At present, Oilco believes there is a 45 chance
  that the field contains oil. Before drilling,
  Oilco can hire (for 100K) a geology firm to
  obtain more information about the likelihood that
  the field will contain oil. Oilco believes there
  is a 50 chance that the geologist will issue a
  favorable report, and a 50 chance of an
  unfavorable report. Given a favorable report,
  there is a 80 chance that the field contains
  oil. Given an unfavorable report, there is a 10
  chance that the field contains oil. Construct a
  decision tree to identify Oilcos possible
  actions. Clearly label each node and provide
  sufficient information (e.g., payoff,
  probability) on each node and branch.

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Example 2
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Expected Value of Perfect InformationExpected
Value of Sample Information

• EVPI EMV free perfect information EMV with no
  information
• How much would you pay for perfect information?
• EVSI EMV with free sample information EMV
  with no information
• Suppose a market research shows that the
  probabilities of having a low, med., high demand
  are 0.25, 0.50, 0.25.
• How much would you pay for sample information
  (e.g., market research)?