Management Science

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Management Science
QM 6433 -- Fall 2004

• Decision Theory Applications

Instructor John Seydel, Ph.D.
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Student Objectives

• Summarize basic statistics and probability
  concepts
• Work with discrete probability distributions
• Model/solve decision analysis problems according
  to the EMV selection criterion
• Using decision trees
• Using payoff matrices
• Strengthen spreadsheet modeling skills
• Use Excel to support decision theory applications

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First, Some Administrative Stuff

• Questions about the course?
• Materials (e.g., syllabus, homework, . . . )
• Policies (e.g., exams, grading, . . . )
• Other . . . ?
• Collect homework, etc.
• Prerequisite sheets
• Chapter 1 questions
• Chapter 15 (attempts) 4(d), 5(a,e), 6(e),
  7(a,e)
• Stat/Excel exercises hold revise for next
  meeting
• Expectations

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Review of Basic Statistics

• Purpose of descriptive statistics
• To summarize many observed values (often to use
  as parameters)
• Especially, to summarize their variation
• Note observed values generally represent a
  subset, not the entire population or process
• Typical means/measures for summarizing numeric
  data
• Univariate
• Graphical histogram
• Location average, median, quantiles
• Variation range, standard deviation
• Multivariate
• Graphical scatterplot
• Location (conditional) slope, intercept
• Variation R2, Syx
• We generally need some sort of decision support
  system (e.g., Excel) to take care of the mundane
  aspects of analysis
• Lets look at the review exercise . . .

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Spreadsheet Design Guidelines

• Organize the data, then build the model around
  the data.
• Do not embed numeric constants in formulas.
• Things which are logically related should be
  physically related.
• Use formulas that can be copied.
• Column/rows totals should be close to the
  columns/rows being totaled.
• The English-reading eye scans left to right, top
  to bottom.
• Use color, shading, borders and protection to
  distinguish changeable parameters from other
  model elements.
• Use text boxes and cell notes to document various
  elements of the model.

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Now, Some Probability Fundamentals

• First, what is probability?
• Its just a numeric value we assign to how
  certain we feel something is
• Value is always between 0 and 1 (i.e., 0 and
  100)
• So, how do we determine it?
• Then, what do we do with it?

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Probability Comments

• For decision problems that occur more than once,
  we can often estimate probabilities from
  historical data.
• Other decision problems (such as . . . ?)
  represent one-time decisions where historical
  data for estimating probabilities dont exist.
• In these cases, probabilities are often assigned
  subjectively based on interviews with one or more
  domain experts.
• Highly structured interviewing techniques exist
  for soliciting probability estimates that are
  reasonably accurate and free of the unconscious
  biases that may impact an experts opinions.
• We will focus on techniques that can be used once
  appropriate probability estimates have been
  obtained.

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Determining Probability

• Consider enrollments at ASU in 2004
• Could decrease substantially
• Could decrease slightly
• Could stay essentially the same
• Could increase slightly
• Could increase substantially
• Consider demand for newspapers at a vending
  machine
• What are the possible states of nature?
• What are the associated probabilities?
• Also, level of awareness among students
• These are all probability distributions
• Distribution list of possible outcomes and
  their corresponding probabilities

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So, What Do We Do With It?

• Use it to choose courses of action
• Determine essentially a certainty equivalence
• Gives us a single number
• This is the expected value (sometimes, EMV)
• Its just a weighted average Sxp(x)
• Examples (EMV calculations from probability
  distributions)
• Newspaper vending machine problem (x12)
• Brendas Ski Shop (Problem 15.4, xlarge)

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Recall OR/MS Tools to be Addressed

• Linear programming (e.g., Crop Planting case)
• Queuing theory (e.g., ER Staffing case)
• Multicriteria analysis
• Simulation modeling analysis
• Decision analysis (e.g., Vending Machine case)

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Recall the Scientific Problem Solving Process

• Basic framework
• Define the problem
• Determine criteria of importance
• Define decision variables
• Identify constraints
• Consider alternatives
• Identify them
• Evaluate them
• Select best one
• Implement solution
• Monitor and revise solution re-solve if
  appropriate
• Note other incarnations (specific applications)
• MIS systems development life cycle
• Marketing customer decision process

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Consider Essentially Any Decision

• Two problem aspects involved
• Courses of action
• What choices we have
• Examples which job, how many papers, . . .
• States of nature
• Events out of our control
• Examples whos elected, weather, court
  decisions, economy
• Example vending machine problem
• States of nature are described by probability
  distributions
• We can use decision theory approaches to assist
  us with many problems we encounter

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Comparing Alternatives (via EMV)

• This is what decision theory is all about
• Once certainty equivalence values are calculated
  for each alternative, that with the best value is
  chosen
• Two approaches are commonly used for structuring,
  modeling, and solving decision analysis problems
• Payoff matrix simple decisions, 1 variable
• Decision tree complex decisions, multiple
  variables
• Example vending machine problem revisited
• Note the application of the problem-solving
  framework

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A Summary of the Procedure

• Determine alternatives
• For each alternative
• Determine outcomes (e.g., monetary values)
  possible
• Determine probabilities for those outcomes
• Create model (matrix or tree)
• Determine EMV for each alternative
• Make choice
• Best EMV?
• Consider risk
• Postoptimality (e.g., sensitivity) analysis?

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A Good Application of the Payoff Matrix Approach

• Problem 15.7 in text
• Before putting together the matrix
• List the cost parameters
• Determine the profit functions
• Matrix cell values
• We could calculate each payoff individually
• But the logic is the same for all cells
• Hence, a single formula should work (using Excel)
• Need, however, to use mixed referencing
• Thats the hard part the rest is just applying
  the EMV calculations (SUMPRODUCT)

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Summary of Objectives

• Summarize basic statistics and probability
  concepts
• Work with discrete probability distributions
• Model/solve decision analysis problems according
  to the EMV selection criterion
• Using decision trees
• Using payoff matrices
• Strengthen spreadsheet modeling skills
• Use Excel to support decision theory applications

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Appendix
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Work Expectations

• Written work type
• Computational work
• Pencil, graph paper, straightedge
• Computer printout
• Fit to page (when appropriate)
• Annotate with pencil as necessary
• General guideline be reasonable e.g., if it
  doesnt lend itself to typing, do it manually or
  with computer output

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Newspaper Vending Machine Case

• Monetary information
• Cost per paper 0.50
• Revenue per paper
• 1.00 if sold
• Nothing otherwise
• Decision determine best value for x, how many
  papers to stock
• Alternatives 10, 11, 12, 13
• Criteria (objectives)?
• Criteria volume, profit
• Model
• Use a decision tree approach
• Note Not necessarily all papers will be sold
• Must incorporate the demand distribution

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Consider the Demand Probability Distribution

• Indicate these on a decision tree
• Or incorporate these into a payoff matrix . . .

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Website Development

• Recall the traditional SDLC (systems development
  life cycle)
• Start by identifying user requirements
• Design a solution
• Construct, test, and implement solution
• Monitor and maintain
• Web design (actually, development) model is based
  upon the SDLC

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Customer Decision Process
The second step in the construction of the online
offering is the articulation of the customer
decision process for the various product
categories
Flowers Example
Problem Recognition

• Need recognition, potentially triggered by a
  holiday, anniversary or everyday events

• Search for ideas and offerings, including
• Available online and offline stores
• Gift ideas and recommendations
• Advice on selection style and match

Prepurchase
Information Search
Evaluation of Alternatives

• Evaluation of alternatives along a number of
  dimensions, such as price, appeal, availability,
  etc.

Purchase
Purchase Decision

• Purchase decision
• Message selection (medium and content)

Satisfaction

• Post-sales support
• Order tracking
• Customer service

Postpurchase
Loyalty

• Education on flowers and decoration
• Post-sale perks

Disposal