Management Science

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Management Science
QM 6433 -- Spring 2004

• Introduction to Decision Modeling

Instructor John Seydel, Ph.D.
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Student Objectives

• Locate course materials
• Outline major course components
• Summarize the modeling decision making process
• Discuss the scientific problem solving process
• Contrast what-if analysis, optimization,
  goal-seeking, sensitivity analysis
• Create, analyze, and criticize simple math models
• Represents simple problems as spreadsheet models
• Use Excel for basic data analysis

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Course Materials

• Start with course website
• www.clt.astate.edu/jseydel/qm6433
• Under construction (always evolving)
• Major items
• Syllabus
• Grading
• Text
• Expectations
• Handouts (i.e., links thereto)
• Homework

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Lets Look at Some Mini-Cases

• Form discussion teams with students near you
• Approximately 4 per team
• Exchange names, email addresses, and phone
  numbers
• Elect a spokesperson
• Remember who you are
• Teammates
• Spokesperson
• Mini-cases to be addressed
• Newspaper vending machine decision
• Staffing of ER physicians
• Agricultural decision crop planting

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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
• Whats missing . . . ?

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Consider the Demand Probability Distribution
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Vending Machine Case Solution

• Add probability values to the decision tree
• Calculate expected monetary value (EMV) for each
  alternative
• Choose the alternative with the highest EMV
• Now, consider how the decision would have been
  different if volume had been used as the decision
  criterion

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Another Case ER Planning

• Friday nights how many physicians (x) needed?
• Basic summary info
• l 7 per hour
• m 3 per hour
• Decision tree . . . ?
• Determine a reasonable course of action

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Solution to ER Planning Case

• Need to determine which criterion is most
  important
• Waiting time (average, maximum, . . . )?
• Number waiting?
• Utilization?
• Costs . . . ?!
• Must use complex formulae to analyze this
• Alternative spreadsheet model
• Note results for various values of x
• Now, which is the best choice???

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A Third (and Final) Case

• Read An Agricultural Decision
• Discuss in small groups?
• Address
• Whats the decision involved?
• What objectives might be involved?
• What limits the progress on the objectives?
• What info do we have available and how reliable
  is it?
• Model and solve . . .

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Crop Planting Case

• Revenue 270/acre (melons) 300/acre (loupes)
• Cost data
• Fertilizer 4.00/acre (melons) 3.00/acre
  (loupes)
• Labor 10.00/acre (melons) 12.50/acre
  (loupes)
• Resources
• Water
• Usage 50 gal/acre (melons) 75 gal/acre
  (loupes)
• Available 6000 gal/day
• Land available 100 acres
• Criteria costs, volume, profit
• Solve via trial and error
• Tabulate info
• Play what-if with the decision variables
• Consider a decision tree representation

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Using a Spreadsheet

• Enter key data into certain cells
• Use formulae to display results of various
  decisions
• Tinker with the decision variables
• Demonstration . . .
• Alternative use the Solver !
• Profit maximization
• Compare result with volume maximization

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Review of the Cases

• Three different decision models
• Single decision variable
• Vending machine
• ER decision
• Two decision variables crop planting
• Stochastic inputs
• Vending machine
• ER decision
• Deterministic inputs crop planting
• Optimization
• Vending machine
• Crop planting
• Description ER decision
• Framework to be discussed momentarily
• All require computer support

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Now, an Abbreviated Course Outline

• Specific techniques
• Decision analysis
• Queuing theory
• Linear programming
• Project management concepts tools
• Simulation modeling analysis
• Multicriteria analysis
• General concepts and techniques (integrated
  throughout course)
• Spreadsheet modeling techniques
• Basic modeling concepts

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Our Recurring Framework Scientific Problem
Solving Process

• Problem solving is based upon decision making
• The 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

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We Will Be Using Various Decision Models

• Models involve
• Inputs
• Uncontrollable (e.g., costs)
• Controllable aka decision variables
• Outputs i.e., the results
• A solution
• The course of action to be taken
• That is, the values chosen for the decision
  variables
• Note
• Models are simplified versions of the things they
  represent
• A valid model accurately represents the relevant
  characteristics of the object or decision being
  studied

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Another Framework Models For Decision Support

• Two (or three) general model classifications
• Descriptive indicate what results will occur,
  given various input combinations
• Deterministic (generally no variation in outputs)
• Stochastic (output variation involved)
• Prescriptive indicate what values the
  controllable should be in order to achieve
  desired output results
• Note the difference in focus
• Descriptive models describe the outputs
• Prescriptive models prescribe the inputs
• (Varies somewhat from text framework)

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Benefits of Modeling

• Economy - it is often less costly to analyze
  decision problems using models.
• Timeliness - models often deliver needed
  information more quickly than their real-world
  counterparts.
• Feasibility - models can be used to do things
  that would be impossible.
• A structured, modeling approach to decision
  making helps us make good decisions, but cant
  guarantee good outcomes.
• Models give us insight understanding that
  improves decision making.

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Another Look at Model Components

• Inputs
• Decision variables (controllable inputs)
• Parameters (uncontrollable inputs)
• Criteria (with objectives, goals)
• Constraints
• Solution procedure
• Refer back to the scientific problem-solving
  process
• The problem definition stage refers to the first
  3 of these
• The alternatives stage refers to the 4th

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Typical Solution Procedures

• Tinkering with controllable inputs (i.e.,
  decision variables)
• What-if analysis
• Optimization (or satisficing)
• Goal seeking
• Sensitivity analysis
• Involves tinkering with uncontrollable inputs
• Seeks to test quality of decision, effect of
  assumptions, etc.

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Why Use Quantitative Methods for Decision Support?

• Compare and contrast
• Satisficing (searching for an acceptable
  solution)
• Optimization
• Tendency is to satisfice
• Quant methods reduce cost of search and thus make
  optimization more desirable

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Now, Some Data Analysis, an Excel Review

• Refer to survey data from review exercises
• ASU students
• Opinions regarding publishing instructor
  evaluations
• First, copy the data into a blank Excel worksheet
• Then use Excel to help out some with the
  calculations, etc.
• Univariate analysis Credits
• Bivariate analysis Level vs. Credits

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Summary of Objectives

• Locate course materials
• Outline major course components
• Summarize the modeling decision making process
• Discuss the scientific problem solving process
• Contrast what-if analysis, optimization,
  goal-seeking, sensitivity analysis
• Create, analyze, and criticize simple math models
• Represents simple problems as spreadsheet models
• Use Excel for basic data analysis

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Appendix
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Getting The Data From The Web

• On the web page
• Select only the data (no titles, etc.) if
  possible
• Right-click and then click on Copy
• Switch window to blank Excel worksheet
• Select top left cell
• Click on Paste button
• Remove unwanted artifacts (columns, labels, etc.)
• Convert to usable data
• Select top left cell of blank worksheet
• Use the VALUE() function
• Copy formula to remainder of cells
• Select variable to be analyzed
• Copy Past Special to clean worksheet

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Univariate Analysis (Quantitative Data)

• Describing the variation in Credits
• Recall univariate analysis tools
• Histogram (informal, visual analysis)
• Descriptive statistics
• Measures of location
• Measures of variation
• Now, some analysis
• Basic descriptive statistics (n, min, max, xbar,
  s)
• Histogram
• No good Excel function
• Need to create a flexible table/chart
• Reference material see Handouts page

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Bivariate Analysis (Quantitative Data)

• Hypothesis experienced students are likely to
  be more familiar with issues
• Appropriate analysis
• Examine Level vs Credits
• That is, Level b0 b1Credits
• Tools
• Scatterplot (i.e., XY chart)
• Regression (using Excel functions)
• b0
• b1
• R2
• Syx
• Reference material see Handouts page