MODELING AND ANALYSIS

1
MODELING AND ANALYSIS
CONTENT 1. Influence Diagrams 2. Spreadsheets
3. Decision Analysis of Few Alternatives 4.
Optimisation Models 5. Heuristics 6.
Simulation 7. Multidimensional Modelling 8.
Visual Spreadsheets
2
Influence diagrams

• Influence diagram is a graphic representation
  of a model that shows the various types of
  variables (decision, independent, result) in a
  problem and how they are related to each other.

decisionvariable
uncontrollable variable
result variable
3
Example. Profit Income - Expenses Income
Units sold ? Unit price Units sold 0.5 ? Amount
used in advertisement Expenses Unit cost ?
Units sold Fixed cost
Fixedcost
Expenses
Unitcost
Profit
Income
Amount usedin advertisement
Units sold
Unitprice
4
Spreadsheets

• (Electronic) spreadsheet most popular end-user
  modeling tool
• Incorporate a large number of financial,
  statistical, mathematical logical, date and
  time, string functions
• External add-in functions for solving specific
  classes of models
• Macro-sequences of commands
• What-if analysis, goal seeking
• Some functions for database management (data
  collection, querying, sorting)
• Interactions with other tools
• Popular spreadsheets Microsoft Excel, Lotus 1-2-3

5
(No Transcript)
6
Decision Analysis of Few Alternatives

• Decision analysis lists the alternatives with
  their forecasted contributions to the goal and
  the probability of realising such a contribution
• appropriate when the number of alternatives is
  not too large
• Single goal situations
• Decision trees
• Decision tables

Investment Example One goal Maximize the yield
after one year Yield depends on the status of the
economy (Solid growth, Stagnation,Inflation).
7

• 1. If there is solid growth in the economy, bonds
  will yield 12 percent stocks, 15 percent and
  time deposits, 6.5 percent
• 2. If stagnation prevails, bonds will yield 6
  percent stocks, 3 percent and time deposits,
  6.5 percent
• 3. If inflation prevails, bonds will yield 3
  percent stocks will bring a loss of 2 percent
  and time deposits will yield 6.5 percent
• Payoff Table
• Decision variables (the alternatives)
• Uncontrollable variables (the states of the
  economy)
• Result variables (the projected yield)

8

• Treating Uncertainty
• Optimistic approach take the best possible
  outcome of each alternative and select the best
  among them (stocks)
• Pessimistic approach take the worst possible
  outcome of each alternative and select the best
  among them (CDs).

9

• Treating Risk
• Use known probabilities
• Risk analysis Compute expected values

120.5 6 0.3 30.2 8.4

• Can be dangerous!
• example.
• probability that the money 1,000 will be
  doubled 0.9999
• probability of loss of 500,000 0.0001
• expected value of investment
• 0.9999 (2.000 - 1.000) 0.0001 (-500.000 -
  1000) 999.9 - 50.10 949

10

• Multiple Goals
• Goals considered yield, safety, and liquidity

11
Optimisation Models

• 1. Mathematical programming
• Family of tools designed to allocate limited
  resources among various activities to optimise a
  measurable goal.
• Linear programming
• Appropriate for the problems with the following
  characteristics
• 1. Limited quantity of economic resources
• 2. Resources are used in the production of
  products or services.
• 3. Two or more ways (solutions, programs) to use
  the resources
• 4. Each activity (product or service) yields a
  return in terms of the goal
• 5. Allocation is usually restricted by
  constraints

12

• Problem is composed of
• Decision variables
• Objective function relates the decision
  variables to the goal and measures goal
  attainment and is to be maximised (minimised)
• Constraints linear inequalities or equalities
  that relate the variables
• Optimal solution the best, found
  algorithmically

13
Heuristics

• Heuristics are informal, judgmental knowledge of
  area which can be used to arrive at "good"
  enough solutions to some complex problems.
• Gives satisfactory solution more quickly and
  cheaply than optimisation models.
• Good for solving ill-structured problems,
  or for complex well-structured problems
  (large-scale combinatorial problems that have
  many potential solutions to explore)
• Drawbacks
• usually can be used only for the specific
  situation for which they are designed
• may give a poor solution

14
Simulation

• Simulation is a technique for conducting
  experiments(e.g. what-if analysis).
• Simulation imitates reality and capture its
  richness
• Involves the testing of specific values of the
  decision or uncontrollable variables in the
  model and observing the impact on the output
  variables.

• Simulation Methodology
• Set up a model of a real system and conduct
  repetitive experiments
• 1. Problem Definition
• 2. Construction of the Simulation Model
• 3. Testing and Validating the Model
• 4. Design of the Experiments
• 5. Conducting the Experiments
• 6. Evaluating the Results
• 7. Implementation

15

• Advantages of Simulation
• Time compression
• Descriptive, not normative
• The model is built from the manager's
  perspective
• Wide variation in problem types
• Can experiment with different variables
• Allows for real-life problem complexities
• Easy to obtain many performance measures
  directly
• Frequently the only DSS modeling tool for
  handling problems

16
Limitations of Simulation 1. Cannot guarantee an
optimal solution. 2. Slow and costly construction
process. 3. Cannot transfer solutions and
inferences to solve other problems. 4. So easy to
sell to managers, may miss analytical
solutions. 5. Software is not so user friendly.
17

• Types of simulation
• Probabilistic one or more uncontrollable
  variables are probabilistic

• Time-dependent and time-independent simulation
• Visual Simulation
• Object-Oriented Simulation

18

• Multidimensional Modelling
• Enables managers to work with 3 or more
  dimensions.
• Visual Spreadsheets
• Users visualise the models and formulae using
  influence diagram.
• Visual Interactive Modelling
• Uses computer graphic display to present the
  impact of different management decision.
• Also called
• Visual interactive problem solving
• Visual interactive modeling
• Visual interactive simulation

19

• Summary
• Influence diagrams show graphically the
  interrelationships of a model
• Spreadsheets have many extended capabilities,
  including what-if analysis, goal seeking,
  optimisation and simulation.
• Decision tables are useful for modelling and
  solving simple decision making problems.
• The major tool in optimisation is mathematical
  programming.
• Heuristic programming involves problems solving
  using general rules or intelligent search.
• Simulation involves experiments with a model
  that assumes the appearance of reality.
• Multidimensional modelling allows users to
  easily create models and display the results in
  different ways.
• Visual spreadsheets present spreadsheet
  modelling and result in an influence diagram
  format.
• Visual interactive simulation is increasingly
  being used.