1. Modeling & Analysis
By Daniel Damaris NS

2. Modeling & Analysis
Structure of some successful models and methodologies
Decision analysis
Decision trees
Optimization
Heuristic programming
Simulation

3. Modeling & Analysis Topics
Optimization via mathematical programming
Heuristic programming
Simulation
Multidimensional modeling -OLAP
Visual interactive modeling and visual interactive simulation
Quantitative software packages - OLAP
Model base management
Modeling for MSS
Static and dynamic models
Treating certainty, uncertainty, and risk
Influence diagrams
MSS modeling in spreadsheets
Decision analysis of a few alternatives (decision tables and trees)

4. Categories of Models

5. Modeling for MSS Key element in most DSS
Necessity in a model-based DSS
Can lead to massive cost reduction/revenue increases
Modeling:
Statistic Model (Regression Analysis)
Financial Model
Optimization Model (Linear Programming)

6. Static & Dynamic Analysis
Static Analysis
Single snapshot
Dynamic Analysis
Dynamic models
Evaluate scenarios that change over time
Time dependent
Trends and patterns over time
Extend static models

7. Influence Diagram Graphical representations of a model
Model of a model
Visual communication
Some packages create and solve the mathematical model
Framework for expressing MSS model relationships
Rectangle = a decision variable
Circle = uncontrollable or intermediate variable
Oval = result (outcome) variable: intermediate or final
Variables connected with arrows

8. Influence Diagram (cont.)

9. Influence Diagram (cont.)

10. Influence Diagram (cont.)

11. Influence Diagram (cont.)

12. Decision Support Mathematic Model

13. Decision Support Mathematic Model

14. The MSS Mathematic Model

15. MSS Modeling with Spreadsheet

16. MSS Modeling with Spreadsheet

17. Treating Certainty, Uncertainty & Risk

18. Decision Tables and Trees
Single Goal Situations
Decision tables
Decision trees

19. Decision Tables Investment example
One goal: maximize the yield after one year
Yield depends on the status of the economy
(the state of nature)
Solid growth
Stagnation
Inflation

20. Possible Situations
1. If solid growth in the economy, bonds yield 12%; stocks 15%; time deposits 6.5%
2. If stagnation, bonds yield 6%; stocks 3%; time deposits 6.5%
3. If inflation, bonds yield 3%; stocks lose 2%; time deposits yield 6.5%

21. View Problem as a Two-Person Game
Decision variables (alternatives)
Uncontrollable variables (states of economy)
Result variables (projected yield)

22. Investment Problem Decision Table Model
States of Nature
Solid Stagnation Inflation
Alternatives Growth
Bonds 12% 6% 3%
Stocks 15% 3% -2%
CDs 6.5% 6.5% %

23. Treating Uncertainty
Optimistic approach
Pessimistic approach

24. Treating Risk Use known probabilities
Risk analysis: compute expected values
Can be dangerous

25. Decision Under Risk and Its Solution
Solid Stagnation Inflation Expected
Growth Value
Alternatives
Bonds 12% 6% 3% 8.4% *
Stocks 15% 3% -2% 8.0%
CDs 6.5% 6.5% % 6.5%

26. Decision Tree Other methods of treating risk Multiple goals
Simulation
Certainty factors
Fuzzy logic
Multiple goals
Yield, safety, and liquidity

27. Multiple Goals Alternatives Yield Safety Liquidity
Bonds 8.4% High High
Stocks 8.0% Low High
CDs 6.5% Very High High

28. Discrete vs. Continuous Probability Distribution
Daily Discrete Continuous
Demand Probability
Normally distributed with
a mean of 7 and a
standard deviation of 1.2
9 .2

29. Linear Programming Allocation Problem 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

30. LP Allocation Model Rational economic assumptions
1. Returns from allocations can be compared in a common unit
2. Independent returns
3. Total return is the sum of different activities’ returns
4. All data are known with certainty
5. The resources are to be used in the most economical manner
Optimal solution: the best, found algorithmically

31. Linear Programming Decision variables Objective function
Objective function coefficients
Constraints
Capacities
Input-output (technology) coefficients

32. Lindo LP Product-Mix Model
<< The Lindo Model: >>
Max X X2
Subject to
Labor) X X2 <=
Budget) X X2 <=
Market 1) X1 >= 100
Market 2) X2 >= 200
END

33. Lindo LP Product-Mix Model
<< Generated Solution Report >>
LP OPTIMUM FOUND AT STEP
OBJECTIVE FUNCTION VALUE 1)
VARIABLE VALUE REDUCED COST X X

34. Lindo LP Product-Mix Model
ROW SLACK OR SURPLUS DUAL PRICES
LABOR)
BUDGET)
MARKET1)
MARKET2)
NO. ITERATIONS=

35. Lindo LP Product-Mix Model
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X INFINITY
X INFINITY
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
LABOR
BUDGET INFINITY
MARKET INFINITY
MARKET

36. Lindo LP Product-Mix Model (with computer program)
<< The Model >>>
MODEL:
! The Product-Mix Example;
SETS:
COMPUTERS /CC7, CC8/ : PROFIT, QUANTITY, MARKETLIM ;
RESOURCES /LABOR, BUDGET/ : AVAILABLE ;
RESBYCOMP(RESOURCES, COMPUTERS) : UNITCONSUMPTION ;
ENDSETS
DATA:
PROFIT MARKETLIM =
8000, 100,
12000, 200;
AVAILABLE = , ;

37. Lindo LP Product-Mix Model (with computer program)
UNITCONSUMPTION =
300, 500,
10000, ;
ENDDATA
MAX PROFIT * QUANTITY) ;
@FOR( RESOURCES( I):
@SUM( COMPUTERS( J):
UNITCONSUMPTION( I,J) * QUANTITY(J)) <= AVAILABLE( I));
@FOR( COMPUTERS( J):
QUANTITY(J) >= MARKETLIM( J));
! Alternative
@BND(MARKETLIM(J), QUANTITY(J), ));

38. Lindo LP Product-Mix Model (with computer program)
<< (Partial ) Solution Report >>
Global optimal solution found at step:
Objective value:
Variable Value Reduced Cost
PROFIT( CC7)
PROFIT( CC8)
QUANTITY( CC7)
QUANTITY( CC8)
MARKETLIM( CC7)
MARKETLIM( CC8)
AVAILABLE( LABOR)
AVAILABLE( BUDGET)

39. Lindo LP Product-Mix Model (with computer program)
UNITCONSUMPTION( LABOR, CC7)
UNITCONSUMPTION( LABOR, CC8)
UNITCONSUMPTION( BUDGET, CC7)
UNITCONSUMPTION( BUDGET, CC8)
Row Slack or Surplus Dual Price

40. Heuristic Programming
Cuts the search
Gets satisfactory solutions more quickly and less expensively
Finds rules to solve complex problems
Finds good enough feasible solutions to complex problems
Heuristics can be
Quantitative
Qualitative (in ES)

41. When to Use Heuristics 1. Inexact or limited input data
2. Complex reality
3. Reliable, exact algorithm not available
4. Computation time excessive
5. To improve the efficiency of optimization
6. To solve complex problems
7. For symbolic processing
8. For making quick decisions

42. Advantages of Heuristics
1. Simple to understand: easier to implement and explain
2. Help train people to be creative
3. Save formulation time
4. Save programming and storage on computers
5. Save computational time
6. Frequently produce multiple acceptable solutions
7. Possible to develop a solution quality measure
8. Can incorporate intelligent search
9. Can solve very complex models

43. Limitations of Heuristics
1. Cannot guarantee an optimal solution
2. There may be too many exceptions
3. Sequential decisions might not anticipate future consequences
4. Interdependencies of subsystems can influence the whole system
Heuristics successfully applied to vehicle routing

44. Heuristic Types Construction Improvement Mathematical programming
Decomposition
Partitioning

45. Modern Heuristic Methods
Tabu search
Genetic algorithms
Simulated annealing

46. Simulation
Technique for conducting experiments with a computer on a model of a management system
Frequently used DSS tool

47. Major Characteristics of Simulation
Imitates reality and capture its richness
Technique for conducting experiments
Descriptive, not normative tool
Often to solve very complex, risky problems

48. Advantages of Simulation
1. Theory is straightforward
2. Time compression
3. Descriptive, not normative
4. MSS builder interfaces with manager to gain intimate knowledge of the problem
5. Model is built from the manager's perspective
6. Manager needs no generalized understanding. Each component represents a real problem component
(More)

49. Advantages of Simulation
7. Wide variation in problem types
8. Can experiment with different variables
9. Allows for real-life problem complexities
10. Easy to obtain many performance measures directly
11. Frequently the only DSS modeling tool for nonstructured problems
12. Monte Carlo add-in spreadsheet packages

50. 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

51. Simulation Methodology
Model real system and conduct repetitive experiments
1. Define problem
2. Construct simulation model
3. Test and validate model
4. Design experiments
5. Conduct experiments
6. Evaluate results
7. Implement solution

52. Simulation Types Probabilistic Simulation Discrete distributions
Continuous distributions
Probabilistic simulation via Monte Carlo technique
Time dependent versus time independent simulation
Simulation software
Visual simulation
Object-oriented simulation

53. Multidimensional Modeling
Performed in online analytical processing (OLAP)
From a spreadsheet and analysis perspective
2-D to 3-D to multiple-D
Multidimensional modeling tools: 16-D +
Multidimensional modeling - OLAP (Figure 5.6)
Tool can compare, rotate, and slice and dice corporate data across different management viewpoints

54. Entire Data Cube from a Query in PowerPlay

55. Graphical Display of the Screen (Courtesy Cognos Inc.)

56. Environmental Line of Products by Drilling Down (Courtesy Cognos Inc.)

57. Drilled Deep into the Data (Courtesy Cognos Inc.)

58. Visual Spreadsheets
User can visualize models and formulas with influence diagrams
Not cells--symbolic elements

59. Visual Interactive Modeling (VIM) and Visual Interactive Simulation (VIS)
Also called
Visual interactive problem solving
Visual interactive modeling
Visual interactive simulation
Use computer graphics to present the impact of different management decisions.
Can integrate with GIS
Users perform sensitivity analysis
Static or a dynamic (animation) systems

60. Generated Image of Traffic at an Intersection from the Orca Visual Simulation Environment (Courtesy Orca Computer, Inc.)

61. Visual Interactive Simulation (VIS)
Decision makers interact with the simulated model and watch the results over time
Visual interactive models and DSS
VIM
Queueing

62. Thank You !