1. CHAPTER 5 Modeling and Analysis
Good morning, everybody. Simon and I are going to introduce chapter 5, modeling and analysis.
The first major components of DSS was introduced in chapter 4, the database and its management.
In this chapter, we will introduce the second major component: the model base and its management.

2. Outline 5.1 Opening vignette 5.2 Modeling for MSS
5.3 Static and dynamic models
5.4 Treating certainty, uncertainty, and risk
5.5 Influence diagrams
5.6 MSS modeling in spreadsheets
5.7 Decision analysis of a few alternatives (decision tables and trees)
5.8 Optimization via mathematical programming
Here is the outline that I’m going to introduce to you. From 5.1 opening vignette to 5.8 optimization via mathematical programming.

3. 5.1 Opening Vignette (p.166)
DuPont simulates rail transportation system and avoids costly capital expense

4. 5.2 Modeling for MSS Key element in most DSS
Necessity in a model-based DSS
Can lead to massive cost reduction / revenue increases

5. Major Modeling Issues Problem identification Environmental analysis
Variable identification
Forecasting
Multiple model use
Model categories or selection (Table 5.1)
Model management (Section 5.16)
Knowledge-based modeling (Chapter 6)
(It’s important to analyze the scope of problem domain and dynamics of the environment.)
DSS can include several models, which represents a different part of the decision-making problem.
Table 5.1 classifies DSS models into seven groups and list several representative techniques for each category.

7. 5.3 Static and Dynamic Models
Static Analysis
Single snapshot
Dynamic Analysis
Dynamic models represent scenarios that change over time
Time-dependent
Trends and patterns over time
DSS model can be classified as static or dynamic.
Static models take a snapshot of a situation. During this snapshot everything occurs in a single interval.For instance, a decision on whether to or buy a product or not.

8. 5.4 Treating Certainty, Uncertainty, and Risk
Certainty Models
Easy to develop and solve
Yield optimal solution
Uncertainty
Information unavailable
Risk
The actual probabilities are known
Estimate the risk
When we build models, any of these conditions can occur.
If a decision-making problem is under certainty, we can easily choose the best solution.
For uncertainty, we do not know the probabilities of events occurring in the future. More information is unavailable.
For risk, sometimes the actual probabilities of events occurring in the future are known, and we have decision-making under risk.
Other times, we make estimates of the risk and presume the risk situation occurs.

9. 5.5 Influence Diagrams Graphical representations of a model
Visual communication
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
Example (Figure 5.1)
Influence diagrams appear in several formats. Bodily(1985) suggested the following conventions.

10. 5.5 Influence Diagrams Considering the following profit model:
Profit= income-expenses
Income= units sold * unit price
Units sold= 0.5*amount used in ad
Expenses= unit cost * units sold+ fixed cost
The tortuous arrow means uncertainty relationship.
And we have to put a tilde above the risk variable’s name.

11. 5.5 Influence Diagrams Representative software products Analytica
DecisionPro
DATA Decision Analysis Software
Definitive Scenario
PrecisionTree

12. 5.6 MSS Modeling in Spreadsheets
Spreadsheet: most popular end-user modeling tool
Powerful functions: financial, statistical, mathematical, and other functions
Add-in functions
Important for analysis, planning, modeling
The spreadsheet is the most popular end-user modeling tool because it incorporates many powerful functions.
Add-ins were developed for structuring and solving specific model classes.

13. 5.6 MSS Modeling in Spreadsheets
Other important feature:
What-if analysis
Goal seeking
Data management
Programmability(macro)
Microsoft Excel & Lotus1-2-3
Static and dynamic models can be built in a spreadsheet(Figure 5.3, Figure 5.4)
We can do what-if analysis because it’s easy to change a cell’s value and immediately see the result.
Goal seeking is performed by indicating a target cell, and a changing cell.
Database management can be performed, or parts of a database can be imported for analysis.
The programming productivity of building DSS can be enhanced with the use of macros.
Microsoft Excel, Lotus1-2-3 Two most important popular spreadsheet package

14. 5.6 MSS Modeling in Spreadsheets
Excel spreadsheet static model example

15. 5.6 MSS Modeling in Spreadsheets
Excel spreadsheet dynamic model example

16. 5.7 Decision Analysis of Few Alternatives (Decision Tables and Trees)
Finite and not too large number of alternatives
Single-goal situations
Decision situations that involve a finite and not too large number of alternatives are modeled by an approach called decision analysis. The can be evaluated to select the best alternative.
Single-goal situation can be modeled with decision tables or decision trees.Multiple goals can be modeled with several other technique described later.

17. 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
An investment company is considering investing in one of three alternatives: bonds, stocks, or certificates of deposit. The company is interested in one goal: maximizing the yield on the investment after 1 year.
The word stagnation means the economy is not prosperity.

18. Decision Tables 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%
The alternatives are the decision variables. The states of nature are uncontrollable variables. And the yield is the result variable.
Decision
Variables

19. Treating Uncertainty Optimistic approach
Assume that the best possible outcome of each alternative will occur and then selects the best of the best
Pessimistic approach
Assume that the worst possible outcome for each alternative will occur and selects the best one of those
There are several methods of handling uncertainty. For example, the optimistic approach assumes that the best possible outcome of each alternative will occur and then selects the best of the best.
The pessimistic approach assumes that the worst possible outcome for each alternative will occur and selects the best one of those.

20. Treating Risk
Risk analysis: Use known probabilities to compute expected values (Table 5.3)
Can be dangerous
An infinitesimal chance of a catastrophic loss may cause the expected value reasonable
12(0.5)+6(0.3)+3(0.2)=8.4
The most common method for solving this risk analysis problem is to use known probabilities to compute the expected values, and then select the alternative with the largest expected value.
For example, in table5.3, investing in bonds yields an expected return of 8.4%.

21. Decision Trees Graphically show the relationship of the problem
Can handle complex situations in a compact form
The word compact here means something not complicated.

22. Multiple Goals
A simplified investment case of multiple goals is shown in Table 5.4
Multicriteria decision-making software packages- Analytic Hierarchy Process(e.g., Expert Choice software) is a leading one
There are many decision analysis and multicriteria decision-making software packages. Analytic Hierarchy Process is a leading one to solve multicriteria decision-making problem.

23. 5.8 Optimization via Mathematical Programming
Linear programming (LP)
Best-known technique in optimization
Used extensively in DSS
Mathematical Programming
Family of tools to solve managerial problems in allocating scarce resources among various activities to optimize a measurable goal

24. 5.8 Optimization via Mathematical Programming
LP Allocation Problem Characteristics
Limited quantity of economic resources
Resources are used in the production of products or services
Two or more ways (solutions, programs) to use the resources
Each activity (product or service) yields a return in terms of the goal
Allocation is usually restricted by constraints

25. LP Allocation Model Rational economic assumptions
Returns from allocations can be compared in a common unit
Independent returns
Total return is the sum of different activities’ returns
All data are known with certainty
The resources are to be used in the most economical manner
Solutions can be infinite or finite
Optimal solution: at least one best solution, found algorithmically

26. Linear Programming Components of LP problem
Decision variables
Objective function
Objective function coefficients
Constrains
Capacities
Input-output coefficients
Two best known modeling system: Lindo & Lingo
The value of decision variables are unknown and are searched for.

27. Lindo LP Product-Mix Model DSS in Focus 5.4
The product-mix model described in Chapter 2 (p.61)
Objective function
X1, X2: Decision variables
<< The Lindo Model: >>
MAX X X2
SUBJECT TO
LABOR) X X2 <=
BUDGET) X X2 <=
MARKET1) X1 >= 100
MARKET2) X2 >= 200
END
Constraints
Input-output coefficients indicate resource utilization for a decision variable.(300,500)
You can see the detail information, like solution report of this problem on page 184.
Thank you for your listening.
Capacities

28. 5.9 Heuristic Programming (1)
Determination of optimal solution could involve amount of time and cost in some complex decision problems.
Simulation approach may be lengthy, complex, inaccurate.
Therefore, by using heuristics we can arrive at satisfactory solutions more quickly and less expensively.

29. Heuristic Programming (2)
Finding rules that help to solve complex problems.
Finding ways to retrieve and interpret information on each experience.
Finding methods that lead to a computational algorithm or general solution.

30. Heuristic Programming (3)
Are used for solving ill-structured problems.
Can be used to provide satisfactory to certain complex well-structured problems
More cheaply and quickly than optimization algorithms
But only for the specific situation.
Heuristics may obtain a poor solution.

31. Heuristic Programming (4)
the approach of using heuristics to at feasible and “good enough” solutions to complex problems
“good enough” = 90%-99.9% of the objective value of an optimal solution.
Can be quantitative or qualitative.

32. Methodology (1) Searching Learning Evaluating Judging Knowledge

33. Methodology (2) Tabu search Genetic algorithms
“remember” high-quality and low-quality solutions.
Move toward to high-quality solutions, away from low-quality solutions.
Genetic algorithms
Start with a set of randomly solutions.
Recombine pairs of solutions to produce offspring.

34. When to use Heuristics Input data are inexact or limited.
Reality is so complex that optimization models can’t be used.
Exact algorithm is not available.
Can combine heuristics and optimization to improve efficiency.
Optimization or simulation are not economical, or taking an amount of time.
Symbolic processing is involved.
Quick decisions, no computerization.

35. Advantages Simple to understand. Training people to be creative.
Save formulation time.
Save computer programming and storage requirement.
Save computer running time.
Produce multiple acceptable solutions.
Develop a measure of the solution quality.

36. Limitations Not always optimal solutions
Too many exceptions to the rules
Sequential decision choices can fail to anticipate future consequences of each choices.

37. 5.10 Simulation
To assume the appearance of the characteristics of reality.
A technique for conducting experiments with computer on a model of a management system.
Simulation is one of the most commonly used tools of DSS.

38. Major Characteristics
Simulation “imitates” reality.
A technique for conducting experiments
Simulation is a descriptive tool.
Simulation is used only when a problem is too complex to be treated by numerical optimization techniques.

39. Advantages of Simulation (1)
Simulation theory is fairly straightforward.
A great amount of time compression can be attained.
Simulation is descriptive rather than normative.
An accurate simulation model requires an intimate knowledge of the problem.
The simulation model is built form the manager’s perspective and decision structure.
The simulation model is built for one particular problem.

40. Advantages of Simulation (2)
Simulation can handle an extremely wide variety of problem types.
The manager can experiment with different variables and different alternatives.
Allows for inclusion of the real-life complexities of problem.
It’s easy to obtain a wide variety of performance measures.
The only modeling tool for DSS where problems can be non-structured.

41. Limitations of Simulation
An optimal solution can’t be guaranteed.
Constructing a simulation model can often be a slow and costly process.
Solutions and inferences from a simulation are not transferable to other problems.
Simulation software is not so user-friendly.

42. The Methodology of Simulation (1)
Real-World
problem
Problem
definition
Construct
The
Simulation
model
Test and
Validate
The
model
Design the
Simulation
experiments
Conduct the
experiments
Implement
The
results
Evaluate
The
results

43. The Methodology of Simulation (2)
Problem definition
The real-world problem is examined and classified.
Construction of the simulation model
Involves the determination of the variables and their relationships and gathering necessary data.
Testing and validating the model
The simulation model must properly represent the system.

44. The Methodology of Simulation (3)
Design of the experiments
Two important and conflicting objectives：accuracy and cost.
Conducting the experiments
Involves issues ranging from random number generation to presentation of the results.
Evaluating the results
Determine the meaning of the results.
Implement

45. Types of Simulation Probabilistic simulation
One or more of the variables are probabilistic.
Discrete distribution or Continuous distribution.
Time-dependent versus Time-independent simulation
Simulation software (5.15)
Visual Simulation (5.14)
Object-Oriented Simulation

46. 5.11 Multidimensional Modeling-OLAP
Managers need to work with three or more dimensions.
The solution is provided by multidimensional modeling tools.
Most multidimensional analysis systems are embedded in online analytical processing (OLAP) systems.

47. OLAP
The goal of OLAP is to capture the structure of real-world data and provide support to the decision maker.
OLAP reports are interactive reports that are highly formatted, easily deployed, and effortless to use.
Figure 5.6A, 5.6B, 5.6C, 5.6D

48. OLAP
Business intelligence tools – user simply access a data warehouse and direct the software to show the data in interesting ways and automatically build model.

49. 5.12 Visual Interactive Modeling & Visual Interactive Simulation (1)
Conventional simulation：
Simulation does not allow decision makers to see how a solution evolves over time.
Decision makers are not an integral part of simulation development and experimentation
If the results do not match the intuition or judgment of the decision maker, a confidence gap occurs.

50. Visual Interactive Modeling & Visual Interactive Simulation (2)
One of the most exciting developments in computer graphics is visual interactive modeling (VIM).
VIM uses computer graphic displays to present the impact of different management decisions.
VIM can represent a static or a dynamic system.

51. Visual Interactive Modeling & Visual Interactive Simulation (3)
Is one of the most exciting dynamic VIMs.
VIS allows the end user to watch the progress of the simulation model in a animated form.
Basic philosophy of VIS is that decision makers can interact with the simulated model and watch the results develop over time.

52. Visual Interactive Modeling & Visual Interactive Simulation (4)
VIMs and DSS
VIM in DSS has used in several operations management decisions.
Waiting-line management (queuing)
VIM approach can be used in conjunction with artificial intelligence.
General-purpose commercial dynamic VIM software is readily available.

53. 5.13 Quantitative Software Packages - OLAP
Some DSS tools offer several subroutines for constructing quantitative models.
Statistics, financial analysis, accounting, and management science.
In addition, many DSS tools can easily interface with powerful standard quantitative software packages.

54. Quantitative Software Packages
Statistical packages
Typical functions：mean, median, variance, standard deviation, t-test, various types of regression correlations.
Excel, SPSS, Minitab, SAS.
Now statistical software is considered a decision-making tool.
It’s embedded in data mining and OLAP tools.

55. Quantitative Software Packages
Management science packages
There are several hundred management science packages on the market for models ranging from inventory control to project management.

56. Quantitative Software Packages
Revenue management
Involves models that attempt to stratify an organization’s customers, estimate demands, establish prices for each category of customer, and dynamically model all.
Other specific DSS applications
P.203

57. 5.14 Model Base Management (1)
Model base management system (MBMS) is a software package with capabilities similar to DBMS.
There are no standardized MBMS：
There are too many standard model classes.
Each model class have several approaches for solving problems, depending on problem.
Each organization uses models differently
MBMS capabilities require expertise and reasoning capabilities.

58. Model Base Management (2)
Some desirable MBMS capabilities：
Control
Flexibility
Feedback
Interface
Redundancy reduction
Increased consistency

59. Model Base Management (3)
Modeling languages
Some popular mathematical programming model languages include Lingo, AMPL, and GAMS.
Relational model base management system
Object-oriented model base and its management
Models for database and MIS design and their management