1. Modeling

2. Models Iconic model (scale models) The least abstract type of model
physical replica of a system
Ex: scale model of F16

3. Models Analog model Ex: blueprint of a house or machine.
An abstract, symbolic model of a system that behaves like the system but looks different
More abstract than iconic models.
Ex: blueprint of a house or machine.

4. Models Mental model Mathematical (quantitative) model
The mechanisms or images through which a human mind performs sense-making in decision making.
Used when there are qualitative factors.
ex: when airplane pilots consider whether to fly.
Mathematical (quantitative) model
A system of symbols and expressions that represent a real situation

5. Models The benefits of models
Model manipulation is much easier than manipulating a real system
Models enable the compression of time
The cost of modeling analysis is much lower
The cost of making mistakes during a trial-and-error experiment is much lower when models are used than with real systems

6. Models The benefits of models (cont.)
With modeling, a manager can estimate the risks resulting from specific actions within the uncertainty of the business environment
Mathematical models enable the analysis of a very large number of possible solutions
Models enhance and reinforce learning and training
Models and solution methods are readily available on the Web

7. DSS Modeling Current trends Multidimensional analysis (modeling)
A modeling method that involves data analysis in several dimensions
Influence diagram
A diagram that shows the various types of variables in a problem (e.g., decision, independent, result) and how they are related to each other

8. Static and Dynamic Models
Static models
Models that describe a single interval of a situation
Dynamic models
Models whose input data are changed over time (e.g., a five-year profit or loss projection)

9. MSS Modeling with Spreadsheets
Models can be developed and implemented in a variety of programming languages and systems
The spreadsheet is clearly the most popular end-user modeling tool because it incorporates many powerful financial, statistical, mathematical, and other functions

10. MSS Modeling with Spreadsheets

11. MSS Modeling with Spreadsheets
Other important spreadsheet features include what-if analysis, goal seeking, trial and error, optimization , data management, and programmability
Most spreadsheet packages provide fairly seamless integration because they read and write common file structures and easily interface with databases and other tools
Static or dynamic models can be built in a spreadsheet

12. MSS Modeling with Spreadsheets

13. Optimization via Mathematical Programming
A family of tools designed to help solve managerial problems in which the decision maker must allocate scarce resources among competing activities to optimize a measurable goal
Optimal solution: The best possible solution to a modeled problem
Linear programming (LP): A mathematical model for the optimal solution of resource allocation problems. All the relationships are linear

14. LP 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

15. Linear Programming Steps
1. Identify the …
Decision variables
Objective function
Objective function coefficients
Constraints
Capacities / Demands
2. Represent the model
LINDO: Write mathematical formulation
EXCEL: Input data into specific cells in Excel
3. Run the model and observe the results
Line

16. LP Example The Product-Mix Linear Programming Model MBI Corporation
Decision: How many computers to build next month?
Two types of mainframe computers: CC7 and CC8
Constraints: Labor limits, Materials limit, Marketing lower limits CC7 CC8 Rel Limit Labor (days) <= 200,000 /mo Materials ($) 10,000 15,000 <= 8,000,000 /mo Units 1 >= 100 Units 1 >= 200 Profit ($) 8,000 12,000 Max Objective: Maximize Total Profit / Month

17. LP Solution

18. LP Solution Decision Variables: X1: unit of CC-7 X2: unit of CC-8
Objective Function:
Maximize Z (profit)
Z=8000X X2
Subject To
300X X2  200K
10000X X2  8000K
X1  100
X2  200

19. Sensitivity, What-if, and Goal Seeking Analysis
Assesses impact of change in inputs on outputs
Eliminates or reduces variables
Can be automatic or trial and error
What-if
Assesses solutions based on changes in variables or assumptions (scenario analysis)
Goal seeking
Backwards approach, starts with goal
Determines values of inputs needed to achieve goal
Example is break-even point determination

20. Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking
Sensitivity analysis tests relationships such as:
The impact of changes in external (uncontrollable) variables and parameters on the outcome variable(s)
The impact of changes in decision variables on the outcome variable(s)
The effect of uncertainty in estimating external variables
The effects of different dependent interactions among variables
The robustness of decisions under changing conditions

21. Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking
Sensitivity analyses are used for:
Revising models to eliminate too-large sensitivities
Adding details about sensitive variables or scenarios
Obtaining better estimates of sensitive external variables
Altering a real-world system to reduce actual sensitivities
Accepting and using the sensitive (and hence vulnerable) real world, leading to the continuous and close monitoring of actual results
The two types of sensitivity analyses are automatic and trial-and-error

22. Automatic sensitivity analysis
Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking
Automatic sensitivity analysis
Automatic sensitivity analysis is performed in standard quantitative model implementations such as LP (Linear Programming)
Trial-and-error sensitivity analysis
The impact of changes in any variable, or in several variables, can be determined through a simple trial-and-error approach

23. Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking
A process that involves asking a computer what the effect of changing some of the input data or parameters would be

24. Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

25. Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking
Asking a computer what values certain variables must have in order to attain desired goals

26. Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

27. Computing a break-even point by using goal seeking
Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking
Computing a break-even point by using goal seeking
Involves determining the value of the decision variables that generate zero profit