# 4 Year Profit Projection

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```					Chapter 4

MODELING AND
ANALYSIS
Model component
• Data component provides input data
• User interface displays solution
• It is the model component of a DSS that actually solves
the problem – it is the heart of any DSS
Modeling Steps
• Determine the Principle of Choice (or Result / Dependent
variable) Eg. Profit
• Perform Environmental Scanning & Analysis to identify all
Decision / independent variables
• For this,
– one can use Influence diagrams (Cognitive modeling)
– how did you model the car loan payment ? (assignment #2)
• Identify an existing model that relate the dependent and
independent variables
• If needed, develop a new model from scratch
– Eg. Factor analysis
• Multiple models: If needed divide the problem into sub-
problems and fit a model for each sub-problem
– Eg. Factor analysis, followed by Regression
Eg. Economy
Static, Dynamic, Multi-Dimensional Models

• Static models
Models describing a single interval (Fig 4.2). Parameter
values may be considered stable (eg. Interest rate)
• Dynamic models
Models whose input data are changed over time. E.g., a
five-year profit or loss projection; a spreadsheet model
may capture inflation, business cycle of economy; see
also Fig 4.3.
• Multidimensional models
A modeling method that involves data analysis in several
dimensions
Multi-dimensional modeling in Excel
Multi-dimensional view

(ABC Hardware,
Equipment type
Laptop,
Full warranty)=1000 units

Warranty type

Vendor
Model Categories

• Optimization
– Algorithms (Simplex in LP)
• Decision Analysis
– Decision-Table/Tree
• Simulation
– Uses experimentation, random generator
• Predictive
– Forecasting using regression, time-series analysis
• Heuristics
– Logical deduction using if-then rules (eg. Expert Systems)
– This is a qualitative model
• Other
– What if, goal-seeking, multiple goals
Optimization
• Every LP problem is composed of:
– Decision variables
– Objective function
– Constraints
– Capacities
Optimization
• Do Exercise #7
Sensitivity analysis

• A study of the effect of a change in an input variable on
the overall solution

• By studying each variable in turn, one can identify the
‘sensitive’ variables

• Helps evaluate robustness of decisions under changing
conditions

• Revising models to eliminate too-large sensitivities
Matching model & decision environments

• Certainty
A condition under which it is assumed that only one result
is associated with a decision (easier to model)

• Uncertainty
For a given decision, possible outcomes are unknown;
even if known, probabilities cannot be calculated due to
lack of data. (most difficult to model) Eg. Testing a new
rocket / product

• Risk
Possible outcomes are known & data is available to
calculate probabilities of occurrence of each outcome for
a given decision
Decision Tables under Risk/Uncertainty

Choose Decision D3 since it has the largest Expected Monetary Value.
Decision Trees under risk/uncertainty
Decision trees in Excel using Precision-Tree Add-in
Simulation
• An imitation of reality (eg. market fluctuations)
• Creates random scenarios

• Major characteristics
– Simulation is a technique for conducting experiments
– Simulation is a descriptive rather than a
normative/prescriptive method
– Simulation is normally used only when a problem is
too unstructured to be treated using numerical
optimization techniques
Simulation
• Advantages
– A great amount of time compression can be attained
– Simulation can handle an extremely wide variety of problem types
(eg. queuing, inventory, market returns, product demand variations)
– Simulation produces many important performance measures

• Disadvantages
– An optimal solution cannot be guaranteed
– Simulation model construction can be a slow and costly process
– Solutions and inferences from a simulation study are usually not
transferable to other problems
Simulation
Simulation Exercise

Enter this data as shown.

Select cell C20.
Type, =RAND(), Enter.
Copy C20 all the way down to C34.
Select D20.
Type, VLOOKUP(C20,\$C\$7:\$D\$16,2).
Copy cell D20 all the way down to D34.
Select F24.
Type, =Average(D20:D34).
Select F25.
Calculate SD.
What-if, Goal-seek, Multiple goals

• What-if: Similar to sensitivity analysis, but focus is on
generating the revised solution when an input value is
changed.

• Goal-seek: Calculates the value of an input necessary
to achieve a desired level of output (goal). Eg. How
many hours to study to get an A?

• Multiple goals: Finds a compromise solution. Eg. Group
decision environments, usually based on utility analysis
(Analytical Hierarchy Process-Chapter 10)
Goal-seek Exercise
Scenarios

• A statement of assumptions about the operating
environment of a particular system at a given time; a
narrative description of the decision-situation setting
• Scenarios are especially helpful in simulations and
what-if analyses
• Possible scenarios
–   The worst possible scenario
–   The best possible scenario
–   The most likely scenario
–   The average scenario
Do Exercise #8
Problem solving search methods
• DSS uses these in the Design & Choice phases

Eg. LP

Eg. Chess
(large RAM)

Eg. Chess

Eg. Med
diagnosis

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