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 modelsModels describing a single interval (Fig 4.2). Parameter values may be considered stable (eg. Interest rate)

• Dynamic modelsModels 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 modelsA modeling method that involves data analysis in several

dimensions

Multi-dimensional modeling in Excel

Multi-dimensional view

Vendor

Warranty type

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

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

• RiskPossible 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. Meddiagnosis