decision support systems -modeling and analysis

8/3/2019 Decision Support Systems -Modeling and Analysis

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Prof. Rushen Chahal

DSS -Modeling and

Analysis

Prof. Rushen Chahal



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Modeling and Analysis

Major DSS component

Model base and model management

CAUTION - Difficult Topic Ahead Familiarity with major ideas

Basic concepts and definitions

Tool--influence diagram

Model directly in spreadsheets

Prof. Rushen Chahal



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Structure of some successful models andmethodologies

Decision analysis Decision trees

Optimization

Heuristic programming

Simulation

New developments in modeling tools / techniques

Important issues in model base management


Prof. Rushen Chahal



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Topics 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)

Optimization via mathematical programming

Heuristic programming Simulation

Multidimensional modeling -OLAP

Visual interactive modeling and visual interactive simulation

Quantitative software packages - OLAP

Model base managementProf. Rushen Chahal



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Modeling for MSS

K ey element in most DSS

Necessity in a model-based DSS

Can lead to massive cost reduction /revenue increases

Prof. Rushen Chahal



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Good Examples of MSS

Models DuPont rail system simulation model (opening

vignette)

Procter & Gamble optimization supply chainrestructuring models (case application 5.1)

Scott Homes AHP select a supplier model (case

application 5.2)

IMERYS optimization clay production model

(case application 5.3)

Prof. Rushen Chahal



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Major Modeling Issues

Problem identification

Environmental analysis

Variable identification Forecasting

Multiple model use

Model categories or selection (Table 5.1)

Model management

K nowledge-based modeling

Prof. Rushen Chahal



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Static and Dynamic Models

Static Analysis

Single snapshot

Dynamic Analysis Dynamic models

Evaluate scenarios that change over time

Time dependent

Trends and patterns over time

Extend static models

Prof. Rushen Chahal



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Treating Certainty,

Uncertainty, and Risk

Certainty Models

Uncertainty

Risk

Prof. Rushen Chahal



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Influence Diagrams

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

Example (Figure 5.1)

Prof. Rushen Chahal



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FIGURE 5.1 An Influence Diagram for the Profit Model.

~

Amount used in advertisementProfit

Income

Expense

Unit Price

Units Sold

Unit Cost

Fixed Cost

Prof. Rushen Chahal



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Analytica Influence Diagram of a MarketingProblem: The Marketing Model (Figure 5.2a)

(Courtesy of Lumina Decision Systems, Los Altos,

CA)

Prof. Rushen Chahal



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Analytica: Price Submodel (Figure 5.2b)(Courtesy of Lumina Decision Systems, Los Altos,

CA)

Prof. Rushen Chahal



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Analytica: Sales Submodel (Figure 5.2c)(Courtesy of Lumina Decision Systems, Los Altos,

CA)

Prof. Rushen Chahal



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MSS Modeling inSpreadsheets

Spreadsheet: most popular end-user modeling tool

Powerful functions

Add-in functions and solvers Important for analysis, planning, modeling

Programmability (macros)

(More)

Prof. Rushen Chahal



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What-if analysis

Goal seeking

Simple database management

Seamless integration

Microsoft Excel

Lotus 1-2-3

Excel spreadsheet static model example of a simple

loan calculation of monthly payments (Figure 5.3) Excel spreadsheet dynamic model example of a

simple loan calculation of monthly payments andeffects of prepayment (Figure 5.4)

Prof. Rushen Chahal



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Decision Analysisof Few Alternatives

(Decision Tables and Trees)

Single Goal Situations

Decision tables

Decision trees

Prof. Rushen Chahal



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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

Prof. Rushen Chahal



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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%

Possible Situations

Prof. Rushen Chahal



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View Problem as a Two-PersonG

amePayoff Table 5.2

Decision variables (alternatives)

Uncontrollable variables (states of economy)

Result variables (projected yield)

Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition

Copyright 2001, Prentice Hall, Upper Saddle River, NJProf. Rushen Chahal



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Table 5.2: Investment ProblemDecision Table Model

States of Nature

Solid Stagnation Inflation

Alternatives Growth

Bonds 12% 6% 3%

Stocks 15% 3% -2%

CDs 6.5% 6.5% 6.5%

Prof. Rushen Chahal



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Treating Uncertainty

Optimistic approach

Pessimistic approach

Prof. Rushen Chahal



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Treating Risk

Use known probabilities (Table 5.3)

Risk analysis: compute expected values

Can be dangerous

Prof. Rushen Chahal



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Table 5.3: Decision Under Risk and ItsSolution

Solid Stagnation Inflation Expected

Growth Value

Alternatives .5 .3 .2

Bonds 12% 6% 3% 8.4% *

Stocks 15% 3% -2% 8.0%

CDs 6.5% 6.5% 6.5% 6.5%

Prof. Rushen Chahal



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Decision Trees

Other methods of treating risk Simulation

Certainty factors

Fuzzy logic

Multiple goals

Yield, safety, and liquidity (Table 5.4)

Prof. Rushen Chahal



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Table 5.4: Multiple Goals

Alternatives Yield Safety Liquidity

Bonds 8.4% High High

Stocks 8.0% Low High

CDs 6.5% Very High High

Prof. Rushen Chahal



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Table 5.5: Discrete vs. Continuous

Probability Distribution

Daily Discrete Continuous

Demand Probability

5 .1 Normally distributed with

6 .15 a mean of 7 and a

7 .3 standard deviation of 1.2

8 .25

9 .2

Prof. Rushen Chahal



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Optimization viaMathematical Programming

Linear programming (LP)

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

Prof. Rushen Chahal



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LP AllocationProblem 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

Prof. Rushen Chahal



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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

Prof. Rushen Chahal



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Linear Programming Decision variables

Objective function

Objective function coefficients

Constraints

Capacities

Input-output (technology) coefficients

Line

Prof. Rushen Chahal



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Lindo LP Product-Mix ModelDSS in Focus 5.4

<< The Lindo Model: >>

MAX 8000 X1 + 12000 X2

SUBJECT TO

LABOR) 300 X1 + 500 X2 <= 200000

BUDGET) 10000 X1 + 15000 X2 <= 8000000

MARKET1) X1 >= 100

MARKET2) X2 >= 200

END

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<< Generated Solution Report >>

LP OPTIMUM FOUND AT STEP 3

OBJECTIVE FUNCTION VALUE

1) 5066667.00

VARIABLE VALUE REDUCED COST

X1 333.333300 .000000

X2 200.000000 .000000

Prof. Rushen Chahal



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ROW SLACK OR SURPLUS DUAL PRICES

LABOR) .000000 26.666670

BUDGET) 1666667.000000 .000000

MARKET1) 233.333300 .000000

MARKET2) .000000 -1333.333000

NO. ITERATIONS= 3

Prof. Rushen Chahal



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RANGES IN WHICH THE BASIS IS UNCHANGED:

OBJ COEFFICIENT RANGES

VARIABLE CURRENT ALLOWABLE ALLOWABLECOEF INCREASE DECREASE

X1 8000.000 INFINITY 799.9998

X2 12000.000 1333.333 INFINITY

RIGHTHAND SIDE RANGESROW CURRENT ALLOWABLE ALLOWABLE

RHS INCREASE DECREASE

LABOR 200000.000 50000.000 70000.000

BUDGET 8000000.000 INFINITY 1666667.000

MARKET1 100.000 233.333 INFINITYMARKET2 200.000 140.000 200.000

Prof. Rushen Chahal



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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)

Prof. Rushen Chahal



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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

Prof. Rushen Chahal



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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 measure8. Can incorporate intelligent search

9. Can solve very complex models

Prof. Rushen Chahal



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Limitations of Heuristics

1. Cannot guarantee an optimal solution

2. There may be too many exceptions

3. Sequential decisions might not anticipate futureconsequences

4. Interdependencies of subsystems can influence the whole

system

Heuristics successfully applied to vehicle routing

Prof. Rushen Chahal



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Simulation

Technique for conducting experiments with a

computer on a model of a management system

Frequently used DSS tool

Prof. Rushen Chahal



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Major Characteristics ofS

imulation

Imitates reality and capture its richness

Technique for conducting experiments

Descriptive, not normative tool

Often to solve very complex, risky problems

Prof. Rushen Chahal



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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)

Prof. Rushen Chahal



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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 (@Risk)

Prof. Rushen Chahal



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Limitations of Simulation

1. Cannot guarantee an optimal solution

2. Slow and costly construction process

3. Cannot transfer solutions and inferences to solve other

problems4. So easy to sell to managers, may miss analytical solutions

5. Software is not so user friendly

Prof. Rushen Chahal



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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

Prof. Rushen Chahal



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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

Prof. Rushen Chahal



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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

Prof. Rushen Chahal



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Entire Data Cube from a Query inPowerPlay (Figure 5.6a)

(Courtesy Cognos Inc.)

Prof. Rushen Chahal



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Graphical Display of the Screenin Figure 5.6a (Figure 5.6b)


Prof. Rushen Chahal



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Environmental Line of Products byDrilling Down (Figure 5.6c)


Prof. Rushen Chahal



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Drilled Deep into the Data: Current Month, WaterPurifiers, Only in North America (Figure 5.6d)


Prof. Rushen Chahal



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Visual Spreadsheets

User can visualize models and

formulas with influence diagrams

Not cells--symbolic elements

Prof. Rushen Chahal



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Visual Interactive Modeling ( VIS) and Visual Interactive Simulation ( VIS)

Visual interactive modeling (VIM) (DSS In Action 5.8)

Also called

Visual interactive problem solving

Visual interactive modeling Visual interactive simulation

Use computer graphics to present the impact of differentmanagement decisions.

Can integrate with GIS

Users perform sensitivity analysis

Static or a dynamic (animation) systems (Figure 5.7)

Prof. Rushen Chahal

Generated Image of Traffic at an Intersection



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Generated Image of Traffic at an Intersectionfrom the Orca Visual Simulation Environment

(Figure 5.7)(Courtesy Orca Computer, Inc.)

Prof. Rushen Chahal



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Visual Interactive Simulation( VIS)

Decision makers interact with the simulated

model and watch the results over time

Visual interactive models and DSS

VIM (Case Application W5.1 on book¶s Web site)

Queueing

Prof. Rushen Chahal



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Quantitative Software Packages-OLAP

Preprogrammed models can expedite DSS

programming time

Some models are building blocks of other models

Statistical packages

Management science packages

Revenue (yield) management

Other specific DSS applications

including spreadsheet add-ins

Prof. Rushen Chahal



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Model Base Management

MBMS: capabilities similar to that of DBMS

But, there are no comprehensive model base management

packages Each organization uses models somewhat differently

There are many model classes

Within each class there are different solution approaches

Some MBMS capabilities require expertise and reasoning

Prof. Rushen Chahal



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Desirable Capabilities ofMBMS

Control

Flexibility

Feedback

Interface

Redundancy reduction

Increased consistency

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MBMS Design Must Allowthe DSS User to:

1. Access and retrieve existing models.

2. Exercise and manipulate existing models

3. Store existing models

4. Maintain existing models

5. Construct new models with reasonable effort

Prof. Rushen Chahal



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Modeling languages

Relational MBMS

Object-oriented model base and its

management

Models for database and MIS design and their

management

Prof. Rushen Chahal



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SUMM ARY

Models play a major role in DSS

Models can be static or dynamic

Analysis is under assumed certainty, risk, oruncertainty

Influence diagrams

Spreadsheets

Decision tables and decision trees

Spreadsheet models and results in influence diagrams

Optimization: mathematical programming

(More)

Prof. Rushen Chahal



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Linear programming: economic-based

Heuristic programming

Simulation - more complex situations

Expert Choice

Multidimensional models - OLAP

(More)

Prof. Rushen Chahal



Quantitative software packages-OLAP (statistical, etc.)

Visual interactive modeling (VIM)

Visual interactive simulation (VIS) MBMS are like DBMS

AI techniques in MBMS

decision support systems -modeling and analysis

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