CHAPTER 5

Modeling and Analysis

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

Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th editionCopyright 2001, Prentice Hall, Upper Saddle River, NJ

Structure of some successful models and methodologies– Decision analysis– Decision trees– Optimization– Heuristic programming – Simulation

New developments in modeling tools / techniques

Important issues in model base management

Modeling and Analysis

Modeling and Analysis 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 management

Modeling for MSS

Key element in most DSS

Necessity in a model-based DSS

Can lead to massive cost reduction / revenue increases

Good Examples of MSS Models

DuPont rail system simulation model (opening vignette)

Procter & Gamble optimization supply chain restructuring 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)

Major Modeling Issues

Problem identification Environmental analysis Variable identification Forecasting Multiple model use Model categories or selection (Table 5.1) Model management Knowledge-based modeling

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

Treating Certainty, Uncertainty, and Risk

Certainty Models

Uncertainty

Risk

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)

FIGURE 5.1 An Influence Diagram for the Profit Model.

~Amount used in advertisement

Profit

Income

Expense

Unit Price

Units Sold

Unit Cost

Fixed Cost

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

(Courtesy of Lumina Decision Systems, Los Altos, CA)

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

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

MSS Modeling in Spreadsheets

Spreadsheet: most popular end-user modeling tool Powerful functions Add-in functions and solvers Important for analysis, planning, modeling Programmability (macros)

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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 and effects of prepayment (Figure 5.4)

Decision Analysis of Few Alternatives

(Decision Tables and Trees)

Single Goal Situations

Decision tables

Decision trees

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

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

View Problem as a Two-Person GamePayoff Table 5.2

Decision variables (alternatives)

Uncontrollable variables (states of economy)

Result variables (projected yield)

Table 5.2: Investment Problem Decision 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%

Treating Uncertainty

Optimistic approach

Pessimistic approach

Treating Risk

Use known probabilities (Table 5.3)

Risk analysis: compute expected values

Can be dangerous

Table 5.3: Decision Under Risk and Its Solution

Solid Stagnation Inflation ExpectedGrowth 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%

Decision Trees

Other methods of treating risk– Simulation– Certainty factors– Fuzzy logic

Multiple goals

Yield, safety, and liquidity (Table 5.4)

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

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

Optimization via Mathematical 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

LP Allocation 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

LP Allocation Model

Rational economic assumptions1. 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

Linear Programming

Decision variables Objective function Objective function coefficients Constraints Capacities Input-output (technology) coefficients

Line

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

<< 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

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

RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGESVARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 8000.000 INFINITY 799.9998 X2 12000.000 1333.333 INFINITY

RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE LABOR 200000.000 50000.000 70000.000 BUDGET 8000000.000 INFINITY 1666667.000MARKET1 100.000 233.333 INFINITYMARKET2 200.000 140.000 200.000

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)

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

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 measure

8. Can incorporate intelligent search

9. Can solve very complex models

Limitations of Heuristics

1. Cannot guarantee an optimal solution

2. There may be too many exceptions

3. Sequential decisions might not anticipate future consequences

4. Interdependencies of subsystems can influence the whole system

Heuristics successfully applied to vehicle routing

Simulation

Technique for conducting experiments with a computer on a model of a management system

Frequently used DSS tool

Major Characteristics of Simulation

Imitates reality and capture its richness

Technique for conducting experiments

Descriptive, not normative tool

Often to solve very complex, risky problems

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

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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)

Limitations of Simulation

1. Cannot guarantee an optimal solution

2. Slow and costly construction process

3. Cannot transfer solutions and inferences to solve other problems

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

5. Software is not so user friendly

Simulation Methodology

Model real system and conduct repetitive experiments1. Define problem

2. Construct simulation model

3. Test and validate model

4. Design experiments

5. Conduct experiments

6. Evaluate results

7. Implement solution

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

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

Entire Data Cube from a Query in PowerPlay (Figure 5.6a)(Courtesy Cognos Inc.)

Graphical Display of the Screen in Figure 5.6a (Figure 5.6b)

(Courtesy Cognos Inc.)

Environmental Line of Products by Drilling Down (Figure 5.6c)

(Courtesy Cognos Inc.)

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

(Courtesy Cognos Inc.)

Visual Spreadsheets

User can visualize models and formulas with influence diagrams

Not cells--symbolic elements

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 different management decisions.

Can integrate with GIS Users perform sensitivity analysis Static or a dynamic (animation) systems (Figure 5.7)

Generated Image of Traffic at an Intersection from the Orca Visual Simulation Environment (Figure 5.7)

(Courtesy Orca Computer, Inc.)

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

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

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

Desirable Capabilities of MBMS

Control Flexibility Feedback Interface Redundancy reduction Increased consistency

MBMS Design Must Allow the 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

Modeling languages Relational MBMS Object-oriented model base and its management Models for database and MIS design and their

management

SUMMARY

Models play a major role in DSS Models can be static or dynamic Analysis is under assumed certainty, risk, or

uncertainty– Influence diagrams– Spreadsheets– Decision tables and decision trees

Spreadsheet models and results in influence diagrams Optimization: mathematical programming

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Linear programming: economic-based Heuristic programming Simulation - more complex situations Expert Choice Multidimensional models - OLAP

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Quantitative software packages-OLAP (statistical, etc.) Visual interactive modeling (VIM) Visual interactive simulation (VIS) MBMS are like DBMS AI techniques in MBMS