CHAPTER 5

Modeling and Analysis

Outline 5.1 Opening vignette 5.2 Modeling for MSS 5.3 Static and dynamic models 5.4 Treating certainty, uncertainty, and risk 5.5 Influence diagrams 5.6 MSS modeling in spreadsheets 5.7 Decision analysis of a few alternatives

(decision tables and trees) 5.8 Optimization via mathematical programming

5.1 Opening Vignette (p.166)

DuPont simulates rail transportation system and avoids costly capital expense

5.2 Modeling for MSS

Key element in most DSS

Necessity in a model-based DSS

Can lead to massive cost reduction / revenue increases

Major Modeling Issues

Problem identification Environmental analysis Variable identification Forecasting Multiple model use Model categories or selection (Table 5.1) Model management (Section 5.16) Knowledge-based modeling (Chapter 6)

5.3 Static and Dynamic Models

Static Analysis Single snapshot

Dynamic Analysis Dynamic models represent scenarios that change over

time Time-dependent Trends and patterns over time

5.4 Treating Certainty, Uncertainty, and Risk

Certainty Models Easy to develop and solve Yield optimal solution

Uncertainty Information unavailable

Risk The actual probabilities are known Estimate the risk

5.5 Influence Diagrams

Graphical representations of a model Visual communication 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)

5.5 Influence Diagrams

Considering the following profit model:

Profit= income-expenses

Income= units sold * unit price

Units sold= 0.5*amount used in ad

Expenses= unit cost * units sold+ fixed cost

5.5 Influence Diagrams

Representative software products Analytica DecisionPro DATA Decision Analysis Software Definitive Scenario PrecisionTree

5.6 MSS Modeling in Spreadsheets

Spreadsheet: most popular end-user modeling tool Powerful functions: financial, statistical,

mathematical, and other functions Add-in functions Important for analysis, planning, modeling

5.6 MSS Modeling in Spreadsheets

Other important feature: What-if analysis Goal seeking Data management Programmability(macro)

Microsoft Excel & Lotus1-2-3 Static and dynamic models can be built in a

spreadsheet(Figure 5.3, Figure 5.4)

5.6 MSS Modeling in Spreadsheets Excel spreadsheet static model example

5.6 MSS Modeling in Spreadsheets

Excel spreadsheet dynamic model example

5.7 Decision Analysis of Few Alternatives

(Decision Tables and Trees)

Finite and not too large number of alternatives

Single-goal situations

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

Decision Tables Possible Situations

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%

DecisionVariables

Treating Uncertainty

Optimistic approach Assume that the best possible outcome of each

alternative will occur and then selects the best of the best

Pessimistic approach Assume that the worst possible outcome for

each alternative will occur and selects the best one of those

Treating Risk

Risk analysis: Use known probabilities to compute expected values (Table 5.3)

Can be dangerous An infinitesimal chance of a catastrophic loss may

cause the expected value reasonable

12(0.5)+6(0.3)+3(0.2)=8.4

Decision Trees

Graphically show the relationship of the problem

Can handle complex situations in a compact form

Multiple Goals

A simplified investment case of multiple goals is shown in Table 5.4

Multicriteria decision-making software packages- Analytic Hierarchy Process(e.g., Expert Choice software) is a leading one

5.8 Optimization via Mathematical Programming

Linear programming (LP) Best-known technique in optimization 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

5.8 Optimization via Mathematical Programming

LP Allocation Problem Characteristics Limited quantity of economic resources Resources are used in the production of products or

services Two or more ways (solutions, programs) to use the

resources Each activity (product or service) yields a return in terms

of the goal Allocation is usually restricted by constraints

LP Allocation Model

Rational economic assumptions Returns from allocations can be compared in a common unit Independent returns Total return is the sum of different activities’ returns All data are known with certainty The resources are to be used in the most economical manner

Solutions can be infinite or finite Optimal solution: at least one best solution, found

algorithmically

Linear Programming

Components of LP problem Decision variables Objective function Objective function coefficients Constrains Capacities Input-output coefficients

Two best known modeling system: Lindo & Lingo

Lindo LP Product-Mix ModelDSS in Focus 5.4

The product-mix model described in Chapter 2 (p.61)

<< 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

Objective function

X1, X2: Decision variables

Constraints

Capacities

5.9 Heuristic Programming (1)

Determination of optimal solution could involve amount of time and cost in some complex decision problems.

Simulation approach may be lengthy, complex, inaccurate.

Therefore, by using heuristics we can arrive at satisfactory solutions more quickly and less expensively.

Heuristic Programming (2)

Finding rules that help to solve complex problems.

Finding ways to retrieve and interpret information on each experience.

Finding methods that lead to a computational algorithm or general solution.

Heuristic Programming (3)

Are used for solving ill-structured problems. Can be used to provide satisfactory to

certain complex well-structured problems More cheaply and quickly than optimization

algorithms But only for the specific situation. Heuristics may obtain a poor solution.

Heuristic Programming (4)

Heuristic programming： the approach of using heuristics to at feasible

and “good enough” solutions to complex problems

“good enough” = 90%-99.9% of the objective value of an optimal solution.

Can be quantitative or qualitative.

Methodology (1)

Searching Learning Evaluating Judging

Knowledge Knowledge

Methodology (2)

Tabu search “remember” high-quality and low-quality

solutions. Move toward to high-quality solutions, away

from low-quality solutions. Genetic algorithms

Start with a set of randomly solutions. Recombine pairs of solutions to produce

offspring.

When to use Heuristics Input data are inexact or limited. Reality is so complex that optimization models

can’t be used. Exact algorithm is not available. Can combine heuristics and optimization to

improve efficiency. Optimization or simulation are not economical, or

taking an amount of time. Symbolic processing is involved. Quick decisions, no computerization.

Advantages

Simple to understand. Training people to be creative. Save formulation time. Save computer programming and storage

requirement. Save computer running time. Produce multiple acceptable solutions. Develop a measure of the solution quality.

Limitations

Not always optimal solutions Too many exceptions to the rules Sequential decision choices can fail to

anticipate future consequences of each choices.

5.10 Simulation

To assume the appearance of the characteristics of reality.

A technique for conducting experiments with computer on a model of a management system.

Simulation is one of the most commonly used tools of DSS.

Major Characteristics

Simulation “imitates” reality. A technique for conducting experiments Simulation is a descriptive tool. Simulation is used only when a problem is

too complex to be treated by numerical optimization techniques.

Advantages of Simulation (1) Simulation theory is fairly straightforward. A great amount of time compression can be

attained. Simulation is descriptive rather than normative. An accurate simulation model requires an intimate

knowledge of the problem. The simulation model is built form the manager’s

perspective and decision structure. The simulation model is built for one particular

problem.

Advantages of Simulation (2) Simulation can handle an extremely wide variety

of problem types. The manager can experiment with different

variables and different alternatives. Allows for inclusion of the real-life complexities of

problem. It’s easy to obtain a wide variety of performance

measures. The only modeling tool for DSS where problems

can be non-structured.

Limitations of Simulation

An optimal solution can’t be guaranteed. Constructing a simulation model can often

be a slow and costly process. Solutions and inferences from a simulation

are not transferable to other problems. Simulation software is not so user-friendly.

The Methodology of Simulation (1)Real-World

problem

Problem definition

ConstructThe

Simulationmodel

Test andValidate

Themodel

Design theSimulation

experiments

Conduct theexperiments

EvaluateThe

results

ImplementThe

results

The Methodology of Simulation (2)

Problem definition The real-world problem is examined and

classified. Construction of the simulation model

Involves the determination of the variables and their relationships and gathering necessary data.

Testing and validating the model The simulation model must properly represent

the system.

The Methodology of Simulation (3)

Design of the experiments Two important and conflicting objectives ： accuracy

and cost.

Conducting the experiments Involves issues ranging from random number

generation to presentation of the results.

Evaluating the results Determine the meaning of the results.

Implement

Types of Simulation

Probabilistic simulation One or more of the variables are probabilistic. Discrete distribution or Continuous distribution.

Time-dependent versus Time-independent simulation

Simulation software (5.15) Visual Simulation (5.14) Object-Oriented Simulation

5.11 Multidimensional Modeling-OLAP

Managers need to work with three or more dimensions.

The solution is provided by multidimensional modeling tools.

Most multidimensional analysis systems are embedded in online analytical processing (OLAP) systems.

OLAP

The goal of OLAP is to capture the structure of real-world data and provide support to the decision maker.

OLAP reports are interactive reports that are highly formatted, easily deployed, and effortless to use.

Figure 5.6A, 5.6B, 5.6C, 5.6D

OLAP

Business intelligence tools – user simply access a data warehouse and direct the software to show the data in interesting ways and automatically build model.

5.12 Visual Interactive Modeling & Visual Interactive Simulation (1)

Conventional simulation： Simulation does not allow decision makers to

see how a solution evolves over time. Decision makers are not an integral part of

simulation development and experimentation If the results do not match the intuition or

judgment of the decision maker, a confidence gap occurs.

Visual Interactive Modeling & Visual Interactive Simulation (2)

One of the most exciting developments in computer graphics is visual interactive modeling (VIM).

VIM uses computer graphic displays to present the impact of different management decisions.

VIM can represent a static or a dynamic system.

Visual Interactive Modeling & Visual Interactive Simulation (3)

Visual Interactive Simulation Is one of the most exciting dynamic VIMs. VIS allows the end user to watch the progress

of the simulation model in a animated form. Basic philosophy of VIS is that decision makers

can interact with the simulated model and watch the results develop over time.

Visual Interactive Modeling & Visual Interactive Simulation (4)

VIMs and DSS VIM in DSS has used in several operations

management decisions. Waiting-line management (queuing) VIM approach can be used in conjunction with

artificial intelligence. General-purpose commercial dynamic VIM

software is readily available.

5.13 Quantitative Software Packages - OLAP

Some DSS tools offer several subroutines for constructing quantitative models. Statistics, financial analysis, accounting, and

management science. In addition, many DSS tools can easily

interface with powerful standard quantitative software packages.

Quantitative Software Packages

Statistical packages Typical functions ： mean, median, variance,

standard deviation, t-test, various types of regression correlations.

Excel, SPSS, Minitab, SAS. Now statistical software is considered a

decision-making tool. It’s embedded in data mining and OLAP tools.

Quantitative Software Packages

Management science packages There are several hundred management

science packages on the market for models ranging from inventory control to project management.

Quantitative Software Packages

Revenue management Involves models that attempt to stratify an

organization’s customers, estimate demands, establish prices for each category of customer, and dynamically model all.

Other specific DSS applications P.203

5.14 Model Base Management (1)

Model base management system (MBMS) is a software package with capabilities similar to DBMS.

There are no standardized MBMS： There are too many standard model classes. Each model class have several approaches for solving

problems, depending on problem. Each organization uses models differently MBMS capabilities require expertise and reasoning

capabilities.

Model Base Management (2)

Some desirable MBMS capabilities： Control Flexibility Feedback Interface Redundancy reduction Increased consistency

Model Base Management (3)

Modeling languages Some popular mathematical programming model

languages include Lingo, AMPL, and GAMS.

Relational model base management system Object-oriented model base and its management Models for database and MIS design and their

management