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Chapter 4

MODELING AND

ANALYSIS


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Learni ng Obj ectiv es Understand the basic concepts of

management support system (MSS)modeling

Describe how MSS models interact withdata and the user

Understand some different, well-known

model classes Understand how to structure decisionmaking with a few alternatives


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Learni ng Obj ectiv es Describe how spreadsheets can be used

for MSS modeling and solution

Explain the basic concepts of

optimization, simulation, and heuristics,

and when to use them

Describe how to structure a linear

programming model


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Learni ng Obj ectiv es Understand how search methods are used

to solve MSS models

Explain the differences among algorithms,

blind search, and heuristics

Describe how to handle multiple goals

Explain what is meant by sensitivity

analysis, what-if analysis, and goal seeking

Describe the key issues of model

management


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MSS Model ing Lessons from modeling at DuPont

By accurately modelingand simulatingits rail

transportation system, decision makers were

able to experiment with different policies andalternatives quickly and inexpensively

The simulation model was developed and

tested known alternative solutions


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MSS Model ing Lessons from modeling for Procter & Gamble

DSS can be composed of several models used

collectively to support strategic decisions in the

company

Models must be integrated

models may be decomposed and simplified

A suboptimization approach may be appropriate

Human judgment is an important aspect of usingmodels in decision making


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MSS Model ing Lessons from additional modeling

applications

Mathematical (quantitative) model

A system of symbols and expressions that

represent a real situation

Applying models to real-world situations can

save millions of dollars or generate millionsof dollars in revenue


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MSS Model ing Current modeling issues

Identification of the problem and

environmental analysis

Environmental scanning and analysis

A process that involves conducting a search

for and an analysis of information in external

databases and flows of information


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Variable identification

Forecasting

Predicting the future

Predictive analytics systems attempt to

predict the most profitable customers, the

worst customers, and focus on identifyingproducts and services at appropriate prices

to appeal to them


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Multiple models: A DSS can include several models,

each of which represents a different part of the

decision-making problem

Model categories

Optimization of problems with few alternatives

Optimization via algorithm

Optimization via an analytic formula

Simulation

Predictive models

Other models


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Model management

Knowledge-based modeling

Current trends

Model libraries and solution technique libraries

Development and use of Web tools

Multidimensional analysis (modeling)A modeling method that involves data analysis in

several dimensions


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MSS Model ing Current trends

Multidimensional analysis (modeling)

A modeling method that involves data

analysis in several dimensions

Influence diagram

A diagram that shows the various types of

variables in a problem (e.g., decision,independent, result) and how they are

related to each other


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Stati c a nd Dynami cModel s Static models

Models that describe a single interval of a

situation

Dynamic models

Models whose input data are changed

over time (e.g., a five-year profit or loss

projection)


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Cert ai nty,Uncertai nty, and Ri sk


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Cert ain ty,Uncertai nty, and Ri sk Certainty

A condition under which it is assumed that future

values are known for sure and only one result is

associated with an action Uncertainty

In expert systems, a value that cannot be

determined during a consultation. Many expert

systems can accommodate uncertainty; that is,

they allow the user to indicate whether he or she

does not know the answer


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Cert ain ty,Uncertai nty, and Ri sk Risk

A probabilistic or stochastic decision

situation

Risk analysis

A decision-making method that analyzes

the risk (based on assumed known

probabilities) associated with different

alternatives. Also known as calculated risk


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MSS Model ingwith Spreadsheets Models can be developed and

implemented in a variety of programming

languages and systems

The spreadsheet is clearly the most

popularend-user modeling toolbecause it

incorporates many powerful financial,

statistical, mathematical, and otherfunctions


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MSS Model ingwith Spreadsheets


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MSS Model ingwith Spreadsheets Other important spreadsheet features include

what-if analysis, goal seeking, data

management, and programmability

Most spreadsheet packages provide fairlyseamless integration because they read and

write common file structures and easily

interface with databases and other tools

Static or dynamic models can be built in aspreadsheet


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MSS Model ingwith Spreadsheets


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Deci sion Ana lysi s wi thDeci sion Tab les and Deci sionTrees Decision analysis

Methods for determining the solution to a

problem, typically when it is inappropriate

to use iterative algorithms


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Deci sion Ana lysi s wi thDeci sion Tab les and Deci sionTrees Decision table

A table used to represent knowledge and

prepare it for analysis in:

Treating uncertainty

Treating risk


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Deci sion Ana lysi s wi thDeci sion Tab les and Deci sionTrees Decision tree

A graphical presentation of a sequence of

interrelated decisions to be made under

assumed risk

Multiple goals

Refers to a decision situation in which

alternatives are evaluated with several,

sometimes conflicting, goals


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The S tructu re ofMathematical M odels forDecision S upport


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The S tructu re ofMathematical M odels forDecision S upport Components of decision support mathematical

models

Result (outcome) variable

A variable that expresses the result of a decision (e.g.,one concerning profit), usually one of the goals of a

decision-making problem

Decision variable

A variable of a model that can be changed andmanipulated by a decision maker. The decision

variables correspond to the decisions to be made,

such as quantity to produce and amounts of resources

to allocate


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The S tructu re ofMathematical M odels forDecision S upport Uncontrollable variable (parameter)

A factor that affects the result of a decision but

is not under the control of the decision maker.

These variables can be internal (e.g., relatedto technology or to policies) or external (e.g.,

related to legal issues or to climate)

Intermediate result variable

A variable that contains the values of

intermediate outcomes in mathematical

models


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Math emati calProgrammi ngOpti mi za tio n Mathematical programming

A family of tools designed to help solve

managerial problems in which the decision

maker must allocate scarce resourcesamong competing activities to optimize a

measurable goal

Optimal solution

A best possible solution to a modeled

problem


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Math emati calProgrammi ngOpti mi za tio n Linear programming (LP)

A mathematical model for the optimal

solution of resource allocation problems.

All the relationships among the variables inthis type of model are linear


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Math emati calProgrammi ngOpti mi za tio n Every LP problem is composed of:

Decision variables

Objective function

Objective function coefficients

Constraints

Capacities

Input/output (technology) coefficients


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Math emati calProgrammi ngOpti mi za tio n


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Math emati calProgrammi ngOpti mi za tio n


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u p e oa s, ens v yAnal ysi s,What- If Anal ysi s, an d G oalSeeki ng Multiple goals

Refers to a decision situation in which

alternatives are evaluated with several,

sometimes conflicting, goals

Sensitivity analysis

A study of the effect of a change in one or

more input variables on a proposed

solution


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u p e oa s, ens v yAnal ysi s,What- If Anal ysi s, an d G oalSeeki ng Sensitivity analysis tests relationships such as:

The impact of changes in external (uncontrollable)

variables and parameters on the outcome

variable(s)

The impact of changes in decision variables on the

outcome variable(s)

The effect of uncertainty in estimating external

variables

The effects of different dependent interactions

among variables

The robustness of decisions under changing

conditions


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u p e oa s, ens v yAnal ysi s,What- If Anal ysi s, an d G oalSeeki ng Sensitivity analyses are used for:

Revising models to eliminate too-large sensitivities

Adding details about sensitive variables or scenarios

Obtaining better estimates of sensitive externalvariables

Altering a real-world system to reduce actual

sensitivities

Accepting and using the sensitive (and hencevulnerable) real world, leading to the continuous and

close monitoring of actual results

The two types of sensitivity analyses are

automatic and trial-and-error


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u p e oa s, ens v yAnal ysi s,What- If Anal ysi s, an d G oalSeeki ng Automatic sensitivity analysis

Automatic sensitivity analysis is performed in

standard quantitative model implementations

such as LP Trial-and-error sensitivity analysis

The impact of changes in any variable, or in

several variables, can be determined througha simple trial-and-error approach


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u p e oa s, ens v yAnal ysi s,What- If Anal ysi s, an d GoalSeeki ng


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u p e oa s, ens v yAnal ysi s,What- If Anal ysi s, an d G oalSeeki ng Goal seeking

Asking a computer what values certain

variables must have in order to attain

desired goals


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u p e oa s, ens v yAnal ysi s,What- If Anal ysi s, an d GoalSeeki ng


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u p e oa s, ens v yAnal ysi s,What- If Anal ysi s, an d G oalSeeki ng Computing a break-even point by using

goal seeking

Involves determining the value of the decision

variables that generate zero profit


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Problem-Solving SearchMethods


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Problem-Solving SearchMethods Analytical techniques use mathematical

formulas to derive an optimal solution

directly or to predict a certain result

An algorithm is a step-by-step searchprocess for obtaining an optimal solution


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Problem-Solving SearchMethods


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Problem-Solving SearchMethods A goalis a description of a desired solution

to a problem

The search steps are a set of possible

steps leading from initial conditions to thegoal

Problem solving is done by searching

through the possible solutions


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Problem-Solving SearchMethods Blind search techniques are arbitrary

search approaches that are not guided

In a complete enumeration all the alternatives

are considered and therefore an optimalsolution is discovered

In an incomplete enumeration (partial search)

continues until a good-enough solution is

found (a form of suboptimization)


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Problem-Solving SearchMethods Heuristic searching

Heuristics

Informal, judgmental knowledge of an

application area that constitutes the rules ofgood judgment in the field. Heuristics alsoencompasses the knowledge of how to solveproblems efficiently and effectively, how toplan steps in solving a complex problem, howto improve performance, and so forth

Heuristic programming

The use of heuristics in problem solving


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Simu lati on Simulation

An imitation of reality

Major characteristics of simulation

Simulation is a technique forconducting

experiments

Simulation is a descriptive rather than a

normative method Simulation is normally used only when a

problem is too complex to be treated using

numerical optimization techniques


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Simu lati on Complexity

A measure of how difficult a problem is in

terms of its formulation for optimization, its

required optimization effort, or its stochasticnature


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Simu lati on Advantages of simulation The theory is fairly straightforward.

A great amount oftime compression can beattained

A manager can experiment with differentalternatives The MSS builder must constantly interact with

the manager

The model is built from the managersperspective. The simulation model is built for one particular

problem


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Simu lati on Advantages of simulation

Simulation can handle an extremely wide variety

of problem types

Simulation can include the real complexities ofproblems

Simulation automatically produces many

important performance measures

Simulation can readily handle relatively

unstructured problems

There are easy-to-use simulation packages


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Simu lati on Disadvantages of simulation

An optimal solution cannot be guaranteed

Simulation model construction can be a slow andcostly process

Solutions and inferences from a simulation studyare usually not transferable to other problems

Simulation is sometimes so easy to explain to

managers that analytic methods are oftenoverlooked

Simulation software sometimes requires specialskills


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Simu lati on


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Simu lati on Methodology of simulation

1. Define the problem

2. Construct the simulation model

3. Test and validate the model4. Design the experiment

5. Conduct the experiment

6. Evaluate the results7. Implement the results


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Simu lati on Simulation types

Probabilistic simulation

Discrete distributions

Continuous distributions

Time-dependent versus time-independent

simulation

Object-oriented simulation

Visual simulation

Simulation software


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Vi sual Interacti veSimu lati on Conventional simulation inadequacies

Simulation reports statistical results at the end

of a set of experiments

Decision makers are not an integral part ofsimulation development and experimentation

Decision makers experience and judgment

cannot be used directly

Confidence gap occurs if the simulation results

do not match the intuition or judgment of the

decision maker


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Vi sual Interacti veSimu lati on Visual interactive simulation orvisual

interactive modeling (VIM)

A simulation approach used in the decision-

making process that shows graphicalanimation in which systems and processes

are presented dynamically to the decision

maker. It enables visualization of theresults of different potential actions


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Vi sual Interacti veSimu lati on Visual Interactive models and DSS

Waiting-line management (queuing) is a good

example of VIM

The VIM approach can also be used inconjunction with artificial intelligence

General-purpose commercial dynamic VIS

software is readily available

Quantit ativ e S oftw are


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Packages and Mo del BaseManagement Quantitative software packages

A preprogrammed (sometimes called

ready-made) model or optimization system.

These packages sometimes serve asbuilding blocks for other quantitative

models

Quantit ativ e S oftw are


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Packages and Mo del BaseManagement Model base management

Model base management system (MBMS)

Software for establishing, updating, combining, and soon (e.g., managing) a DSS model base

Relational model base management system(RMBMS)

A relational approach (as in relational databases) to thedesign and development of a model base management

system Object-oriented model base management system(OOMBMS)

An MBMS constructed in an object-orientedenvironment

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CH04 withFigures