CHAPTER 5 Modeling and Analysis. Outline 5.1 Opening vignette 5.2 Modeling for MSS 5.3 Static and...
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Transcript of CHAPTER 5 Modeling and Analysis. Outline 5.1 Opening vignette 5.2 Modeling for MSS 5.3 Static and...
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