2. 4EK601 - Operations Research
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Operations Research Jan Fábry
http://nb.vse.cz/~fabry
fabry@vse.cz
Jan Fábry
434 NB
http://isis.vse.cz
3. 4EK601 - Operations Research
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Operations Research Jan Fábry
Content
1. Introduction
2. Linear Programming
3. Network Models
4. Inventory Models
5. Waiting Line Models
6. Computer Simulation
7. Multiple Criteria Decision Making
Literature
Jan Fábry - Management Science. UEP,
October 2003.
Presentations: http://nb.vse.cz/~fabry
4. Operations Research - Introduction
Operations Research = Management Science
Alternative Names
operational research
operations analysis
quantitative analysis
quantitative methods
systems analysis
decision analysis
decision science
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Operations Research Jan Fábry
History of OR/MS
World War II
End of the 20th Century
5. Operations Research - Introduction
Lingo (LINDO)
MPL for Windows
XPRESS (FICO)
CPLEX (IBM ILOG)
AIMMS
AMPL
Gurobi
NEOS
MS Excel (FRONTLINE SOLVERS)
SIMPROCESS
SIMUL 8
Matlab
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Operations Research Jan Fábry
Software
6. Operations Research - Introduction
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Operations Research Jan Fábry
Definition
1. MS/OR is the application of scientific methods, techniques
and tools to problems involving the operations of systems so
as to provide those in control of the operations with
optimum solutions to the problems.
2. MS/OR is the application of the scientific method to the
study of the operations of large, complex organizations or
activities.
3. MS/OR is the application of the scientific method to the
analysis and solution of managerial decision problems.
7. Operations Research - Introduction
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Operations Research Jan Fábry
Definition - summary
Application of SCIENTIFIC METHOD
Analysis of MANAGERIAL PROBLEMS
Study of LARGE & COMPLEX SYSTEMS
Finding OPTIMAL SOLUTION
Use of MATHEMATICAL MODELS
Use of COMPUTERS & SPECIAL SW
8. Operations Research - Introduction
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Operations Research Jan Fábry
Modeling Process
Real-World
Problem
Recognition and
Definition of the
Problem
Formulation and
Construction of the
Mathematical
Model
Solution
of the Model
Interpretation
Validation and
Sensitivity Analysis
of the Model
Implementation
9. Operations Research - Introduction
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Operations Research Jan Fábry
Recognition & Definition of the Problem
Processes
Restrictions
Goal
Mathematical Model
Variables
Constraints (equations, inequalities)
Objective function
10. Operations Research - Introduction
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Operations Research Jan Fábry
Mathematical Model
Finding a proper balance between the
level of simplification of reality and
good representation of reality.
Reality Model
Model
Deterministic
Probabilistic
11. Operations Research - Introduction
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Operations Research Jan Fábry
Solution
Infeasible
Feasible
Optimal
Model Interpretation
Sensitivity Analysis
Implementation
Model Validation
12. Operations Research - Introduction
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Operations Research Jan Fábry
Management Science Techniques
Linear Programming
linear objective function – min/max
linear constraints
Integer LP, Binary LP, Mixed Integer LP
Nonlinear Programming
nonlinear objective function
and/or
nonlinear constraints
13. Operations Research - Introduction
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Operations Research Jan Fábry
Management Science Techniques
special type of LP problems
(special structure of model)
transportation problem
assignment problem
Distribution Models
14. Operations Research - Introduction
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Operations Research Jan Fábry
Management Science Techniques
multiple criteria
compromise
limited/unlimited number of alternatives
goal programming
Multiple Criteria Decision Making
16. Operations Research - Introduction
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Operations Research Jan Fábry
Management Science Techniques
how much to order?
when to order?
deterministic/probabilistic models
servers, customers
goal – optimal number of servers
analytical approach, computer simulation
Inventory Models
Waiting Line Models (Queuing Models)
17. Operations Research - Introduction
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Operations Research Jan Fábry
Management Science Techniques
computer experiments with models
complex systems
Computer Simulation
2 or more decision makers
possible strategies
Games Theory