Lecture 1 (1).ppt

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

4EK601 - Operations Research
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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

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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History of OR/MS
 World War II
 End of the 20th Century

 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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Software

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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.

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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

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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

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Recognition & Definition of the Problem
 Processes
 Restrictions
 Goal
Mathematical Model
 Variables
 Constraints (equations, inequalities)
 Objective function

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Mathematical Model
Finding a proper balance between the
level of simplification of reality and
good representation of reality.
Reality Model
Model
 Deterministic
 Probabilistic

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Solution
 Infeasible
 Feasible
 Optimal
Model Interpretation
Sensitivity Analysis
Implementation
Model Validation

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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

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 special type of LP problems
(special structure of model)
 transportation problem
 assignment problem
 Distribution Models

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 multiple criteria
 compromise
 limited/unlimited number of alternatives
 goal programming
 Multiple Criteria Decision Making

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 network – nodes, arcs
 evaluated network
 minimal distance, maximal flow etc.
 planning, scheduling & controlling projects
 CPM, PERT
 Network Models
 Project Management

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 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)

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 computer experiments with models
 complex systems
 Computer Simulation
 2 or more decision makers
 possible strategies
 Games Theory

Lecture 1 (1).ppt

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