This document provides an introduction to operations research. It discusses the history and definitions of operations research, the modeling process, and common management science techniques used in operations research like linear programming, network models, inventory models, waiting line models, computer simulation, and multiple criteria decision making. Examples of operations research software are also listed.

1. Operations Research
4EK601

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

15. Operations Research - Introduction
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Operations Research  Jan Fábry
Management Science Techniques
 network – nodes, arcs
 evaluated network
 minimal distance, maximal flow etc.
 planning, scheduling & controlling projects
 CPM, PERT
 Network Models
 Project Management

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