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Operations Research 4EK601
4EK601 - Operations Research Jan Fábry 434 NB [email protected]
http://nb.vse.cz/~fabry http://isis.vse.cz
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4EK601 - Operations Research Literature Jan Fábry - Management Science. UEP, October 2003.
Content Presentations: http:// nb.vse.cz/~fabry 1.
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Introduction Linear Programming Network Models Inventory Models 5.
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Waiting Line Models Computer Simulation 7.
Multiple Criteria Decision Making
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Operations Research - Introduction Operations Research = Management Science Alternative Names
operational research operations analysis quantitative analysis quantitative methods systems analysis decision analysis decision science History of OR/MS
World War II End of the 20 th Century
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Operations Research - Introduction Software
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 - Introduction 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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Operations Research - Introduction Definition - summary
Application of SCIENTIFIC METHOD
Study of LARGE & COMPLEX SYSTEMS
Analysis of MANAGERIAL PROBLEMS
Finding OPTIMAL SOLUTION
Use of MATHEMATICAL MODELS
Use of COMPUTERS & SPECIAL SW
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Operations Research - Introduction Real-World Problem Modeling Process Recognition and Definition of the Problem Formulation and Construction of the Mathematical Model Implementation Interpretation Validation and Sensitivity Analysis of the Model Solution of the Model
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Operations Research - Introduction Recognition & Definition of the Problem
Processes Restrictions Goal Mathematical Model
Variables Constraints (equations, inequalities) Objective function
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Operations Research - Introduction Mathematical Model Reality
Finding a proper balance between the level of simplification of reality and good representation of reality.
Model
Deterministic Probabilistic Model
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Operations Research - Introduction Solution
Feasible Optimal Infeasible Model Interpretation Model Validation Sensitivity Analysis Implementation
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Operations Research - Introduction 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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Operations Research - Introduction Management Science Techniques
Distribution Models
special type of LP problems (special structure of model)
transportation problem
assignment problem
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Operations Research - Introduction Management Science Techniques
Multiple Criteria Decision Making
multiple criteria
compromise
limited/unlimited number of alternatives
goal programming
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Operations Research - Introduction Management Science Techniques
Network Models
network – nodes, arcs
evaluated network
minimal distance, maximal flow etc.
Project Management
planning, scheduling & controlling projects
CPM, PERT
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Operations Research - Introduction Management Science Techniques
Inventory Models
how much to order?
when to order?
deterministic/probabilistic models
Waiting Line Models (Queuing Models)
servers, customers
goal – optimal number of servers
analytical approach, computer simulation
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Operations Research - Introduction Management Science Techniques
Computer
computer experiments with models
complex systems
Games Theory
2 or more decision makers
possible strategies
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