| Mathematical Methods (4th IIND, year 2008-09) |
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News
Operations Research (the
science of better):
Discipline that applies advanced analytical methods
to take decisions to improve operations of a company.
 , Learn About O.R., The
Executive Guide to Operational Research, Operational
Research and EURO
Life itself is a matter of OR
The current table reflects in a realistic
way the course development during the several sessions.
It allows the student to know in advance what is going
to happen in each session in order to prepare the
subject and to organize its work adequately.
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Date
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Theory
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Readings
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Problems
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Practice
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Sep 29, 08
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Comments
about the syllabus.
Additional
bibliography.
Hand out of class notes
and web page for slides.
Survey (motivation, expectations, difficulty, etc.) |
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M. Bolaños Confidencias
de un headhunter Anales de Mecánica y Electricidad
(LXXXII) II: 38-40 Mar-Abr 2005
FAQs About O.R. & Analytics
J.R. Alonso Una
Universidad nueva El País 12/01/2009
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Sep 29, 08
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LECTURE NOTES
about Optimization mathematical modeling.
INTRODUCTION
TO OPTIMIZATION AND MODELING. OR definition.
Historical introduction.
Optimization definition. Classification of optimization
methods.
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Operations
Research Time Line
J.K. Delson and S.M. Shahidehpour Linear
Programming Applications to Power System Economics,
Planning and Operations IEEE Transactions on
Power Systems (7) 3: 1155-1163 Aug 1992
J. Board, Ch. Sutcliffe and W.T. Ziemba Applying
Operations Research Techniques to Financial Markets
Interfaces Vol 33. No. 2 pp. 12-24 Mar-Apr 2003
H.E. Romeijn et al. A New Linear Programming
Approach to Radiation Therapy Treatment Planning Problems
Operations Research (54) 2: 201-216 Mar-Apr 2006
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Oct 1, 08
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COURSE OPENNING |
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Oct 2, 08
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Model and modeling. Steps in developing a model.
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Th. A. Grossman The
Spreadsheet Analytic Value Chain OR/MS Today Aug
2006 |
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Diet problem. Appliance transportation. |
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Oct 6, 08
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LINEAR
PROGRAMMING MODELING. Transportation problem.
Transhipment problem. Task assignment problem. |
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Oct 6, 08
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MODELING
IN INTEGER LINEAR PROGRAMMING. Knapsack problem.
Set covering problem. Packing problem. Partition problem. |
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Crew assignment.
Problem set # 1 (Production
of three products, Muffins. Job shop. Charter Flights.
Paper roll cut. Car renting. Swimming pools. Connecting
two pipelines. Sequencing five tasks. Exams. Data bases.
Noel lunch.) |
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Oct 8, 08
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Travelling salesman problem
(TSP). |
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Work orders scheduling. Muffins.
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Art
with the travelling salesman problem. |
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Oct 9, 08
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Production of three products.
Job shop.
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Oct 13, 08
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Fixed cost problem. |
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Thermal unit commitment. Charter
flights. |
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Oct 13, 08
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Disjunctive constraints.
Satisfy k of N equations. Selection among N values. Simple
implications. |
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Selecting a basketball team. |
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Oct 15, 08
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Equivalences among logical
propositions. Complex logical propositions. |
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Oct 16, 08
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Paper roll cut. |
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Oct 20, 08
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Car renting. |
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Oct 20, 08
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Swimming pools. |
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Oct 22, 08
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Connecting two pipelines.
Exams. |
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Oct 23, 08
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Sequencing five tasks. |
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Oct 27, 08
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Sequencing five tasks.
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Algebraic
modeling languages.
Transportation problem: mathematical formulation and writing
in GAMS. |
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Oct 27, 08
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Execution and analysis
of the results. |
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Oct 29, 08
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Solution of problem set #
1 (Production
of three products, Muffins. Job shop. Charter Flights.
Paper roll cut. Car renting. Swimming pools. Connecting
two pipelines. Sequencing five tasks. Exams.
Data bases. Noel lunch.)
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Load flow.
Teamwork.
Assignment of optimization
practices with GAMS.
NEOS
Server for Optimization |
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Oct 30, 08
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LECTURE NOTES
about Linear Optimization.
LINEAR
PROGRAMMING.
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Mathematical
Programming Glossary |
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Nov 3, 08
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Hypothesis. Geometry.
Properties. Simplex algorithm. Graphical solution. Standard
form. |
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Nov 3, 08
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Algebraic solution. |
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George
B. Dantzig, the father of linear programming
R.W. Cottle George
B. Dantzig: A Legendary Life in Mathematical Programming
Mathematical Programming (105) 1: 1-8 Jan 2006
R.W. Cottle George
B. Dantzig: Operations Research Icon Operations
Research (53) 6: 892-898 Nov-Dec 2005
J.C. Nash The
(Dantzig) Simplex Method for Linear Programming
Computing in Science & Engineering (2) 1: 29-31 Jan-Feb
2000
R.E. Bixby Solving
Real-World Linear Programs: a Decade and More of Progress
Operations Research (50) 1: 3-15 Jan-Feb 2002 |
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Nov 5, 08
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Multiple optima. |
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Nov 6, 08
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Degeneracy. Characterizing
the solutions. |
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PHPSimplex |
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Nov 10, 08
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Tabular form. |
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Nov 10, 08
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Tabular form. |
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Nov 12, 08
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Product of binary variables. |
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Data bases. |
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Nov 13, 08
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Problem set (1,
2, 3, 8, 9, 24, 22) |
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Nov 19, 08
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MIDTERM EXAM |
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Nov 24, 08
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Solution
of the midterm exam |
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Nov 24, 08
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Obtaining an initial basic feasible
solution: two phase method.
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Nov 26, 08
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DUALITY. Dual problem. |
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Nov 27, 08
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Fundamental properties
of duality. Economical interpretation. Graphical interpretation
of dual variables and of reduced costs. |
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Practical
case report.
Hand in of optimization practical cases with GAMS.
Questions about the modeling difficulties and GAMS practical
case and spent time. |
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Dec 3, 08
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Sensitivity analysis.
Changes in constraint bounds.
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Solution problem set (1,
2, 3, 8, 9, 24, 22)
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Dec 3, 08
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Change in a coefficient
of a non basic variable. Introduction of a new variable.
Change in a coefficient of a basic variable. Introduction
of a new constraint. |
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Dec 4, 08
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Dual simplex method. |
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Dec 10, 08
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LECTURE NOTES
about Mixed integer linear programming.
INTEGER
LINEAR PROGRAMMING. Example case.
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R.E. Gomory Early Integer Programming
Operations Research (50) 1: 78-81 Jan-Feb 2002 |
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Dec 11, 08
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Branch and bound method. |
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Problem set (2,
4) |
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Dec 11, 08
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Survey about modeling.
Presentation
of optimization practical cases. |
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Dec 15, 09
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Presentation of optimization practical cases.
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Dec 15, 09
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Presentation of optimization
practical cases. |
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Dec 17, 09
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Presentation of optimization
practical cases. |
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Dec 18, 09
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Presentation of optimization
practical cases. |
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Jan 9, 09
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LECTURE NOTES
about Dynamic programming.
DETERMINISTIC
DYNAMIC PROGRAMMING. (By stages and with finite
horizon)
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Presentation of optimization practical cases. |
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Jan 12, 09
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Problem set (Exámenes,
Tour de los Paradores, Procesamiento paralelo, Radios,
Campos y tablas, Asignación de generadores, Fiabilidad
de tres componentes) |
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Jan 12, 09
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Solution problem set (Exámenes,
Tour de los Paradores, Procesamiento paralelo, Radios,
Campos y tablas, Asignación de generadores, Fiabilidad
de tres componentes) |
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Jan 14, 09
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Task sequencing in one machine.
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Jan 15, 09
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Problem 5, 6 and 7.
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Comments about GAMS practical cases. |
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Jan 16, 09
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LECTURE NOTES
about Nonlinear optimization.
Modeling NLP.
NONLINEAR
PROGRAMMING. Introduction. Problems without
constraints: optimality conditions.
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H.W. Kuhn Being in the Right Place at
the Right Time Operations Research (50) 1: 132-134
Jan-Febr 2002
Entrevista
a Mar Hershenson Anales de Mecánica y Electricidad
(LXXXII) II: 3-10 Mar-Abr 2005 |
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Jan 19, 09
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Problems with constraints:
optimality conditions. |
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Jan 19, 09
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Necessary and sufficient
Karush-Kuhn-Tucker conditions. |
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Jan 22, 09
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Problem set (Inventarios,
Función cúbica con hiperplanos, Chequeo
de puntos, Objetivo lineal, Problema 2, 3, 4A, 4B, 4C,
Triatlón, Función cúbica, Ciencias
de la complejidad) |
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Feb 26, 09
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Solution problem set (Inventarios,
Función cúbica con hiperplanos, Chequeo
de puntos, Objetivo lineal, Problema 2, 3, 4A, 4B, 4C,
Triatlón, Función cúbica, Ciencias
de la complejidad)
Problems 1, 2, 6 and 8. |
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Jan 26, 09
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Production VI.
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Jan 28, 09
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Production VI. |
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Jan 29, 09
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Distributing company. |
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Feb 6, 08
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TERM EXAM |
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Feb 23, 09
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Solution
of the term exam |
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Feb 23, 09
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Solution
of the term exam |
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Feb 25, 09
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LECTURE NOTES
about Decision theory.
DECISION
THEORY.
Decision criteria. Example.
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G.M. Fernández and M.C. Escribano La Teoría de la Decisión: desde sus orígenes
hasta comienzos del siglo XIX Boletín de
Estadística e Investigación Operativa
(30) 3: 292-312, Nov 2014.
Leonid
Hurwicz, Eric S. Maskin y Roger B. Myerson 2007 Nobel
Price in Economic Sciences "for having laid
the foundations of mechanism design theory"
A. Mas-Colell Leo
Hurwicz, el pionero El País. 21 Octubre
2007
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Feb 26, 09
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Decision trees. Example.
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Mar 2, 09
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Problem 1.
Problem set (I+D,
Contrato de móvil, Pañuelos, El huerto,
El sondeo, Concurso) |
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Mar 2, 09
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Bayesian analysis. Example. |
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Mar 4, 08
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ICAI
CENTENNIAL |
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Mar 5, 09
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Solution Problem set (I+D,
Contrato de móvil, Pañuelos, El huerto,
El sondeo, Concurso) |
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Mar 9, 09
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GAME
THEORY. |
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H. Singh Introduction
to Game Theory and Its Application in Electric Power
Markets IEEE Computer Applications in Power
(12)4: 18-22 Oct 1999
M. Shubik Game Theory and Operations Research: Some
Musings 50 Years Later Operations Research (50)
1: 192-196 Jan-Feb 2002
P. Horner Game
Theory: A 'Nobel' Pursuit OR/MS Today (32) 6
Dec 2005
Aumann's
Work in Game Theory Leads to von Neumann Prize
OR/MS Today (32) 6 Dec 2005
Robert
J. Aumann and Thomas C. Schelling 2005 Nobel Price in
Economic Sciences "for having enhanced our understanding
of conflict and cooperation through game-theory analysis"
John
C. Harsanyi, John F. Nash Jr. and Reinhard Selten 1994
Nobel Price in Economic Sciences "for their pioneering
analysis of equilibria in the theory of non-cooperative
games"
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Mar 9, 09
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Equilibrium on pure and
mixed strategies. |
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Problem set (Móviles,
Caperucita, Suma nula 3x4, Suma nula 2x4, Suma nula 3x5,
Suma nula 4x5) |
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Mar 11, 09
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Solution problem set (Móviles,
Caperucita, Suma nula 3x4, Suma nula 2x4, Suma nula 3x5,
Suma nula 4x5) |
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Mar 12, 09
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Cournot equilibrium. Bertrand
equilibrium. |
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Mar 16, 09
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LECTURE NOTES
about Queuing theory.
QUEUING
THEORY. Introduction
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Mar 16, 09
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Poisson process. M/M/1,
M/M/s and M/M/s/K Systems. |
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C. Moler The
origins of Matlab Matlab News & Notes Dec
2004
C. Moler The
world's largest matrix computation Matlab News
& Notes Oct 2002 |
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Problems 3 and 5. |
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Mar 18, 09
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Problem set (Administración
local, Dos procesadores, Descarga plataformas, Impresora,
Feria, Consultas bancarias, Motores de barco, Aula de
ordenadores) |
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Mar 19, 08
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HOLIDAY |
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Mar 23, 09
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Other queuing systems.
Queuing
systems formulas. |
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Mar 23, 09
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Decision in queuing systems. |
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Solution problem set (Administración
local, Dos procesadores, Descarga plataformas, Impresora,
Feria, Consultas bancarias, Motores de barco, Aula de
ordenadores)
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Mar 25, 09
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WEDNESDAY IS FRIDAY |
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Mar 26, 09
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Problem 29.
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Mar 30, 09
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LECTURE NOTES
about Simulation.
SIMULATION.
Definition. Advantages and drawbacks. Elements of discrete
event simulation.
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A. Patching, T. Lemoine and G. Kern Improving
Car Body Production at PSA Peugeot Citroën Interfaces
(33) 1: 36-49 Jan-Feb 2003 |
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Mar 30, 09
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Structure of a simulation
model. Trace. Case study of a queuing system. |
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Apr 1, 09
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Simulation languages. |
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GPSS
World Slides
GPSS
World Results Slides
GPSS
World Manual
GPSS
World Student Version
J. Banks and R.R. Gibson The
ABCs of Simulation Practice Analytics Magazine
16-21 Spring 2009
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Apr 2, 09
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Instructions and several examples.
Assignment of simulation
practices with GPSS.
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Apr 15, 09
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Case study of a parallel
system. Static reliability of a electric generation system.
Reliability chronological model. |
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J. Van Hecke et. al. Sequential Probabilistic
Methods for Power System Operation and Planning Electra
No. 179 Aug 1998 |
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Apr 16, 09
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Apr 22, 09
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MIDTERM EXAM |
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Apr 27, 09
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Exam review.
April
2009 Exam solution.
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Apr 27, 09
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Exam review.
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Apr 29, 09
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Pseudorandom number generation.
Generation of random variables with continuous and discrete
distributions. |
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C. Moler Random
thoughts. 10^435 years is a very long time Matlab
News & Notes Fall 1995
C. Moler Normal
behavior. Ziggurat algorithm generates normally distributed
random numbers Matlab News & Notes Spring
2001 |
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Problem set (Muelle
circular, El apetito, Combinación de funciones,
Impresoras, Reparación I, Fondos de inversión,
Trabajos a imprimir, Demanda mínima)
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Apr 30, 09
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Inverse transform method.
Simple acceptance-rejection method. Random variables with
a normal distribution. |
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May 4, 09
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Solution problem set (Muelle
circular, El apetito, Combinación de funciones,
Impresoras, Reparación I, Fondos de inversión,
Trabajos a imprimir, Demanda mínima) |
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May 4, 09
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Statistical analysis of the results. |
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May 6, 09
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Statistical analysis of the results. |
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May 7, 09
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LECTURE NOTES
about Optimization models of inventory management.
INVENTORY
MANAGEMENT MODELS.
Static deterministic models of economic order with continuous
revision. Dynamic deterministic models.
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H.E. Scarf Inventory Theory Operations
Research (50) 1: 186-191 Jan-Feb 2002 |
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Lab
report.
Hand in of simulation practices with GPSS. |
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May 11, 09
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Problem set (Taller
de vehículos, Descuento por cantidad, entrega paulatina,
Análisis de gráficas, Texauto, Transporte,
Atlántida, contenedores, Tienda 24 horas) |
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May 11, 09
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Static stochastic models
of economic order with continuous revision. EOQ stochastic
model. |
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May 13, 09
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Stochastic models of economic
order with periodic revision.
Inventory
formulas. |
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May 14, 09
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Solution
problem set (Taller
de vehículos, Descuento por cantidad, entrega paulatina,
Análisis de gráficas, Texauto, Transporte,
Atlántida, contenedores, Tienda 24 horas). |
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May 17, 09
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HOLIDAY |
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INTERNET DAY
Birthday of internet (data network) in 1969.
L. Kleinrock Creating
a Mathematical Theory of Computer Networks Operations
Research (50) 1: 125-131 Jan-Feb 2002
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May 18, 09
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Problems 1, 2, 3, 4,
7, 11, 12, 13, 15, 17 and 23. Other problems to be
done (5, 6, 8, 16, 20, 21 and 24.) |
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May 18, 09
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LECTURE NOTES
about Optimization models based in networks.
OPTIMIZATION
IN NETWORKS. Introduction. |
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Grafos
A. Rodríguez Grafos:
herramienta informática para el aprendizaje y resolución
de problemas reales de teoría de grafos X Congreso
de Ingeniería de Organización. Valencia, España. Septiembre
2006 |
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May 20, 09
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Shortest path problem. |
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Problem set (Environmental
Agency, Freighter, Maximum Flow through a network) |
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May 21, 09
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Spanning tree. |
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May 25, 09
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Maximum flow problem. |
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Solution problem set (Environmental
Agency, Freighter, Maximum Flow through a network) |
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May 25, 09
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Problems 2, 4 5, 6, 7
and 8. |
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May 27, 09
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Minim cost flow problem.
Compatible flow problem. |
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Problems 9 and 10.
Problems to be done (3 and 11.) |
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May 28, 09
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LECTURE NOTES
about Program Evaluation and Review Technique (PERT).
PROJECT
PLANNING AND CONTROL. Critical path. |
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GanttProject.
Microsoft
Project
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Jun 1, 09
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PERT. |
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Problem set (Task
sequencing, Training course, Seven activities with acceleration
cost, Activities with random duration, Investment with
randomness) |
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Jun 1, 09
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Penalties in PERT. |
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Jun 3, 09
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Introducing costs. |
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Solution problem set (Task
sequencing, Training course, Seven activities with acceleration
cost, Activities with random duration, Investment with
randomness) |
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Jun 4, 09
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Problem 1, 2, 4, 7 and
9. |
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Jun 13, 09
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Final
Exam. |
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Sep 9, 09
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Resit
Exam. |
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Departamento de Organizacción Industrial (DOI) |
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Instituto
de Investigación Tecnológica 
