| 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 
