| Mathematical Methods (4th IIND, year 2007-08) |
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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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Oct 1, 07
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Comments
about the syllabus.
Additional bibliography.
Hand out of 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 |
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Oct 1, 07
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LECTURE NOTES
about Optimization mathematical modeling.
INTRODUCTION
TO OPTIMIZATION AND MODELING. OR definition.
Historical introduction.
Optimization definition. Method classification.
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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 2, 07
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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.
Problem set # 1 (Production
of three products, Muffins, Gas mix.) |
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Oct 3, 07
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HOLIDAY |
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Oct 8, 07
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LINEAR
PROGRAMMING MODELING. Transportation problem.
Transshipment problem. Task assignment problem. |
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Oct 8, 07
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MODELING
IN INTEGER LINEAR PROGRAMMING. Knapsack problem.
Set covering problem. |
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Crew assignment. |
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Oct 9, 07
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Packing problem. Partition
problem. |
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Production of three products.
Solution of problem set # 1 (Production
of three products, Muffins, Gas mix.)
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Oct 10, 07
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Muffins.
Problem set # 2 (Job
shop. Gasoline mix. Charter Flights.
Paper roll cut. Car renting. Swimming pools.
Connecting two pipelines. Sequencing five tasks. Exams.
Data bases. Oil tanker. Wineshop-keeper.) |
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Oct 15, 07
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Travelling salesman problem
(TSP). Fixed cost problem. |
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Work orders scheduling. Thermal unit commitment. |
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Art
with the travelling salesman problem. |
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Oct 15, 07
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Disjunctive constraints.
Satisfy k of N equations. Selection among N values. Simple
implications. Equivalences among logical propositions.
Complex logical propositions. |
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Charter flights. |
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Oct 16, 07
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Gas mix. Job shop.
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Oct 17, 07
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Product of binary variables. |
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Selecting a basketball team. |
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Oct 22, 07
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Gasoline mix.
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Oct 22, 07
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Paper roll cut. Car renting. |
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Oct 23, 07
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Algebraic
modeling languages.
Transportation problem: mathematical formulation and writing
in GAMS. |
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Oct 24, 07
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Execution and analysis
of the results. |
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Oct 29, 07
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Swimming pools.
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Oct 29, 07
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Connecting two pipelines. |
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Oct 30, 07
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Exams. Data bases.
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Oct 31, 07
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LECTURE NOTES
about Linear Optimization.
LINEAR
PROGRAMMING. Hypothesis. Geometry.
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Mathematical
Programming Glossary |
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Nov 2, 07
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Properties. Simplex algorithm.
Graphical solution. Standard form. |
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Nov 7, 07
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HOLIDAY |
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Nov 12, 07
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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 12, 07
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Multiple optima. Degeneracy.
Characterizing the solutions. |
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Nov 13, 07
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Sequencing five tasks. Oil tanker. Wineshop-keeper.
Solution of problem set # 2 (Job
shop. Gasoline mix. Charter Flights.
Paper roll cut. Car renting. Swimming pools. Connecting
two pipelines. Sequencing five tasks. Exams.
Data bases. Oil tanker. Wineshop-keeper.)
Problem set # 2 (Digital television,
Water bottles, Production.)
Solution of problem set # 2 (Digital television,
Water bottles, Production.)
Problem set # 3 (Drink
area, Welding robot.)
Solution of problem set # 3
(Drink area,
Welding robot.)
Additional problems from the notes (Underground
planning. Pacific mission. CD edition. Bus planning.
Emergency support. Storage building. Logistics. Task
sequencing in one machine. Truck acquisition. Dieing
machine acquisition. Production and inventory. Postal
office. Railway transportation. Suppliers. Supply. Crude
mix. roll cut. Farm operations. Distribution company.
Route scheduling. Production II. Production VI. Feed
composition. Storage hydro plant. Problem 9 of Task
sequencing.)
Problem 1 of LP.
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Nov 14, 07
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Tabular form. |
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Problem set (1,
2, 3, 8, 9, 24, 22) |
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PHPSimplex |
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Nov 14, 07
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Tabular form. |
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Nov 15, 07
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Nov 21, 07
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MIDTERM EXAM |
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Nov 26, 07
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Solution
of the midterm exam |
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Nov 26, 07
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Obtaining an initial basic feasible
solution: two phase method.
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Nov 27, 07
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DUALITY. Dual problem.
Fundamental properties of duality. Economical interpretation. |
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Survey about modeling. |
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Teamwork formation.
Assignment of optimization practices
with GAMS.
NEOS
Server for Optimization |
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Nov 28, 07
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Graphical interpretation
of dual variables and of reduced costs. |
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Dec 3, 07
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Solution problem set (1,
2, 3, 8, 9, 24, 22)
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Dec 3, 07
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Sensitivity analysis.
Changes in constraint bounds. |
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Dec 4, 07
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HOLIDAY |
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Dec 5, 07
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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. Dual simplex method. |
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Dec 10, 07
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Problem set # 4 (Problems
25 and 28.) Problems 8, 11 and 22.
Solution of problem set # 4
(Problems
25 and 28.) |
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Dec 10, 07
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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, 07
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Branch and bound method. |
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Dec 12, 07
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Problems 4 and 5. |
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Practical
case report.
Hand in of optimization practical cases with GAMS. |
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Dec 17, 07
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LECTURE NOTES
about Dynamic programming.
DETERMINISTIC
DYNAMIC PROGRAMMING. (By stages and with finite
horizon)
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Questions about the modeling difficulties
and GAMS practical case and spent time. |
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Dec 17, 07
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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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Dec 18, 07
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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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Dec 21, 07
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Problem 5, 6 and 7. Task sequencing in one machine.
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Jan 8, 08
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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 9, 08
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Problems with constraints:
optimality conditions. |
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Jan 10, 08
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Necessary and sufficient
Karush-Kuhn-Tucker conditions. |
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Jan 14, 08
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Presentation
of optimization practical cases.
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Jan 14, 08
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Presentation of optimization
practical cases. |
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Jan 15, 08
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Presentation of optimization
practical cases. |
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Jan 16, 08
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Presentation of optimization
practical cases. |
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Jan 21, 08
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Presentation of optimization
practical cases. |
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Jan 21, 08
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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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Jan 22, 08
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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 23, 08
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Production VI.
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Jan 28, 08
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Production VI. |
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Jan 28, 08
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Distributing company. |
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Jan 29, 08
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Distributing company. |
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Jan 30, 08
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Problem 21 of LP. |
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Feb 27, 08
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LECTURE NOTES
about Decision theory.
DECISION
THEORY.
Decision criteria. Example.
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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 27, 08
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Decision trees. Example.
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Feb 28, 08
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Problem 1.
Problem set (I+D,
Contrato de móvil, Pañuelos, El huerto,
El sondeo, Concurso) |
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Feb 29, 08
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Bayesian analysis. Example. |
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Mar 7, 08
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Solution Problem set (I+D,
Contrato de móvil, Pañuelos, El huerto,
El sondeo, Concurso) |
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Mar 11, 08
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GAME
THEORY. |
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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 12, 08
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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 12, 08
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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, 08
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Exam review.
February 2008 Exam
solution. |
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Mar 25, 08
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Cournot equilibrium. Bertrand
equilibrium. |
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Mar 26, 08
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LECTURE NOTES
about Queuing theory.
QUEUING
THEORY. Introduction
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Mar 26, 08
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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 1 and 3. |
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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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Apr 1, 08
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Other queuing systems.
Queuing systems formulas.
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Apr 2, 08
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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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Apr 2, 08
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Decision in queuing systems. |
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Problems 5 and 13.
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Apr 8, 08
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Problem 29.
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Apr 9, 08
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Problem of problem set. |
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Apr 9, 08
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Comments of the students
about the exam. |
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Apr 9, 08
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Comments about the exam. |
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Apr 10, 08
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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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Apr 15, 08
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Structure of a simulation
model. Trace. Case study of a queuing system. |
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Apr 16, 08
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Simulation languages. |
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GPSS
World Slides
GPSS
World Manual
GPSS
World Student Version |
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Apr 16, 08
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Instructions and several
examples. |
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Apr 16, 08
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Questions about decision
and game theory and queuing systems. |
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Apr 17, 08
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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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Instructions and several examples. |
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Apr 23, 08
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MIDTERM EXAM |
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Apr 29, 08
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Exam review.
April 2008 Exam
solution.
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Assignment of simulation
practices with GPSS. |
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Apr 30, 08
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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, 08
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Inverse transform method.
Simple acceptance-rejection method. Random variables with
a normal distribution. |
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May 1, 08
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HOLIDAY |
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May 6, 08
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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 7, 08
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HOLIDAY |
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May 8, 08
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Problems 2, 3 14, 17,
20, 21, 22, 23 and 24. |
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Hand in of flow diagram or pseudocode
of simulation practices with GPSS.
Microsoft
Visio |
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May 13, 08
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Statistical analysis of
the results. |
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May 14, 08
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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 14, 08
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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 15, 08
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HOLIDAY |
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May 17, 08
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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 20, 08
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Static stochastic models
of economic order with continuous revision. EOQ stochastic
model. |
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May 21, 08
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Stochastic models of economic
order with periodic revision.
Inventory formulas.
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May 21, 08
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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 22, 08
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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 27, 08
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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 28, 08
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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 28, 08
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Spanning tree. |
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May 29, 08
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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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Jun 3, 08
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Problems 2, 4 5, 6, 7
and 8. |
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Jun 4, 08
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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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Jun 4, 08
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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 5, 08
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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 10, 08
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Penalties in PERT. |
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Jun 11, 08
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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 11, 08
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Problem 1, 2, 4, 7 and
9. |
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Jun 12, 08
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New problems. |
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Jun 23, 08
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Final Exam. |
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Departamento de Organizacción Industrial (DOI) |
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Instituto
de Investigación Tecnológica 
