| Mathematical Methods (4th IIND, year 2010-11) |
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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 20, 10
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Extract of the syllabus. Additional bibliography.
Hand out of class notes and web page for slides.
Survey (motivation, expectations, difficulty, etc.) |
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J.R. Alonso Una Universidad nueva El País 12/01/2009
FAQs About O.R. & Analytics
Yukio Hatoyama, Prime Minister designate for Japan, has a Ph.D. from Stanford in O.R.
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Sep 20, 10
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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
Decision Support Systems for the Energy Sector (SADSE)
J. Toczek The PuzzlOR
A. Ramos Some IIT Operations Research Models for Electricity
Markets XIV Latin Ibero-American Congress on Operations Research (CLAIO 2008) Cartagena de Indias, Colombia September
2008 (Presentation) Sesión semiplenaria
M. Alvar, A. Arranz, A. Ramos, A. Sánchez, J. Villar Parking place demand and offer assignment
IIT-09-019A
A. Ramos, M.T. Peña, A. Fernández, P. Cucala Mathematical programming approach to underground timetabling problem
for maximizing time synchronization Revista de Dirección, Organización y Administración de Empresas CEPADE 35: 88-95 Junio 2008
S. Cerisola, A. Baillo, J.M. Fernandez-Lopez, A. Ramos, R. Gollmer Stochastic
Power Generation Unit Commitment in Electricity Markets: A Novel Formulation and A Comparison of Solution Methods Operations Research 57 (1): 32-46 Jan-Feb 2009
P. Sánchez-Martín, A. Ramos, J.F. Alonso Probabilistic mid-term transmission planning in a liberalized market
IEEE Transactions on Power Systems 20 (4): 2135-2142 Nov 2005
ROADEF/EURO Challenge 2010: A large-scale energy management problem with varied constraints
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
C. Barnhart, P. Belobaba, A.R. Odoni Applications
of Operations Research in the Air Transport Industry Transportation Science Vol 37. No. 4 pp. 368-391 Nov 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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Sep 24, 10
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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. |
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Sep 24, 10
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MODELING WITH LINEAR PROGRAMMING. Transportation problem. Transhipment problem. Task assignment
problem. |
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Sep 27, 10
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MODELING WITH INTEGER LINEAR PROGRAMMING. Knapsack problem. Set covering problem. Packing problem.
Partition problem. Travelling salesman problem (TSP). |
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TSP Art |
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Team formation.
Assignment of optimization practices with GAMS.
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Sep 27, 10
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Work order scheduling.
Modeling Poblems # 1 |
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Oct 1, 10
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Production of three products. Charter Flights.
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Oct 1, 10
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Bakery.
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Oct 4, 10
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Fixed cost problem. |
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Paper roll cut. |
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Oct 4, 10
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Job shop. Car renting.
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Oct 8, 10
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Disjunctive constraints. Satisfy k of N equations. Selection among N values. Simple implications. |
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Oct 8, 10
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GAMS Development; Optimization: Decision Support Systems for the Energy Sector (SADSE); OR/MS-today Advertisement, August 2009
Team Formation.
Algebraic modeling languages.
Transportation problem: mathematical formulation and writing in GAMS. GOOD OPTIMIZATION MODELING PRACTICES with GAMS (All You Wanted to Know About Practical Optimization but Were Afraid
to Ask) September 2024
GOOD OPTIMIZATION MODELING PRACTICES with Pyomo (All You Wanted to Know About Practical Optimization
but Were Afraid to Ask) September 2024
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Oct 11, 10
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Equivalences among logical propositions. Complex logical propositions. |
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Execution and analysis of the results.
NEOS Server for Optimization |
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Oct 11, 10
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Practical session with GAMS.
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Oct 15, 10
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Selecting a basketball team. |
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Oct 15, 10
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Swimming pools. Connecting two pipelines.
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Oct 18, 10
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Sequencing tasks in two machines. Exams. |
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Oct 18, 10
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Data bases. Noel lunch.
Solution Poblem set # 1
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Optimization cases
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Oct 22, 10
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LECTURE NOTES about Linear Optimization.
LINEAR PROGRAMMING.
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Mathematical Programming Glossary |
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Oct 22, 10
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Hypothesis. Geometry. Properties. Simplex algorithm. Graphical solution. Standard form. |
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Un español resuelve un problema matemático
de hace medio siglo El Mundo 27/05/2010. Premio
Fulkerson 2015 de la Mathematical Optimization Society (MOS) y la American Mathematical Society (AMS)
iMetro: Subway best route calculator
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Oct 25, 10
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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
Un español resuelve un problema matemático de hace medio
siglo El Mundo 26/5/2010
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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Oct 25, 10
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Multiple optima. |
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LP Problems 1, 2, 3, 4, 8, 9, 22, 24 |
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Oct 28, 10
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Degeneracy. Characterizing the solutions. |
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LP Problems 2 |
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Oct 28, 10
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LP Problems 2 |
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Practical case report.
Hand in of optimization practical cases with GAMS.
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Nov 4, 10
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Obtaining an initial basic feasible solution: two phase method. |
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Questions about the modeling difficulties and GAMS practical case and spent time. |
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Nov 4, 10
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Obtaining an initial basic feasible solution: two phase method. |
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Nov 5, 10
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PHPSimplex |
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Nov 5, 10
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Nov 17, 10
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MIDTERM EXAM year 2010-11
MIDTERM EXAM year 2009-10
MIDTERM EXAM year 2008-09
MIDTERM EXAM year 2007-08
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Nov 22, 10
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Exam review.
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Nov 26, 10
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DUALITY. Dual problem. |
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Comments about midterm exam. |
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Nov 29, 10
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Fundamental properties of duality. Economical interpretation. |
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Nov 29, 10
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Graphical interpretation of dual variables and of reduced costs.
Sensitivity analysis. Changes in constraint bounds. Change in a coefficient of a non basic variable. Introduction of a new variable. |
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Dec 3, 10
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Introduction of a new variable. Change in a coefficient of a basic variable. |
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Dec 3, 10
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Introduction of a new constraint. |
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Dec 10, 10
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Dual simplex method. |
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Solution LP Problems 1, 2, 3, 4, 8, 9, 22, 24) |
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Dec 10, 10
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Presentation of optimization practical cases.
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Dec 16, 10
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Presentation of optimization practical cases. |
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Dec 17, 10
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Presentation of optimization practical cases. |
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Dec 17, 10
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Presentation of optimization practical cases. |
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Dec 20, 10
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Presentation of optimization practical cases. |
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Dec 20, 10
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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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Problem Set MIP 2, 4, 1
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Jan 10, 11
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Branch and bound method. |
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Jan 10, 11
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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 14, 11
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Problems with constraints: optimality conditions. |
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Jan 14, 11
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Necessary and sufficient Karush-Kuhn-Tucker conditions. |
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Jan 17, 11
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Problem 2 TERM EXAM year 2008-09
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Jan 17, 11
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Problem 3 TERM EXAM year 2008-09
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Jan 21, 11
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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 21, 11
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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)
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Feb 1, 11
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TERM EXAM year 2010-11
TERM EXAM year 2009-10
TERM EXAM year 2008-09
TERM EXAM year 2007-08
TERM EXAM year 2006-07
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Feb 7, 11
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Exam review. |
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Feb 7, 11
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Exam review. |
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Feb 9, 11
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LECTURE NOTES about Queuing theory.
QUEUING THEORY. Introduction
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Feb 9, 11
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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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Feb 14, 11
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Other queuing systems.
Queuing systems formulas. |
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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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Feb 14, 11
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Administración local, Dos procesadores, Descarga plataformas. |
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Feb 16, 11
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Decision in queuing systems. |
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Impresora, Feria, Consultas bancarias, Motores de barco, Aula de ordenadores
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Feb 16, 11
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Problem 29.
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Feb 28, 11
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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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Assignment of simulation practices with GPSS. |
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Feb 28, 11
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Structure of a simulation model. Trace. Case study of a queuing system. |
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Mar 2, 11
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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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Mar 2, 11
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Instructions and several examples.
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Mar 7, 11
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Instructions and several examples.
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Mar 7, 11
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Practical session with GPSS.
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Mar 9, 11
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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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Mar 9, 11
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Pseudorandom number generation. Generation of random variables with continuous and discrete distributions. Inverse transform method. Simple acceptance-rejection method. |
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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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Mar 14, 11
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Random variables with a normal distribution. |
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Mar 14, 11
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Statistical analysis of the results. |
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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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Mar 15, 11
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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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Mar 16, 11
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Decision trees. Example.
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Mar 16, 11
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Problem 1.
Problem set I+D, Contrato de móvil, Pañuelos, El huerto, El sondeo, Concurso) |
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Mar 21, 11
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Bayesian analysis. Example. |
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Mar 21, 11
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Solution Problem set. I+D, Contrato de móvil, Pañuelos, El huerto, El sondeo, Concurso) |
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Mar 22, 11
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Solution Problem set. I+D, Contrato de móvil, Pañuelos, El huerto, El sondeo, Concurso) |
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Lab report.
Hand in of simulation practices with GPSS. |
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Mar 22, 11
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LECTURE NOTES about Game theory.
GAME THEORY.
Equilibrium on pure and mixed strategies.
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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"
John F. Nash Non-Cooperative Games PhD Thesis. Princeton University. May 1950
A. Meca Génesis y Evolución de la Teoría de Juegos. Sus Orígenes en España Boletín de Estadística e Investigación Operativa Vol 22 No 1 / Enero 2006
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Mar 22, 11
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Problem 22 |
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Mar 23, 11
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Problem 22 |
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Mar 23, 11
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Problem 22 |
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Mar 25, 11
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Problem set Móviles, Caperucita, Suma nula 3x4, Suma nula 2x4, Suma nula 3x5, Suma nula 4x5)
Solution problem set. Móviles, Caperucita, Suma nula 3x4, Suma nula 2x4, Suma nula 3x5, Suma nula 4x5)
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Mar 28, 11
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MIDTERM EXAM year 2010-11
MIDTERM EXAM year 2009-10
MIDTERM EXAM year 2008-09
MIDTERM EXAM year 2007-08
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Apr 4, 11
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Exam review.
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Apr 4, 11
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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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Apr 6, 11
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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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Apr 6, 11
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Static stochastic models of economic order with continuous revision. EOQ stochastic model. |
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Apr 11, 11
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Stochastic models of economic order with periodic revision.
Inventory formulas. |
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Apr 11, 11
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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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Apr 13, 11
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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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Apr 13, 11
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Presentation of simulation practical cases. |
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Apr 27, 11
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Presentation of simulation practical cases. |
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Apr 27, 11
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Presentation of simulation practical cases. |
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May 4, 11
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Presentation of simulation practical cases. |
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May 4, 11
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Presentation of simulation practical cases.
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May 6, 11
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Presentation of simulation practical cases. |
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May 6, 11
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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 9, 11
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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 9, 11
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Spanning tree. |
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May 11, 11
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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 11, 11
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Problems 2, 4 5, 6, 7 and 8. |
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May 16, 11
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Minim cost flow problem. Compatible flow problem. |
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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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Problems 9 and 10.
Problems to be done (3 and 11.) |
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May 16, 11
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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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May 18, 11
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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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May 18, 11
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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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May 23, 11
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Problem 1, 2, 4, 7 and 9. |
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May 23, 11
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Problem 1, 2, 4, 7 and 9. |
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May 25, 11
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Problem 1, 2, 4, 7 and 9. |
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May 25, 11
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Problem 1, 2, 4, 7 and 9. |
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May 31, 11
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FINAL EXAM year 2010-11
FINAL EXAM year 2009-10
FINAL EXAM year 2008-09
FINAL EXAM year 2007-08
FINAL EXAM year 2006-07
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Jul 11, 11
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RESIT EXAM year 2010-11
RESIT EXAM year 2009-10
RESIT EXAM year 2008-09
RESIT EXAM year 2007-08
RESIT EXAM year 2006-07
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Instituto de Investigación Tecnológica 
