| 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
Energy Systems Modeling (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:
Energy Systems Modeling (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) June 2022
GOOD
OPTIMIZATION MODELING PRACTICES with Pyomo (All You Wanted
to Know About Practical Optimization but Were Afraid
to Ask) June 2022
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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 
