| Mathematical Methods (4th IIND, year 2012-13) |
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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 5, 12
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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
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Sep 5, 12
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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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L. Escudero y M.A. López SEIO
y la historia de la IO en España Boletín
de Estadística e Investigación Operativa 28 (1): 24-55,
Feb 2012
F. Petropoulos et al. Operational
Research: Methods and Applications March 2023 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
S. Lumbreras and A. Ramos Optimal
Design of the Electrical Layout of an Offshore Wind
Farm: a Comprehensive and Efficient Approach Applying
Decomposition Strategies IEEE Transactions on
Power Systems 28 (2): 1434-1441, May 2013 10.1109/TPWRS.2012.22049066
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 7, 12
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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 7, 12
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MODELING
WITH LINEAR PROGRAMMING. Transportation problem. Transhipment
problem. Task assignment problem.
MODELING
WITH INTEGER LINEAR PROGRAMMING. Knapsack problem.
Set covering problem. |
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Sep 11, 12
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Packing problem. Partition
problem. Travelling salesman problem (TSP). |
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TSP
Art |
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Sep 11, 12
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Fixed cost problem. |
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Sep 12, 12-S
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Task sequencing in a machine.
Modeling
Poblems # 1
Production of three products.
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Sep 12, 12-S
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Charter Flights. Bakery.
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Team formation. |
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Sep 18, 12
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Disjunctive constraints.
Satisfy k of N equations. Selection among N values. Simple
implications. |
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Selecting a basketball team. |
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Assignment
of optimization practices with GAMS. |
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Sep 18, 12
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GAMS Development; Optimization:
Energy Systems Modeling (SADSE);
OR/MS-today Advertisement, August 2009
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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Sep 19, 12-S
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Paper roll cut.
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Sep 19, 12-S
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Job shop.
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Sep 24, 12
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Car renting. |
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Sep 24, 12
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Swimming pools.
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Sep 26, 12
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Practical session with GAMS.
Execution and analysis of the results.
NEOS
Server for Optimization
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Sep 26, 12
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Equivalences among logical
propositions. Complex logical propositions. |
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Connecting two pipelines. |
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Oct 1, 12-S
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Sequencing tasks in two
machines. Exams. |
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Optimization
cases
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Oct 1, 12-S
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Data bases.
Solution
Poblem set # 1
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Oct 3, 12
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SHORT
EXAM year 2012-13
MIDTERM
EXAM year 2011-12
MIDTERM
EXAM year 2010-11
MIDTERM
EXAM year 2009-10
MIDTERM
EXAM year 2008-09
MIDTERM
EXAM year 2007-08
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Oct 3, 12
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Practical session with
GAMS. |
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Oct 8, 12
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LECTURE
NOTES about Linear Optimization.
LINEAR
PROGRAMMING.
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Mathematical
Programming Glossary
Linear
and Discrete Optimization course from EPFL at coursera.org
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Practical
case report.
Hand in of optimization practical cases with GAMS. |
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Oct 8, 12
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Hypothesis. Geometry.
Properties. Simplex algorithm. Graphical solution. Standard
form. |
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R. Elwes The
algorithm that runs the world New Scientist (2877)
Aug 2012 |
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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 10, 12
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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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Oct 10, 12
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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 15, 12
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Degeneracy. Characterizing the solutions.
Tabular form.
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Oct 15, 12
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Tabular form. |
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Oct 17, 12
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Obtaining an initial basic
feasible solution: two phase method. |
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Javascript
SimpleX
PHPSimplex |
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Oct 17, 12
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DUALITY. Dual problem. |
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Oct 22, 12
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Fundamental properties
of duality. Economical interpretation. Graphical interpretation
of dual variables and of reduced costs. |
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Oct 22, 12
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LP Problems (1, Degeneración,
8) |
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Oct 24, 12
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Sensitivity analysis.
Changes in constraint bounds. Change in a coefficient
of a non basic variable. Introduction of a new variable.
Change in a coefficient of a basic variable. Introduction
of a new constraint. |
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Oct 24, 12
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LP Problems (22) |
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Oct 29 12
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Dual simplex method. |
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Oct 29, 12-S
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LP Problems (2, 3) |
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Oct 31, 12-S
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LP Problems (4, 9, 24) |
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Oct 31, 12-S
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Solution LP Problems 1,
2, 3, 4, 8, 9, 22, 24) |
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Nov 7, 12
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SHORT
EXAM year 2012-13
MIDTERM
EXAM year 2011-12
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 7, 12
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LECTURE
NOTES about Mixed integer linear programming.
INTEGER
LINEAR PROGRAMMING. Example case. Branch and bound
method.
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R.E. Gomory Early
Integer Programming Operations Research (50) 1:
78-81 Jan-Feb 2002 |
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Nov 12, 12-S
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Problem Set MIP 2,
4, 1
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Nov 12, 12
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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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Nov 14, 12
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Problems with constraints:
optimality conditions. |
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Nov 14, 12
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Necessary and sufficient
Karush-Kuhn-Tucker conditions. |
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Nov 19, 12-S
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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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Nov 19, 12-S
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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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Nov 21, 12-S
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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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Nov 21, 12
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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
D. Ríos Varoufakis
en los juegos (no) olímpicos El País 26-jul-2015 Game
Theory course from Stanford University at coursera.org
Game
Theory courses in Open Education DataBase
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Nov 26, 12
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Problem 22 |
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Nov 26, 12-S
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Problem set Móviles,
Caperucita, Suma nula 3x4, Suma nula 2x4, Suma nula 3x5,
Suma nula 4x5) |
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Hand in of the first version of the slides. |
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Nov 28, 12-S
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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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Nov 28, 12
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El
Arte de Presentar
Un ejemplo muy divertido
Kate
Hartman: el arte de la indumentaria de comunicación
Presentation
of optimization practical cases.
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Dec 3, 12
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Presentation of optimization
practical cases. |
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Dec 3, 12
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Presentation of optimization
practical cases. |
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Dec 19, 12-S
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TERM
EXAM year 2012-13
TERM
EXAM year 2011-12
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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Jan 15, 13
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Presentation of optimization
practical cases. |
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Jan 15, 13
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Presentation of optimization
practical cases. |
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Jan 17, 13-S
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Exam review. |
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Jan 17, 13-S
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Exam review. |
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Jan 22, 13
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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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Jan 22, 13
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Decision trees. Example.
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Jan 24, 13
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Bayesian analysis. Example. |
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Jan 24, 13-S
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Problem 1.
Problem set I%20D,
Contrato de móvil, Pañuelos, El huerto, El sondeo, Concurso) |
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Jan 29, 13-S
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Problem 1.
Problem set I%20D,
Contrato de móvil, Pañuelos, El huerto, El sondeo, Concurso) |
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Jan 29, 13-S
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Solution Problem set.
I%20D, Contrato de móvil, Pañuelos, El huerto, El sondeo,
Concurso) |
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Jan 31, 13
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LECTURE
NOTES about Queuing theory.
QUEUING
THEORY. Introduction
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Jan 31, 13
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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
world's largest matrix computation Matlab News
& Notes Oct 2002 |
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Problems 3 and 5. |
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Feb 5, 13
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Other queuing systems.
Decision in 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 5, 13
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Impresora, Feria, Consultas bancarias, Motores de
barco, Aula de ordenadores
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Feb 7, 13
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Administración local,
Dos procesadores, Descarga plataformas. |
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Feb 7, 13
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Problem 29.
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Feb 12, 13
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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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Feb 12, 13
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Structure of a simulation
model. Trace. Case study of a queuing system. |
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Feb 14, 13
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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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Feb 14, 13
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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.
Assignment
of simulation practices with GPSS.
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Feb 19, 13
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Pseudorandom number generation.
Generation of random variables with continuous and discrete
distributions. Inverse transform method. Simple acceptance-rejection
method. Random variables with a normal distribution. Statistical
analysis of the results. |
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C. Moler The
origins of Matlab Matlab News & Notes Dec
2004
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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Feb 19, 13
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Practical session with GPSS.
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Feb 21, 13
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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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Feb 21, 13
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Practical session with GPSS.
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Feb 26-S, 13
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Solution problem set.
Muelle circular, El apetito, Combinación de funciones,
Impresoras |
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Feb 26-S, 13
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Solution problem set.
Reparación I, Fondos de inversión, Trabajos a imprimir,
Demanda mínima |
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Feb 28-S, 13
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Solution problem set.
Reparación I, Fondos de inversión, Trabajos a imprimir,
Demanda mínima
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Mar 1-S, 13
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MIDTERM
EXAM year 2012-13, B
MIDTERM
EXAM year 2011-12
MIDTERM
EXAM year 2010-11
MIDTERM
EXAM year 2009-10
MIDTERM EXAM year 2008-09
MIDTERM
EXAM year 2007-08
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Mar 5, 13
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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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Mar 5, 13
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Static stochastic models
of economic order with continuous revision. EOQ stochastic
model. |
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Mar 7, 13
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Stochastic models of economic
order with periodic revision.
Inventory
formulas. |
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Mar 7, 13
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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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Mar 12, 13
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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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Mar 12, 13
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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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Mar 14, 13
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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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Mar 14, 13
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Shortest path problem. |
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Lab
report.
Hand in of simulation practices with GPSS. |
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Mar 21, 13
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Spanning tree. Maximum
flow problem. |
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Mar 21, 13
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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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Problem set Environmental
Agency, Freighter, Maximum Flow through a network)
Solution problem set. Environmental Agency, Freighter,
Maximum Flow through a network)
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Apr 2, 13
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Presentation
of simulation practical cases. |
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Apr 2, 13
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Presentation of simulation
practical cases. |
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Apr 4, 13
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Open questions |
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Apr 5, 13
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MIDTERM
EXAM year 2012-13, B
MIDTERM
EXAM year 2011-12
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 9, 13
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Presentation of simulation
practical cases. |
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Apr 9, 13
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Presentation of simulation
practical cases. |
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Apr 11, 13
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LECTURE
NOTES about Program Evaluation and Review Technique
(PERT).
PROJECT
PLANNING AND CONTROL. Critical path. |
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OpenProject
ProjectLibre
GanttProject
Microsoft Project
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Apr 11, 13
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PERT. Introducing costs. |
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Apr 16, 13
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Ending date under risk
or uncertainty |
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Apr 16, 13
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Problem 4, 5 and 6 |
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Apr 18, 13
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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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Apr 18, 13
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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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Apr 23, 13
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Apr 23, 13
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Apr 25, 13
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Apr 25, 13
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May 17, 13
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FINAL EXAM year 2012-13
FINAL
EXAM year 2011-12
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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Jun 24, 13
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RESIT EXAM year 2012-13
RESIT
EXAM year 2011-12
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 
