Operations Research I
Nadia Brauner
[email protected]
Introduction
1
Operations Research: let’s meet
Nadia Brauner
Nadia [email protected]
Master Informatique
master-informatique.ujf-grenoble.fr
Professor Grenoble I
Master ROCO
Operations Research,
Laboratory
Operations Research team
Combinatorics and Optimization
Combinatorial Optimization
team
12-13 President of
French OR Society
2
Operations Research: let’s meet
Theoretical Problems
High-multiplicity scheduling (∈ NP?)
Scheduling in Robotic Cells
CO applied to micro-electronics
Industrial problems
ILOG: Complex transportation problems
IFP: Planning of chemical experiments
de Facto: Optimization of circuit testing
Participation to the creation of a startup
OASIC: optimization of the design of
integrated circuits
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Operations Research
Operations Research
Applications
Tools
OR in France
References
Plan
1
Operations Research or Decision Science
2
Applications
3
Tools
4
OR in France
5
References
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Operations Research
Applications
Tools
OR in France
References
Plan
1
Operations Research or Decision Science
2
Applications
3
Tools
4
OR in France
5
References
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Operations Research
Applications
Tools
OR in France
References
Operations Research or Decision Science
Definitions
Cambridge Dictionary
Operational research UK (US operations research)
The systematic study of how best to solve problems in business
and industry
Wikipedia
Operations research, operational research, or simply OR, is the use
of mathematical models, statistics and algorithms to aid in
decision-making
Roadef
Recherche Opérationnelle : approche scientifique pour la résolution
de problèmes de gestion de systèmes complexes
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Operations Research
Applications
Tools
OR in France
References
Operations Research
The science of “how to do more with less”
Tools that
simulate
optimize
plan
the architecture and the operations of industrial and economical
systems
Models for the analysis of complex situations
Allows decision makers to make efficient and robust choices.
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Operations Research
Applications
Tools
OR in France
References
Operations Research
Quantitative approach to produce the best decisions
A field at the interface of mathematics and computer science
extension to algorithms that manipulate more sophisticated
structures: graphs, polyhedrons...
application domain of algorithmic complexity theory
A toolbox of positive and negative methods for solving
optimization problems
Drawing from Lionel Lagarde
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Operations Research
Applications
Tools
OR in France
References
Operations Research
The tools of OR
help and find
a solution where humans couldn’t find any
a solution to original problems for which humans have no
experience
several solutions where humans could only consider one
help estimating the quality of a solution
help confirm / justify decisions
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Operations Research
Applications
Tools
OR in France
References
Plan
1
Operations Research or Decision Science
2
Applications
3
Tools
4
OR in France
5
References
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Operations Research
Applications
Tools
OR in France
References
Operations Research: Applications
Travelling Salesman Problem (TSP)
A travelling salesman, based in Toulon, has to visit clients
throughout France
He wants to make the shortest possible tour
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Operations Research
Applications
Tools
OR in France
References
Operations Research: Applications
Travelling Salesman Problem
Instance: n cities with a distance matrix
Solution: a tour visiting each town, starting and finishing in
Toulon
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Operations Research
Applications
Tools
OR in France
References
Operations Research: Applications
A greedy algorithm for the TSP
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Operations Research
Applications
Tools
OR in France
References
Operations Research: Applications
Transportation
goods
from warehouses to clients
with transportation costs, distances on the arcs
find the best distribution plan
ai iaP
PP
cij
P
min
j
PP
qabj
a
cij xij
X
xij
≤ ai
xij
≥ bj
xij
≥ 0
j∈B
a
X
i∈A
a
A
P
B
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Operations Research
Applications
Tools
OR in France
References
Operations Research: Applications
Applications
Shortest path
What is the shortest path from
Grenoble to Nice by car?
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Operations Research
Applications
Tools
OR in France
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Operations Research: Applications
24h OR
8h: Optimization of the collection and disposal of recyclable
waste
...
15h: Automated dispatching of service vehicles for the
German Automobile Association (ADAC).
16h: The delay management problem in public transportation:
to wait or not to wait?
...
http://www.24hor.org/
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Operations Research
Applications
Tools
OR in France
References
Operations Research: Applications
15 October 2012:
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Operations Research
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OR in France
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The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2012
Alvin E. Roth, Lloyd S. Shapley
English
English (pdf)
Swedish
Swedish (pdf)
Press Release
15 October 2012
The Royal Swedish Academy of Sciences has decided to award The Sveriges Riksbank Prize in Economic Sciences in Memory
of Alfred Nobel for 2012 to
Alvin E. Roth
Harvard University, Cambridge, MA, USA, and Harvard Business School, Boston, MA, USA
and
Lloyd S. Shapley
University of California, Los Angeles, CA, USA
"for the theory of stable allocations and the practice of market design".
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Operations Research
Applications
Tools
OR in France
References
Stable marriage problem
Stable marriage
Women: Alice, Bénédicte, Camille
Men: Elie, François, Gondran
Women’s preferences
A:
B:
C:
G
F
G
E
E
E
F
G
F
Men’s preferences
E:
F:
G:
A
B
A
B
C
C
C
A
B
How to make the pairs?
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Operations Research
Applications
Tools
OR in France
References
Stable marriage problem
A matching is not stable if it contains two persons of opposite sex
who would both prefer each other than their current partners:
F is married with g
G is married with f
F prefers G to g
G prefers F to f
Questions
How to verify that a marriage is stable?
Is it always possible to find stable marriage?
How to calculate a stable marriage whenever it exists?
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Operations Research
Applications
Tools
OR in France
References
Stable marriage problem
Applications
Situations where traditional market mechanisms do not work
Distribute rare, heterogenous and indivisible goods
Allocation of candidates to positions
students - engineering schools
workers - positions
medical students - hospitals
students - universities
Kidney transplant
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Operations Research
Applications
Tools
OR in France
References
Operations Research: Applications
The ROADEF challenges
http://challenge.roadef.org/
2010 A large-scale energy management problem
2009 Disruption management for commercial aviation
(EDF)
(Amadeus)
2007 Technicians and interventions scheduling for
telecommunications
(France Telecom)
2005 A car sequencing problem
(Renault)
2003 Management of the missions of earth observation satellites
(ONERA et CNES)
2001 Frequency assignment problem with polarization constraints
(CELAR, army)
1999 Inventory Management problem
(Bouygues)
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Operations Research
Applications
Tools
OR in France
References
Operations Research: Applications
The challenge ROADEF/EURO 2012
Machine reassignment
Proposed by Google
82 registered teams in 33 countries
30 qualified teams
Junior winners: Polish team
Open Source and Senior winner: bosnian team
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Operations Research
Applications
Tools
OR in France
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Operations Research: Applications
The challenge ROADEF/EURO 2014
Trains don’t vanish !
Proposed by SNCF
35 registered teams
Sprint winner: students from our master
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Operations Research
Applications
Tools
OR in France
References
Operations Research: Applications
The challenge ROADEF/EURO 2015
an Inventory Routing Problem
Proposed by Air Liquide
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Operations Research
Applications
Tools
OR in France
References
http://www.roadef.org/content/roadef/soireeRO.htm
Introduction et historique de la RO
Mesure de performance de la RO
Ingrédients d’une bonne approche RO
L’enseignement de la RO
Le serious game, un outil pour convaincre
Faut-il un modèle simple ou haute fidélité? Solutions robustes
RO, SI et capacités de calcul
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Operations Research
Applications
Tools
OR in France
References
Emmanuel Guyot, Marketing Director and Revenue Management
TF1 PUBLICITE
Yves Caseau, Executive Vice-President BOUYGUES TELECOM
Animation: Denis Montaut, President Eurodécision
Nadia Brauner, President Roadef, G-SCOP
Yvon Quérou, Information Management Officer AIR FRANCE
Jean-Charles Billaut, Professor Tours University
Jean-Paul Hamon, ex Development Executive Vice-President
AMADEUS
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Operations Research
Applications
Tools
OR in France
References
Operations Research: Applications
Applications in
Design, configuration and exploitation
of complex technical systems
(communication networks, Information systems)
Supply chain management
(transportation, production, stocks. . . )
Strategic investment management
and also
health, public instruction, roadways,
mail collection and distribution,
energy production and transportation,
telecommunications, banks, insurance. . .
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Operations Research
Applications
Tools
OR in France
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Operations Research: Applications
Application domains
Production: maximize the profit taking into account the labour
availability, the market demand, the production capacity, the raw
material price. . .
Transportation: minimize the total distance taking into account
the material quantities to be transported, the conveyor capacities,
the points of fuelling. . .
I great impacts in industry:
production, transport, timetable, finance. . .
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Operations Research
Applications
Tools
OR in France
References
Operations Research
Facing a practical decision problem
Mathematical aspects
constraints, objectives, simplifications
Modeling
graphs, linear programming, CP...
Model analysis and solution
complexity analysis: what can be expected for the allocated
time?
algorithm design
Implementation and analysis of results
compare with the demand
iterate with the client if necessary
Solution deployment
Software integration
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Operations Research
Applications
Tools
OR in France
References
Plan
1
Operations Research or Decision Science
2
Applications
3
Tools
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OR in France
5
References
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Operations Research
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OR in France
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Operations Research: Tools
Linear Programming
min cost / max profit
min / max
c1 x1 + c2 x2 . . . cn xn
satisfy the demand
a1 x1 + a2 x2 . . . an xn ≥ b1
with limited resources
a10 x1 + a20 x2 . . . an0 xn ≤ b10
produced quantities
x1 , x2 . . . xn ≥ 0
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Operations Research
Applications
Tools
OR in France
References
Operations Research: Tools
Combinatorial optimization
Find the best solution among a finite but potentially very
large set of possible choices
A CO problem is characterized by:
The presence of choices, to be done among a finite set of
alternatives
A notion of cost, gain or loss
The need to make globally the right choices in order to
optimize the objective function
example: timetables. . .
Combinatorics
Truncated chess-board
http://mathsamodeler.ujf-grenoble.fr/LAVALISE/
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Operations Research
Applications
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OR in France
References
Operations Research: Tools
a
A
a
aP
A
1
PP5
A
P
PP
Aba
vertex
:
a HH
edge HHa
a
Graphs
Weight on the edges = cost, time, distance, capacity. . .
best path from i to j
best route
visiting each town
visiting each edge
...
Representation of networks, precedence constraints in scheduling
product compatibility...
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Operations Research
Applications
Tools
OR in France
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Operations Research: Tools
Other tools
Queueing theory
Stochastic problems
Simulation
Drawing from Lionel Lagarde
At the interface of
computer science: algorithmic
Mathematics: modeling
Economy: management, strategy
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Operations Research
Applications
Tools
OR in France
References
Plan
1
Operations Research or Decision Science
2
Applications
3
Tools
4
OR in France
5
References
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Operations Research
Applications
Tools
OR in France
References
Operations Research: companies in France
Large groups with a R&D department in OR
Airfrance
La SNCF
EDF
France Telecom
Bouygues
GDF Suez
La poste
Renault
Air Liquide
SFR
Google
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Operations Research
Applications
Tools
OR in France
References
Operations Research: companies in France
For the other companies
Specialized consulting companies
Off-the-shelf software
Academic laboratories
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Operations Research
Applications
Tools
OR in France
References
Operations Research: companies in France
Consulting firms
Help companies to set up decision making systems
EURODECISION
Resource optimization by means of advanced technologies in
Operational Research and Applied Mathematics
ARTELYS
Solutions in optimization
...
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Operations Research
Applications
Tools
OR in France
References
Operations Research: companies in France
Software publisher
Libraries dedicated to mathematical problems
ILOG (IBM)
Optimization tools and engines, Visualization software
components, Supply chain applications
COSYTEC
Advanced solutions and products based on constraint
programming technology for resources management &
Optimization
FICO and ARTELYS
Fico XPress: Complete range of modelling and numerical
optimization tools
Knitro: Non-linear optimization
Artelys Kalis: Constraint programming solver
...
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Operations Research
Applications
Tools
OR in France
References
Operations Research: companies in France
Software publisher
libraries dedicated to specific business problems
ALMA: Nesting
ex: petit bateau (clothes), shipyard
AMADEUS: Travel
Centralized reservation platform of travel industry and
management tools for airline companies
Optilogistics: Transportation and logistics
Software for planning and transportation optimization
Ordecsys, Oracle...
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Operations Research
Applications
Tools
OR in France
References
Operations Research: companies in France
Alma: Nesting
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Operations Research
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OR in France
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Operations Research: in France
And in the academic world
survey 2010 by Roadef
≈ 75 teams or laboratories
≈ 1400 members
≈ 700 researchers, professors and assistant professors,
permanent research engineers
≈ 500 PhD students
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Operations Research
Applications
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OR in France
References
Operations Research: to learn more
The white book of operations research in France
How do companies organize
Success stories
Consulting companies and software editors
http://www.roadef.org/
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Operations Research
Applications
Tools
OR in France
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Plan
1
Operations Research or Decision Science
2
Applications
3
Tools
4
OR in France
5
References
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Operations Research
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OR in France
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Bibliography
de Werra, D., Liebling, T.-M., and Hêche, J.-F.
Recherche Opérationnelle pour Ingénieurs, Tome 1.
Presses Polytechniques et Universitaires Romandes, 2003.
Sakarovitch, M.
Optimisation Combinatoire, Graphes et Programmation
Linéaire.
Hermann, Enseignement des sciences, Paris, 1984.
Sakarovitch, M.
Optimisation Combinatoire, Programmation Discrète.
Hermann, Enseignement des sciences, Paris, 1984.
Wolsey, L. A.
Integer Programming.
Wiley-Interscience, 1998.
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Operations Research
Applications
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OR in France
References
Webography
Courses
This presentation
http://www.g-scop.grenoble-inp.fr/~braunern
Complements
Chamilo, use the link with connection
CaseInE
Master program in OR, Combinatorics and Optimization
http://roco.g-scop.grenoble-inp.fr
RO life in France
French OR society
http://www.roadef.org
CNRS Research Group in OR
http://gdrro.lip6.fr
CO and OR seminars in Grenoble
http://www.g-scop.grenoble-inp.fr/
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Operations Research
Applications
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OR in France
References
Webography
Collection of resources for OR
http://www.ensta.fr/~diam/ro/
Software for OR
http://www.coin-or.org/resources.html
Blogs on OR
http://mat.gsia.cmu.edu/blog/
http://mat.tepper.cmu.edu/blog/
International industrial challenges in OR
http://challenge.roadef.org/
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Operations Research
Applications
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OR in France
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Operations Research
As a conclusion
Do the best
minimum cost, best profit, shortest distance, fastest. . .
With the available resources
machine time, memory, man power, raw material, truck. . .
Drawing from L. Lagarde
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