Lecture: Mathematics of Infrastructure Planning (ADM III)
	Summer Semester 2012

LV-Nr.: 3236 L 231

Prof. Dr. Dr. h.c. mult. Martin Grötschel   and   PD Dr. habil. Ralf Borndörfer

News   Downloads  Contents  Registration  Timing   Location   Prerequisites   Contact   Literature   Further Information

News

In the 2012 summer semester we will offer, in the framework of the Berlin Mathematical School (BMS), a course entitled: "Mathematics of Infrastructure Planning (ADM III)". It will be held in English, unless all participants are German speaking.

This is one of the courses offered in the series “Algorithmic Discrete Mathematics” at the Mathematical Institute of TU Berlin. The participants are assumed to be knowledgeable in the topics that are taught in the courses ADM I and ADM II. In this course the students will be made acquainted with (some of) the mathematical methods that are used to plan (and operate) infrastructure. The methodology presented is based on linear and integer programming as well as combinatorial optimization. The students will learn the theory of these methods as well as their employment in concrete examples of infrastructure planning. Lectures and exercises will be offered in an integrated way. The software necessary to treat the cases discussed will be made available. Students are assumed to solve homework exercises.

• The PDF slides of the first two lectures are now available (see Downloads).
• You can also download a virtual machine where we have already installed SCIP, SoPlex, and ZIMPL which you will need for the exercises.

• Stefan Heinz's survey of the ZIB Optimization Suite (second half of the lecture of April 16) is ready for download (PDF file).
  
• First homework assignment:
  "Given an undirected graph G=(V,E), find a system of inequalities and/or equations (plus integrality and/or 0/1-constraints) that guarantees that, for every node w in a given subset W ⊂V, the number of edges that contain node w is
  (a) zero or two. Find also such a system that guarantees that the number of edges containing w is
  (b) nonnegative and even.
  Please deliver solutions of 1 (a) and 1 (b) on April 19 at the beginning of the class.

• The next two exercises (and the data for the exercise 2) can be downloaded.

• The sheets of the lecture of April 19 can be downloaded, as well as a ZIMPL model and the data.

• The next exercises can be downloaded.

FYI:
The SCIP developers team is constantly trying to improve both the software and the documentation of the ZIB Optimization Suite. Every participant is kindly invited to report troubles they might have had when using Zimpl, SCIP or Soplex, or suggestions how to improve the documentation by sending an email to hendel@zib.de. Those suggestions will be collected and made available online as soon as possible.

• The requested lecture notes of Ralf Borndörfer can be downloaded (handwritten).

• The first half of the class on May 10 will be given by Dr. Ann Bixby. Ann has a MS and a PhD in Industrial Engineering from Northwestern University. (She took optimization courses at TU Berlin as an exchange student 1991-1992 and is the daughter of Bob Bixby, the co-founder of CPLEX and Gurobi.) Ann has worked for Aspen Technology since 2000 and is currently Supply Chain Advisor/North America Supply Chain Team Lead. She will report about a project with a beef manufacturer and about her job and career in general.

• The PDF slides of the May 3 and 7 lectures and the Exercise sheet 4 are available (see Downloads).

• Room change: Please observe that the lecture of May 10 will take place in the following room of the BMS floor of the TU math building: MA 212.
• All participants of the class are invited to the Matheonfest on May 10 that will start at 19:00 in the TU Audimax (be there in time).
• All participants of the class are invited to the Euler Lecture in the afternoon of May 11 in Potsdam.
• The PDF slides of the lectures on May 3 and 7 have been updated (see Download of May 3, 2012)

• The exercise sheets 5 and 6 are available (see Downloads).

• The PDF slides of the "Graph Colouring and Frequency Assignment" lecture, partly presented on May 10, are available (see Downloads).

• The PDF slides of the "FTTx network planning" lecture, presented on May 14, are available (see Downloads).

• The data concerning exercise sheet 5 can be downloaded now (see Downloads)
• The exercise sheet 7 (exercises 20-25) is available, see Downloads.

• We exchanged the data concerning exercise sheet 5, see the same Downloads of May 21, 2012.

• The PDF file of the paper "Design of Survivable Networks" (authors: Grötschel, Monma, Stoer (1995)) we will talk about today, is available, see Downloads.
• The PDF file of the paper "Integer Polyhedra Arising from Certain Network Design Problems with Connectivity Constraints" (authors: Grötschel, Monma (1990)) is available too, see Downloads.
• Exercise sheet 8 is available (exercises 26-29), see Downloads.

• The 21st International Symposium on Mathematical Programming (ISMP 2012) will take place in Berlin August 19-24, see http://ismp2012.mathopt.org. Students who are interested in helping to organize the conference, please contact Madeleine Theile (mailto: theilemath.tu-berlin.de).
  This job will be governed by a dedicated contract with TUBS and is, in particular, independent of a student assistant position that you might already have, e.g., at ZIB or TUB.
  Questions about payment, available jobs, health insurance issues etc. can be discussed with Madeleine.
• The requested lecture notes (lecture of May 21 and lecture of June 4, 2012) of Ralf Borndörfer can be downloaded (handwritten).

• Next Thursday, June 14, 2012 our first "Matheon Industry Seminar" will take place at TU Berlin, room MA 041, start: 17:00 h. Ivo Nowak (Lufthansa Systems) will talk about "Robust Airline Planning". More information can be downloaded (see Downloads).
• The status quo of your credit points is available under the item Further Information.

• Exercise sheet 9 can be downloaded, see Downloads.

• Exercise sheet 10 and corresponding data can be downloaded, see Downloads.

• The PDF slides "Verkehrsoptimierung: Umlaufplanung & Dienstplanung" that were presented in the lecture on June 11 are available (see Downloads).

• Exercise sheet 11 can be downloaded, see Downloads.

The lecture notes (lecture of June 18, 2012) of Ralf Borndörfer can be downloaded (handwritten), see Downloads.

• Two sets of PDF slides about "Gas Network Optimization" that were presented in the lecture on June 21 are available, see Downloads.

• Concerning Oral Examinations:
  Two days for oral examinations are offered by R. Borndörfer and M. Grötschel: Monday, July 23 and Tuesday, July 24, 2012.
  For each exam, 45 min. are scheduled. Every day, starting at 9:00 h there will be four examinations up to 12:00 h, and further six examinations from 13:00 to 17:30 h.
  If you want to participate, send an e-mail with your full name, study program and Matrikelnummer to Bettina Kasse, kasse@zib.de.
  The order is first come first served, i.e., whoever sends the first e-mail will be examined on Monday at 9:00 h, and so on.
  All examinations will take place at Konrad-Zuse-Zentrum in room 3034.

• The Lecture notes of Benjamin Hiller (lecture of June 25, 2012) can be downloaded, see Downloads.

• Exercise sheet 12 can be downloaded, see Downloads.

• Exercise sheet 13 can be downloaded, see Downloads.

• FYI: Next optimization seminar will take place on Wednesday, July 4, 2012, 14:00 h, at Zuse Institute, room 3028.
  Speaker: Marco Blanco, ZIB
  Title: "LP-based approximation algorithms for the capacitated facility location problem"
  Abstract:
  One of the most prominent open problems in the area of approximation algorithms is finding a linear programming based, constant factor approximation algorithm for the capacitated facility location (CFL) problem. In this talk, I present some partial results that make progress on this question. I will describe an LP-rounding algorithm inspired on the work of Levi, Lodi and Sviridenko; as well as a primal-dual schema that generalizes the algorithm for single demand CFL by Carnes and Shmoys. This is joint work with Ricardo Fukasawa, Jochen Könemann and Zacharias Friggstad and was carried out during the preparation of my Masters thesis at the University of Waterloo.

• The lecture notes (lecture of June 28, 2012) of Marco Blanco can be downloaded (handwritten), see Downloads.

• FYI:
  Registration deadline for the organization of the oral examinations in ADM III at Zuse Institute Berlin (July 23 and July 24, 2012 at ZIB, room 3034): July 15, 2012, 23:59 h!
  Please note that you have to register for the oral exam at the "Examination Office, Team 2, of TU Berlin.
  

• The lecture notes (lecture of July 9, 2012) of Ralf Borndörfer can be downloaded (handwritten), see Downloads.

• FYI:
  Examinations concerning this lecture took place on July 23/24. Congratulations to all participants who passed successful the exam.
  We offer a second examination date for students who were unable to take part on July 23/24.
  Those students can register for oral exam in ADM III at Zuse Institute on October 9 or October 12, 2012. Please send an email to kasse@zib.de.
  

Downloads

• April 13, 2012: PDF slides of the lectures of April 12 and April 16, 2012
• April 13, 2012: Virtual Machine (2 GB) (README.txt)
• April 17, 2012: Survey of the ZIB Optimization Suite
• April 19, 2012: Exercise sheet 1, Exercise sheet 2, Data concerning exercise sheet 2
• April 20, 2012: PDF slides of lecture of April 19, ZIMPL model, Data
• April 26, 2012: Exercise sheet 3
• April 27, 2012: Lecture Notes of April 23 and 26 (handwritten)
• May   3, 2012: PDF slides of May 3 and 7 lectures, Exercise sheet 4
• May 10, 2012: Exercise sheet 5, Exercise sheet 6
• May 14, 2012: PDF slides of "Graph Colouring and Frequency Assignment" lecture
• May 15, 2012: PDF slides of "FTTx network planning" lecture
• May 21, 2012: Data concerning exercise sheet 5, Exercise sheet 7
• May 31, 2012: PDF files: "Design of Survivable Networks", and "Integer Polyhedra Arising from Certain Network Design Problems with Connectivity Constraints",
                         Exercise sheet 8
• June   5, 2012: Handwritten lecture notes of Ralf Borndörfer: Lecture of May 21, 2012, lecture of June 04, 2012
• June   6, 2012: Detailed information about the first "Matheon Industry Seminar".
• June   7, 2012: Exercise sheet 9
• June 14, 2012: Exercise sheet 10, Data concerning exercise sheet 10
• June 18, 2012: PDF slides "Traffic Planning" of June 11
• June 19, 2012: Exercise sheet 11
• June 20, 2012: Handwritten lecture notes of Ralf Borndörfer: Lecture on June 18, 2012
• June 21, 2012: PDF slides "Gas Network Optimization", Part I and Part II of June 21
• June 27, 2012: Lecture notes of Benjamin Hiller: Lecture on June 25, 2012 and Exercise sheet 12
• July    2, 2012: Exercise sheet 13
• July    4, 2012: Handwritten lecture notes of Marco Blanco: Lecture on June 28, 2012
• July 17, 2012: Handwritten lecture notes of Ralf Borndörfer: Lecture on July 9, 2012

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Content

Our modern society relies on the availability of efficient infrastructure for communication, transportation, energy and water supply, health care, to mention just a few examples. Infrastructure is expensive; infrastructure design has a long term impact and many decisions are almost irreversible.

Today, infrastructure design is usually in the hands of politicians and planning engineers; mathematics rarely plays a significant role. However, due to the long term effects and the costs involved it is mandatory to use great care in the associated decision making processes (if possible using appropriate mathematical tools) in order to obtain best possible results and to ensure optimal usability. Topics of this type will be addressed in this course. Students will learn how to approach infrastructure planning problems and how to model the problems arising as optimization problems. They will study the solution methods available and in what size ranges infrastructure problems can be attacked today. At the end of the course the students should be able to address significant problems of infrastructure planning on their own and should have learnt with which methods they can be handled.

The focus of the mathematical methodology taught in this course will be on integer and combinatorial optimization. Nonlinear and stochastic optimization models will be addressed as well.

Applications of infrastructure planning abound. We just mention issues such as: network and line planning in public transport, facility location, gas pipeline and electricity network design, city toll and parking space control, traffic light control and route guidance, electronic ticketing, intermodal transport and railway network capacity auctioning. Under this heading long term planning for infrastructure concentration and deconstruction (for instance for an aging society) or long term staff recruitment can be treated as well.

Several of these practical problems have been addressed in projects at the Zuse Institute and will be mentioned in the course. Some will be introduced in detail.

We will also provide the data of some practical examples and expect the students to solve these with software such as ZIMPL and SCIP which will be made available to all participants. Exercises will be integrated into the lectures. The students are expected to solve homework assignments.

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Registration

Students will be requested to register during the first lecture. Arrangements for homework assignments will discussed during that as well.

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Timing

Two classes of ninety minutes per week, on Monday and Thursday, starting at 16:15 h.

First lecture on Thursday, April 12, 2012 at 16:15 h.

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Location

The lecture will take place at: TU Berlin, Math Building, room MA 313.

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Prerequisites

Knowledge in computer-oriented mathematics (COMA), combinatorial linear and integer programming (ADM I and ADM II) is expected.

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Contact



Office	Name	Consultation-hours	Room	Phone	Email
Office at TU Berlin:	Martin Grötschel	on appointment	Room: MA 302	314-23266	Please use: groetschelzib.de
Office at Zuse Institute:	Martin Grötschel	on appointment	Room: 3025	84185-210	groetschelzib.de
Office Zuse Institute:	Ralf Borndörfer	on appointment	Room: 3033	84185-243	borndoerferzib.de

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Literature

There is no book that covers the content of the course. Bibliographies will be provided for each chapter of the class. In general, students should make themselves familiar with the software provided within the ZIB Optimization Suite.

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Further Information

The lecture is classified as an ADM III course with 10 ECTS credit points and is an advanced Berlin Mathematical School (BMS) class.
Please, find here the status quo of your credit points.
Criteria for scientific acquisition:
50 % of the exercise points.

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Last changes: August 2, 2012