Welcome to the course!
- The first lecture is given on Tuesday 20 March 2018 at 10:00–11:45 in the lecture room Euler.
- (180320) Downloads for Lecture 1
- (180321) Downloads for Lecture 2
- (180321) Assignment 1 is now published, under Assignments
- (180323) Downloads for Lecture 3
- (180410) Downloads for Lecture 4
- (180411) Downloads for Lecture 5
- (180413) Downloads for Lecture 6
- (180413, afternoon) Updated downloads for Lecture 6
- (180417) Downloads for Lecture 7
- (180417) Downloads for Lecture 8a
- (180417) Downloads for Lecture 8b
- (180417) Note that you need to define a project group (of maximum two persons) in PingPong to be able to hand in your project report. Since PingPong requires some "hand work" after the group definition has been done, you should no longer hesitate to do this
- (180418) The second course evaluation meeting will be held on Friday, May 4 at 12:15–13:00 in room MV:L12.
- (180419) Don't forget to hand in your individual collaboration report on Assignment 1 before 23:55 today
- (180419) Assignment 2 is now published, under Assignments
- (180420) A complementary illustration for Lecture 8b, slide 10/21
- (180423) Downloads for Lecture 9
- (180424) Downloads for Lecture 10
- (180425) Reminder: Check feedback on Assignments 1, deadline for revision is 4th of may, see PingPong for details.
- (180427) Updated links in the downloads for Lecture 10
- (180502) Due to technical issues the deadlines for Assignment 2 have been postponed for one day; check PingPong for the new deadlines.
- (180502) Downloads for Lecture 11
- (180503) Downloads for Lecture 12
- (180507) Assignment 3a has been slightly updated; see Assignments
- (180507) Downloads for Lecture 13
- (180508) Course literature on Multiobjective Optimization: Copies from the book Optimization in Operations Research by R. L. Rardin (1998) pp. 373–387, are kept outside Ann-Brith's office, room MV:L2087. Make sure to get your (paper) copy – or other relevant literature on Multiobjective Optimization.
- (180508) Notes from the mid-course evaluation meeting are now published in PingPong
- (180514) Downloads for Lecture 14
- (180514) The detailed schedule for the oral presentations of Assignment 3 is now published, under Assignments
- TimeEdit schedule. Note that there will be mandatory presentations during week 21 (May, 21–25) which are not yet in this schedule.
- For your assignment work, Linux lab-rooms are reserved; see the TimeEdit schedule. Presence is not mandatory but teachers will be available at times published under Latest news.
- The course has an activity page in PingPong which will be used for the hand-in of all assignments.
Examiner and lecturer
Professor, Mathematical Sciences
Email: email@example.com, Tel: 772 5378, Room: L2087
Exercise assistant and assignment advisor
Ph.D. student, Mathematical Sciences
Email: firstname.lastname@example.org, Tel: 772 1094, Room: L2033
Exercise assistant and assignment advisor
Industrial Ph.D. student, Mathematical Sciences and Fraunhofer-Chalmers Research Centre for Industrial Mathematics
Email: email@example.com, Tel: 772 4275 or 772 1094, Room: L2033,
The course (i) and exercise (ii) books are available in both Swedish and English and sold by Cremona.
Complementary material (iii) (mainly from the book Optimization in Operations Research by R. L. Rardin; Prentice-Hall, 1998) will be handed out during the course.
- English version:
- Swedish version:
Course plan and contentsPreliminary course plan (180313) including time plan and deadlines.
Lecture notes are published regularly under Latest news.
Recommended exercises—problem solving sessions (the list below is updated each week).
Note that there are two options each week for the problem solving sessions, of which you are typically assumed to visit at most one. Typically, Wednesday sessions are given by Edvin and Thursday sessions by Quanjiang.
|Session||Dates||Topics||Recomended Exercises||Teacher exercises|
|1||21/3, 22/3||Mathematical modelling||3.1 b,c,d; 3.5, 3.10, 3.12, 3.15||3.1 a,e,f; 3.4, 3.6, 3.14|
Linear optimization and the simplex method
||2.4, 2.6, 4.2, 4.6, 4.10, 4.11, 4.15||4.5, 4.13|
Sensitivity analysis and duality theory
||5.1, 5.5, 6.6, 6.8, 6.10, 6.15||5.4|
|4||25/4, 26/4||Integer linear optimization and the branch-and-bound algorithm||
13.5, 13.6, 13.9, 15.6
(13.8, 13.15, 15.3, 15.12, 15.14)
Cutting plane methods, minimal cover, Lagrangean duality
14.4, 14.8, 17.9
(14.1, 14.3, 14.6, 14.9, 17.8)
|6||9/5||Network optimization: minimum spanning tree and shortest path algorithms||8.10, 8.12, 8.17a (8.18, 8.38ab)||examples|
|7||16/5, 17/5||Nonlinear optimization: convexity and the KKT conditions||9.8, 9.10, 11.4, (9.4, 11.6)||11.3|
Computer exercises and software
- Linear optimization and software
In order to prepare for the assignments, you are recommended to do this computer exercise on linear optimization and software.
- AMPL and optimization solver software
- There are licenses for AMPL/CPLEX installed on Chalmers Linux system. For use of these licenses within the course, start by printing the command vcs-select -p ampl-MVE165-20180125 in a terminal window
- AMPL licenses including several optimization solvers to install on your private computer can be downloaded from the the course's PingPong event. This software is time limited and may only be used within the course.
The modelling language AMPL is described in the book AMPL: A Modeling Language for Mathematical Programming, which can be downloaded as pdf-files.
- AMPL-CPLEX User's Guide
The user's guide is available here.
Reference literature for Matlab
Tobin A. Driscoll, Learning MATLAB, ISBN: 978-0-898716-83-2 (published by SIAM)
- Integer linear optimization software
A java-applet (10MB) for learning the branch-and-bound algorithm for solving integer optimization problems.
- Beware that this is a beta-version (developed in a bachelor's project)
- To run on Linux: Download the file and place it in a suitable folder. Open a terminal window and move to the folder where the jar-file is placed. Type ' java -jar BandBWithTSP.jar '.
- Assignments are performed in groups of (maximum) two persons.
- The project groups must be defined on the course's activity page in PingPong under "Project groups".
- Observe that the name of your project group must be exactly "FirstName1 Surname1 - FirstName2 Surname2".
- Deadlines for handing in the reports are indicated in the course plan.
- Oral presentations of Assignment 3 will be held by the students during week 21 (23–24 May).
- Detailed schedule for the presentations.
- Assignment 1—Biodiesel supply chain
- Assignment information
- AMPL directives for sensitivity ranging are found in Chapter 8 in the AMPL-CPLEX User's Guide
- Assignment 2—Application to maintenance scheduling
- Assignment information
- Links to the articles (reachable from Chalmers' domain):
- Almgren, Andréasson, Patriksson, Strömberg, Wojciechowski, and Önnheim (2012): "The opportunistic replacement problem: theoretical analyses and numerical tests"
- Gustavsson, Patriksson, Strömberg, Wojciechowski, and Önnheim (2014): "Preventive maintenance scheduling of multi-component systems with interval costs"
- AMPL-files: uh.run, uh-stor.mod, uh-stor.dat, uh-small.mod, uh-small.dat, cgcut.mod
- Link to AMPL users guide with CPLEX directives
- Assignment 3
- Note that you should choose a time slot and a specific assignment from the doodle before you start working with the assignment.
- Each group chooses one of the Assignments 3a–3b from a "doodle" revealed in PingPong, under "Assignments", from 18:00, Friday, May 4. This choice also determines the time when your assignment is to be orally presented. Your choice must be made at the latest on Monday, May 7 – after that, the doodle poll will be closed.
- Each group shall then present their assignment during ~12 minutes, including time for questions. A laptop and projector will be available for the presentations.
- You will be asked to provide (written) feedback on each others oral presentations. This will be organized during the respective seminars.
- Note that presence is mandatory at one full seminar (i.e., approximately 90 minutes).
- The seminar hours are Wednesday 23rd of May 10–12, 13–15, and 15–17, and Thursday 24th of May 10–12.
- A detailed schedule for the oral presentations will be published here.
- Assignment 3a - Windpower investment and generation
- Assignment 3b - The Scandinavian electricity system
The course content is defined by the literature references (i), (ii), and (iii) in the course plan. The importance of each moment of the course is defined by the respective emphasis given by the lectures, exercises, and assignment tasks.
- In order to pass the course, the student should provide (in
groups of maximum two persons):
- written reports of three assignments,
- (individually) a written opposition to Assignment 2, and
- an oral presentation of Assignment 3.
- Presence is compulsory at at least one full seminar occasion (2*45minutes, Students' presentations of Assignment 3, week 21).
The oral presentations of Assignment 3 are held by the students during week 21 (the specific scheduled TBD)
- To be able to receive a grade higher than 3 or G, the written reports and opposition as well as the oral presentation must be of high quality. Students aiming at grade 4, 5, or VG must also pass an oral exam.
- The oral exam will cover the theoretical material, including problem solving, as defined in the course plan for the books by Lundgren et al. and Henningsson et al., and including the supplementary material on multiobjective optimization (from Rardin's book). The emphasis on the different subjects is mainly defined by the notes from the lecture series of the theoretical material and from the problem solving sessions.
The oral exam is organized as follows:
- The student receives 4–5 exercises and may study these for 1/2 hour in a separate room.
- The oral examination will then take place for 1/2 hour.
- No equipment except for pen, ruler, rubber, and paper are allowed during any part of the oral exam.
- The oral exams are given during the exam weeks, on the dates 28/5, 31/5, 1/6, and 4/6. Each student eligible for the oral exam will receive and invitation to sign up for this.
The randomly selected course representatives are presented in PingPong.
Being a student representative means that you are responsible for evaluating the course together with the examiner/course responsible and the program board of the program that gives the course.
The evaluation process consists of three parts:
- The student representatives and the teacher are expected to have two informal meetings during the course. The first one should be in the first study week, the second one after approximately half the course. The first meeting is mostly for you to get acquainted, the second one are for the student representatives to give feedback to the teacher on the progress of the course.
- After the course an evaluation questionnaire is sent out. The examiner will get a chance to add extra questions to the standard questionnaire.
- After the course, there will be an evaluation meeting where the student representatives and the examiner/course responsible for the course have a meeting together with the program board of the program who gives the course, discussing the courses' advantages and potential for improvement. This meeting will be held in study week 3–6 in the study period after the examination. The examiner invites the participants to this meeting.