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SF2863 Systems engineering,   2015

  • Official KTH information on the course

    • This page is updated during the course to provide the latest information and material.

    Latest exam
  • Exam, January 2016
  • Solutions, January 2016,

  • Exam, March 2016
  • Solutions, March 2016,



    • For information about the practical details regarding exams; signing up, placement et.c. see the student affairs office

  • Some detailed course information (KursPM)



    • Home assignments

    Here the home assignments of the course will be posted.
    The first home assignment is now available:
  • Home assignment number 1. Updated version. (question 9 in old version is cancelled, and somethings are now explained more carefully)
    • Deadline: Wednesday November 25, at 17.00 sharp !

    Formation of groups and final report submission
    I have now set up a course page at BILDA that will be used to organize the groups and homework logistics, called SF2863. I am new to this so let me know if it is not working properly. This is how I planned that everything should work:
    When you log in to Bilda on the course page you can join a group for the homeworks. There are two versions of the homework and there are two different sets of groups, HAxx and HByy. Join the first available group. (With lowest number of xx or yy, so that we fill up the groups from beginning and have the same number of A and B groups if possible. If you already started on one of the version (A/B) you should choose the first one available in that category.) Each group should have two members and you should coordinate with somebody to work with. (unless you have special reasons to do it alone).

    Since some people have difficulties in finding a coworker for the homework, I have made a doodle to try to help you on this. If you are looking for somebody to work with, enter your emailadress in the doodle and help other students to form groups, group generation. Note that this doodle is only for finding a homework partner, then you should log in to Bilda and join a group together.

    The second homeassignment is now available.
  • Home assignment number 2.
    • Deadline: Friday December 11, at 17.00.

    More information about how to to submit your report will be given later.
    Doodle for group generation This time we will not accept groups with just one person.


    Supplementary Course Material

    Some material will be posted here during the course.
  • On spare parts optimization. (Manuscript.)
  • On marginal allocation - MALLOC. (Manuscript.)


    • Supplementary Material from Lectures

  • Introduction slides from the class.
    These slides are used to describe the course, and then the rest of the first lecture will be used to introduce discrete time Markov chains.
    The first two-three lectures will be a brief introduction to Markov processes, so for students who have taken a Markov process course there will be some repetition.
  • Matlab example illustrating the different possibilities for the behavior of the n-step transition matrix when n, the number of steps, grows large.
    For those who are extra mathematically interested you may have a look at these concept mentioned during the classes.
  • In Lecture 2 we use results that are derived from the The Perron-Frobenius theorem. It is an important Theorem in the field, but is not included in the course, for further info see, e.g., Wikipedia.
  • Periodicity explaining the periodic property of Markov chains
  • In the classification of states of Markov chains we talked about equivalence classes, and use the slide
  • duel example, from Lecture 2.
  • More on Poisson processes, and you find the Hitchhikers paradox mentioned at lecture 4 on page 14-15, and the three different definitions of Poisson processes showed at lecture 4 on page 3.
  • Kendall's queueing systems notation introduced at Lecture 4.
  • Slides from the lecture on systems of queues. Queues in series, product form solution and Jackson Networks. Derivation of Global Little's formula from the local version.
  • Slides from lecture 8
    • on Marginal Allocation.
  • Lecture 10 Newsvendor problem and Marginal allocation

  • Lecture 11 Deterministic dynp slides Shortest route slide
  • Lecture 13, Probabilistic Dynamic Programming figure, explaining the recursive dependence.
  • Here are pdf-files for the Markov Decision Process prototype example and the various solutions to this problem that will be presented at the last lectures:

    Supplementary Material from Exercises

  • The Exercise book is available on KTH Social.

    Exercises that will be solved in class
  • Exercise class 1: Markov processes 1.4a,b, 1.11, management of construction equipment, Cat and Mouse problem.
  • Exercise class 2: Queueing theory 2.10a-d, 2.5a-c, and 2.11 a-b.
  • Exercise class 3: Jackson networks 2.1, 20120612-1
  • Exercise class 4: Marginal allocation - The satellite. The Satellite. (Manuscript.)
  • Exercise class 5: Inventory theory, Taxi-driver EOQ with discount, 3.3 Newsvendor
  • Exercise class 6: Inventory theory 3.5, deterministic review model - Boat problem, selling oil 20080530-2
  • Exercise class 7: Dynamic programming, Knapsack problem 5.5, Distributing Scientists
  • Exercise class 8: DynP 4.4 extended version, Markov decision problems 20120612-3 if time allows
  • Exercise class 9: Markov decision problems with discount

    Some material from the exercise classes will be posted here during the course.
  • State classification, OH shown during exercise session 2.
  • The Satellite. (Manuscript.)
    This material will be used on exercise session 4, Monday November 23, and we recommend that you read through it before.



  • Last years version of the formula sheet for the exam . It will be similar this year too.
  • Recommended exercises. UPDATED!
  • Some basic results from Probability theory
    (If you have some more questions on these things, send me an email) For a longer description, see the web text pages of the course book, Chapter 24.

    • Old exams

  • Exam, April 2015
  • Solutions, April 2015,

  • Exam, January 2015
  • Solutions, January 2015,

  • Re-exam, March 2014
  • Solutions, March 2014,

  • Exam, January 2014
  • Solutions, January 2014,

  • Exam, June 2013
  • Solutions, June 2013,
  • Exam, December 2012
  • Solutions, December 2012 , DynP graphical solution
  • Exam, June 2012
  • Solutions, June 2012
  • Exam, December 2011
  • Solutions, December 2011
  • Exam, June 2011
  • Solutions, June 2011
  • Exam, December 2010
  • Solutions, December 2010
  • Exam, June 2010
  • Solutions, June 2010
  • Exam, December 2009
  • Solutions, December 2009

    • Suggested reading in the book before (or after) the lectures:

    Please note that in the 10th edition Chapter 16 is called 29 and is not in the physical book, but available as a pdf web chapter. Here are links to the web chapters for both 9th edition and 10th edition When you buy the book you get an access code.

    Lecture 1:     Course introduction. Markov chains
                            9th edition:   Sections 1.1-1.3, 16.1-16.3.
                            10th edition: Sections 1.1-1.3, 29.1-29.3,
    Lecture 2:     Markov processes
                            9th edition:   Sections 16.4-16.5, 16.8.
                            10th edition: Sections 29.4-29.5, 29.8
    Lecture 3:     Sections 17.1-17.5
    Lecture 4:     Section 17.6,
    Lecture 5:     Section 17.9,
    Lecture 6:     On spare parts optimization (manuscript) sections 1 and 5.
    Lecture 7:     On marginal allocation (manuscript)
    Lecture 8:     On spare parts optimization (manuscript) sections 2.
    Lecture 9:     Sections 18.1-18.3.
    Lecture 10:   Sections 18.7, 18.4.
    Lecture 11:   9th edition  : Sections 10.1-10.3,
                        10th edition: Sections 11.1-11.3
    Lecture 12:   9th edition  : Sections 10.4-10.5, 19.1-19.2
                        10th edition: Sections 11.4-11.5, 19.1-19.2,
    Lecture 13:   9th edition  : Sections 19.4.
                        10th edition: supplement 1
    Lecture 14:   Guest Lecture
    Lecture 15:   9th edition  : Sections 19.5.
                        10th edition: supplement 2