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SF2863 Systems engineering,   2013

  • Official KTH information on the course

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

    Please note that the LP formulation for determining the optimal policy for Markov decision processes will not be examined this year.

  • Some detailed course information (KursPM)


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

  • Exam, January 2014
  • Solutions, January 2014,


    • Home assignments

  • Home assignment number 1.
    • Deadline: Wednesday November 20, at 13.15 sharp !

  • Home assignment number 2.
    • Deadline: Friday December 13, at 13.15 sharp !
    Correction: In question one, "marginal increase in expected downtime" should be replaced with "marginal decrease in EBO".
    Since many people have difficulties in forming groups of four I have made a doodle to try to help you on this. If you are in a group smaller than 4 persons, enter your names in the doodle and help other students to form the groups, group generation.


    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.
  • 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.
  • The Perron-Frobenius theorem is an important Theorem in the field, but is not included in the course, for furter 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.
  • More on Poisson processes, and you find the Hitchhikers paradox mentioned at lecture 3 on page 14-15, and the three different definitions of Poisson processes showed at lecture 4 on page 3.
  • Kendall's queueing systems notation.
  • Slides from the lecture on systems of queues. Queues in series and Jackson Networks.
  • Slides from lecture 7
    • on Marginal Allocation.
  • Slides from lecture 9
    • on METRIC model.
  • Lecture 10 Newsboy problem and Marginal allocation

  • Lecture 11 Deterministic dynp slides Shortest route slide
  • Lecture 12, 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 presented at the lectures:
    • Description Description (short) Formulation of the prototype example and all stationary solutions
    • Policy improvement policy improvement of the MDP policy optimization
    • Policy improvement with discounting policy improvement of the discounted MDP policy optimization
    • From the last class, about LP formulation. Please note that there will be no examination on the LP formulations. LP LP-formulation of the MDP policy optimization


    Supplementary Material from Exercises

  • The Satellite. (Manuscript.)
    This material will be used on tuesday November 26.
  • 2.5c solution to one of the problems in exercise session nr 2. (that was not finished due to the time constraint)
  • Exercise session 6 Distributing Scientists problem formulation




  • Last years version of the formula sheet for the exam . It will be similar this year too.
  • Recommended exercises.
  • Errata for the exercises 2010. (Old version) The errors in the 2010 version have been corrected in the 2011 version. Let me know if you find some errors in the 2011 version, (or other manuscripts), and I will publish corrections here.
  • 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, 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
  • Exam in SF2862 (not SF2863), June 2009.
    (ex. 3 is not so relevant for our course)
  • Solutions, June 2009.
  • Exam in SF2862 (not SF2863), March 2009.
    (ex. 3 is not so relevant for our course)
  • Solutions, March 2009.

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

    Lecture 1:     Sections 1.1-1.3, 16.1-16.7.
    Lecture 2:     Sections 16.8, 17.4.
    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 2 and 5.
    Lecture 7:     On marginal allocation (manuscript)
    Lecture 8:     On spare parts optimization (manuscript) sections 3-4.
    Lecture 9:     Sections 18.1-18.3, and problem 18.3-11.
    Lecture 10:   Sections 18.7.
    Lecture 11:   Sections 18.4, 10.1-10.3
    Lecture 12:   Sections 10.4-10.5, 19.1-19.2, 19.4
    Lecture 13:   Sections 19.5.
    Lecture 14:   Guest Lecture
    Lecture 15:   Sections 19.3, 19.5. (not successive approximations)

    Studentinformation