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KTH / Teknikvetenskap / Matematik / Optimeringslära och systemteori

SF2863 Systems engineering,   2012

  • Official KTH information on the course

  • Some detailed course information (KursPM)


  • Latest exams
  • Exam, June 2013
  • Solutions, June 2013,

  • Exam, December 2012
  • Solutions, December 2012 , DynP graphical solution



  • Supplementary Course Material

    Some material will be posted here during the course.
  • On spare parts optimization. (Manuscript.)
  • On marginal allocation - MALLOC. (Manuscript.)
  • The Satellite. (Manuscript.)
  • Home assignment number 1.
  • Deadline: Tuesday November 6, at 15.15 sharp !

  • Home assignment number 2.
  • Deadline: Thursday November 29, at 13.15 sharp !

  • 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.
  • Periodicity explaining the periodic property of Markov chains

    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.
  • In the classification of states of Markov chains we talked about equivalence classes.

  • Slides from the lecture on systems of queues. Queues in series and Jackson Networks.

  • Slides from lecture 8
  • on Marginal Allocation.
  • Newsboy problem and Marginal allocation
  • Deterministic dynp slides Shortest route slide
  • Probabilistic Dynamic Programming figure, explaining the recursive dependence.
  • Notes from exercise session number 6 stochastic inventory
  • NEW! Here are pdf-files for the prototype example and the various solutions to this problem presented at the lectures:
  • Notes from exercise 9 MDP example 5.8 - The dam and 5.8


  • 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 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 10.1-10.3, 18.4.
    Lecture 12:   Sections 19.1-19.3.
    Lecture 13:   Sections 10.4-10.5, 19.4.
    Lecture 14:   Guest Lecture
    Lecture 15:   Sections 19.5-19.6. (not successive approximations)


    Studentinformation