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SF2863 Systems engineering,   2014

  • Official KTH information on the course

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



  • Some detailed course information (KursPM)


    • Latest exams
  • Exam, April 2015
  • Solutions, April 2015,

  • Exam, January 2015
  • Solutions, January 2015,


    • Home assignments

    Here the home assignments of the course will be posted.
    The first home assignment is now available:
  • Home assignment number 1.
    • Deadline: Thursday November 20, at 13.15 sharp !
    The last theory needed for the home assignment will be covered on Lecture 3, November 11.
  • Home assignment number 2.
    • Deadline: Tuesday December 16, at 13.15 sharp !

    Doodle for 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.
    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.
  • 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 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, 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 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 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, 2.13
  • Exercise class 4: Marginal allocation - The satellite. The Satellite. (Manuscript.) This material will be used on thursday November 27.
  • Exercise class 5: Inventory theory, EOQ with discount
  • Exercise class 6: Inventory theory 3.5, deterministic review model - Boat problem
  • Exercise class 7: Dynamic programming, Knapsack problem 5.5, Distributing Scientists
  • Exercise class 8: DynP, Markov decision problems
  • Exercise class 9: Markov decision problems with discount




  • 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

  • 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:

    (This is updated as we go along for 2014)
    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 on the web When you buy the book you get an access code.

    Lecture 1:     Sections 1.1-1.3, 16.1-16.3.
    Lecture 2:     Sections 16.4-16.5,16.8,
    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 13:   9th edition  : Sections 19.4.                     10th edition:
    Lecture 15:   9th edition  : Sections 19.5.
                        supplement 2

    Studentinformation