Mathematical investigation of a model of the school timetabling problem

  • David Tomkins

    Student thesis: Doctoral ThesisDoctor of Philosophy


    The task of constructing school timetables - which is
    a laborious one - seems an obvious problem for a computer. The
    early attempts to solve this problem were simply of a ‘trial and
    error' type and did not depend upon any mathematical theory.
    However, it soon became evident that the problem could be formulated
    in precise mathematical terms - but only at the expense of simplifying
    the timetable requirements.

    The development of analytical models suggests the
    desirability of finding criteria which will determine, at every
    stage of the construction of a timetable, whether or not it is
    susceptible of being completed.

    No such criteria have as yet been found, and the
    problem may well prove to be insoluble in general.

    In this thesis the known models have been surveyed and
    have been compared with the requirements of a timetable in an actual
    school. These requirements are described in detail. An attempt has
    then been made to consider how the analysis of a realistic timetable
    can be carried further and what kind of mathematical techniques are
    applicable to the problem.

    There appear to be two aspects of the problem:
    i) to discover the above criteria and so enable the ‘ideal’ computer
    timetabling system to be developed;
    ii) to develop an efficient ‘compromise’ solution.
    To facilitate the search for the required criteria we
    define a mathematical structure which we have called a Latin Form.
    This enables us to apply some of the language and results of
    transversal theory to the problem.

    A ‘compromise' procedure is described and illustrated
    by reference to different parts of a school - sixth form, upper and
    lower school - systematically linked.

    It is further shown how the search for solutions to
    some particular timetabling problems may be greatly facilitated
    by the use of graph theory, transversal theory and Latin Forms.
    Date of Award1972
    Original languageEnglish


    • Mathematical investigation
    • model
    • school timetabling problem

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