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Methods for Tackling the Timetabling Problem

Timetabling belongs to the class of constraint satisfaction problems and is essentially an example of a resource-constrained scheduling problem, which is NP-hard [19, 5]. Here, resources are physical entities, for example: students, rooms, overhead projectors, and so on. Time periods can also be thought of as resources.

In general, timetabling problems are always NP-complete [18], which means there is no known algorithm that can find an optimal solution in a time that is bounded by a polynomial of the problem size. As a result, these problems are often solved by means of heuristics - solution procedures that focus on finding a feasible schedule of ``good'' (as opposed to optimal) quality within an acceptable amount of time.

Traditionally, timetabling has been approached by means of linear programming (LP) with binary variables, plus some heuristics. For example, if i identifies a teacher, j identifies a time interval and k identifies a class then the binary variable tex2html_wrap_inline2239 if teacher i has class k at time-interval j; tex2html_wrap_inline2247 otherwise. Suppose we have a set of data as small as 20 teachers, 30 time intervals, and 10 classes. If we use the LP approach to obtain a feasible schedule out of this data, then we need to deal with over 6000 variables to represent the problem, and tex2html_wrap_inline2249 possible states. Clearly the problem becomes intractable even for very small numbers of variables.

 




Saleh Elmohamed
Thu Sep 4 11:43:55 EDT 1997