The Timetabling Problem

A problem that does not have a well-defined objective function (as in the traveling salesman problem (TSP), for example) to optimize and belongs to the class of constraint satisfaction problems is the NP-complete <#285#>professors and classes<#285#> timetabling problem [#2##1#, #3##1#, #27##1#]. Briefly, the general problem is stated as follows: For a certain school with #tex2html_wrap_inline1558# professors, #tex2html_wrap_inline1560# classes, #tex2html_wrap_inline1562# classrooms and lecture halls, and #tex2html_wrap_inline1564# students, it is required to schedule #tex2html_wrap_inline1566# professor-class pairs within a time limit of #tex2html_wrap_inline1568# time slots producing a legal schedule. A legal schedule needs to be found such that no professor, class, or student is in more than one place at a time, and no room is expected to accommodate more than one lesson at a time or more students than its capacity. Figure #relationship#287> sketches the approximate relationship between the various entities of the timetabling problem.

#figure289#
Figure: The relationship between various entities of TTP where P: professors, C: classes, S: students, R: rooms, and I: time periods. The direction of the arrow is the direction of the assignment.