A Mathematical Model for Classroom-Period Schedule Defragmentation

Engineering studies (mechanical, electrical, civil, chemical etc.) it is of great importance to efficiently use available space particulary labs with expensive equipment according to the given time schedule. In order to accomplish this demanding condition this paper propose a mathematical approach to classroom-period schedule optimization. This paper proposes a heuristic mathematical approach to a better use of the available classroom space for a given time table of courses at a university. Model building starts with a definition of two dimensional matrix consisting of of two ordered sets: classroom set and daily period set. In each row (classroom) of the matrix we allocate one, two and three period fragments or the corresponding one, two and three subsets of the considered daily periods set. Then, we introduce the classroom occupation parameter defined for each classroom as ratio of its occupied periods and total available periods. In the paper the defragmentation procedure is defined as relocation of the one, two and three period fragments from their current classroom location to some other classroom location, mantaining always the given courses time table. The defragmentation procedure begins from the classroom with the smallest classroom occupation parameter value moving first three, then two and finally one period fragments to the respective free classroom location with the largest occupation paremeter value. The relocation process continoues until all free classroom location are found. In the paper " A Software Solution For A Mathematical Model of Classroom-Period Schedule Defragmentation ", which should be considered and rewiewed as the second part of this paper, the authors have developed the corresponding computer software for the model. The model and the software are illustrated by applying them to the University of Mostar.