The Teaching Space Allocation Problem with Splitting

Abstract

A standard problem within universities is that of teaching space allocation which can be thought of as the assignment of rooms and times to various teaching activities. The focus is usually on courses that are expected to fit into one room. However, it can also happen that the course will need to be broken up, or 'split', into multiple sections. A lecture might be too large to fit into any one room. Another common example is that of seminars or tutorials. Although hundreds of students may be enrolled on a course, it is often subdivided into particular types and sizes of events dependent on the pedagogic requirements of that particular course.Typically, decisions as to how to split courses need to be made within the context of limited space requirements. Institutions do not have an unlimited number of teaching rooms, and need to effectively use those that they do have. The efficiency of space usage is usually measured by the overall 'utilisation' which is basically the fraction of the available seat-hours that are actually used. A multi-objective optimisation problem naturally arises; with a trade-off between satisfying preferences on splitting, a desire to increase utilisation, and also to satisfy other constraints such as those based on event location and timetabling conflicts. In this paper, we explore such trade-offs. The explorations themselves are based on a local search method that attempts to optimise the space utilisation by means of a 'dynamic splitting' strategy. The local moves are designed to improve utilisation and satisfy the other constraints, but are also allowed to split, and un-split, courses so as to simultaneously meet the splitting objectives.

Towards improving the utilization of university teaching space

“…Also, courses can need splitting into smaller events, called sections, because they are too large for the rooms or there is a recommended section size. We study this "splitting problem" in Beyrouthy et al (2006a).…”

University space planning and space-type profiles

“…Students enrolled in that module should attend all of those taught meetings, and such meetings are called classes. In [Beyrouthy et al, 2007a[Beyrouthy et al, , 2008a, we have allocated classes of a module to roomslots, but when the number of students of a class is larger then the room size, we are required to split it so that it fits. Also, there are often pedagogical reasons in order to split classes, for example, tutorials should 'by definition' be small groups.…”

“…In a series of papers , 2007a, 2009, 2008a, Beyrouthy, 2008, we have been setting the scientific foundations for better space planning and for determining which levels of utilisation ought to be achievable within a given institutional context. That is, we introduced new models, and solution methods, aimed at understanding this low value and at improving the utilisation of teaching space within a university setting.…”

“…This maximisation of U A is performed in the presence of appropriate sets of constraints, typically conflict constraints between events, but also, for example, 'location penalties' for placing events in 'incorrect' departments. In addition, the work has also studied the case in which some teaching activities, such as tutorials, require splitting into small groups [Beyrouthy et al, 2007a[Beyrouthy et al, , 2008a. Note, it is not our intention to discuss details of course timetabling and associated algorithms here.…”

“…It is the purpose of this paper to extend and enhance previous methods so as to quantify the interaction between space-type mixing and profiles and the achievable utilisations. The work is done in the context of the 'Teaching Space Allocation problem with splitting' [Beyrouthy et al, 2007a, 2008a, Beyrouthy, 2008. We give evidence that tightly matching spacetypes when performing activities allocation, using the current spaceprofile, has a detrimental effect on the utilisation.…”