Abstract. There is a perception that teaching space in universities is a rather scarce resource. However, some studies have revealed that in many institutions it is actually chronically under-used. Often, rooms are occupied only half the time, and even when in use they are often only half full. This is usually measured by the "utilisation" which is defined as the percentage of available 'seat-hours' that are employed. Within real institutions, studies have shown that this utilisation can often take values as low as 20-40%.One consequence of such a low level of utilisation is that space managers are under pressure to make a more efficient use of the available teaching space. However, better management is hampered because there does not appear to be a good understanding within space management (nearterm planning) of why this happens. Nor, a good basis within space planning (long-term planning) of how best to accommodate the expected low utilisations. This motivates our two main goals: (i) To understand the factors that drive down utilisations, (ii) To set up methods to provide better space planning.Here, we provide quantitative evidence that constraints arising from timetabling and location requirements easily have the potential to explain the low utilisations seen in reality. Furthermore, on considering the decision question "Can this given set of courses all be allocated in the available teaching space?" we find that the answer depends on the associated utilisation in a way that exhibits threshold behaviour: There is Contact Author (Authors listed alphabetically.) 2 Towards Improving Utilisation a sharp division between regions in which the answer is "almost always yes" and those of "almost always no". Through analysis and understanding of the space of potential solutions, our work suggests that better use of space within universities will come about through an understanding of the effects of timetabling constraints and when it is statistically likely that it will be possible for a set of courses to be allocated to a particular space. The results presented here provide a firm foundation for university managers to take decisions on how space should be managed and planned for more effectively. Our multi-criteria approach and new methodology together provide new insight into the the interaction between the course timetabling problem and the crucial issue of space planning.

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.

Universities planning the provision of space for their teaching requirements need to do so in a fashion that reduces capital and maintenance costs whilst still providing a high quality level of service. Space plans should aim to provide sufficient capacity without incurring excessive costs due to over-capacity. A simple measure used to estimate over-provision is utilisation. Essentially, the utilisation is the fraction of seats that are used in practice, or the ratio of demand to supply. However, studies usually find that utilisation is low, often only 20-40%, and this is suggestive of significant over-capacity.Our previous work has given methods to improve such space planning. They identify a critical level of utilisation as the highest level that can be achieved whilst still reliably satisfying the demand for places to allocate teaching events. In this paper, we extend such work to incorporate the notions of event-types and space-types. Teaching events have multiple 'event-types', such as lecture, tutorial or workshops, and there are generally corresponding space types. Matching the type of an event to a room of a corresponding space type is generally desirable. However, realistically, allocation happens in a mixed spacetype environment where teaching events of a given type are allocated to 1 rooms of another spacetype e.g. tutorials will borrow lecture theatres or workshop rooms.We propose a model and methodology to quantify the effects of spacetype mixing and establish methods to search for better spacetype profiles; where the term "space-type profile" refers to the relative numbers of each type of space. We give evidence that these methods have the potential to improve utilisation levels. Hence the contribution of this paper is twofold. Firstly, we present informative studies of the effects of space-type mixing on utilisation, and critical utilisations. Secondly, we present straightforward though novel methods to determine better space-type profiles, and give an example in which the resulting profiles are indeed significantly improved.