The Teaching Space Allocation Problem with splitting

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.

Threshold effects in the Teaching Space Allocation Problem with Splitting

Universities aim for good “Space Management” so as to use the teaching space efficiently. Part of this task is to assign rooms and time-slots to teaching activities with limited numbers and capacities of lecture theaters, seminar rooms, etc. It is also common that some teaching activities require splitting into multiple events. For example, lectures can be too large to fit in one room or good teaching practice requires that seminars/tutorials are taught in small groups. Then, space management involves decisions on splitting as well as the assignments to rooms and time-slots. These decisions must be made whilst satisfying the pedagogic requirements of the institution and constraints on space resources. The efficiency of such management can be measured by the “utilisation”: the percentage of available seat-hours actually used. In many institutions, the observed utilisation is unacceptably low, and this provides our underlying motivation: to study the factors that affect teaching space utilisation, with the goal of improving it. We give a brief introduction to our work in this area, and then introduce a specific model for splitting. We present experimental results that show threshold phenomena and associated easy-hard-easy patterns of computational difficulty. We discuss why such behaviour is of importance for space management.

University space planning and space-type profiles

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 provided 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 this body of work to incorporate the notions of event-types and space-types. Teaching events have multiple ‘event-types’, such as lecture, tutorial, workshop, etc., 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 space-type environment where teaching events of a given type are allocated to rooms of another space-type; e.g., tutorials will borrow lecture theatres or workshop rooms.

We propose a model and methodology to quantify the effects of space-type mixing and establish methods to search for better space-type 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.

Distributed Region-Based Memory Allocation and Synchronization

We present DRASync, a region-based allocator that implements a global address space abstraction for MPI programs with pointer-based data structures. The main features of DRASync are: (a) it amortizes communication among nodes to allow efficient parallel allocation in a global address space; (b) it takes advantage of bulk deallocation and good locality with pointer-based data structures; (c) it supports ownership semantics of regions by nodes akin to reader–writer locks, which makes for a high-level, intuitive synchronization tool in MPI programs, without sacrificing message-passing performance. We evaluate DRASync against a state-of-the-art distributed allocator and find that it produces comparable performance while offering a higher-level abstraction to programmers.