The Development and Application of Mathematical Models for Planning and Resource Allocation at the University of Stirling

Abstract

The objective of the research described in this dissertation is to examine the planning and resource allocation problems of universities and to investigate whether scientific management methods and in particular mathematical models can be used with advantage in this context. The approach adopted was to consider these questions in the particular case of one university (the University of Stirling). The national system of university planning and finance in the UK is described. This provides the framework within which the University’s planning decisions are made. A description of the academic system and history of the University of Stirling leading u to the problems of planning for the 1977-82 quinquennium is then given. A survey of work carried out elsewhere in this field is presented and a number of general purpose models for university planning developed elsewhere are described. This is followed by a general discussion of philosophies of resource allocation in UK universities. For a number of reasons, it proved to be impractical to attempt to adapt one of the general purpose models developed elsewhere to Stirling University’s planning problems. Hence, a planning model is constructed from first principles, a modular form being used. This model is then use to investigate possible development plans for the 1977-82 quinquennium. After general consideration of possible growth during the quinquennium the model is used to attempt to explore consequences of possible development plans. The first study which was carried out (the ‘base-line’ study) was based on achieving desired expansion through simply extrapolating present developments. This study projected certain undesirable consequences (such as some Stirling departments becoming excessively large). This study was followed by another which took into account likely introduction of new academic developments and certain other factors suggested as desirable by University decision-makers. A comprehensive critique of these plans is presented. In particular, the University’s chance of obtaining desired student numbers is explored. This is followed by two sensitivity analyses. In the first, consequences of possible shortfalls in student numbers in different subject areas are considered. The second considers consequences of possible changes in University internal resource allocation policy. The consequences of the latter turn out to be far more far-reaching. The possibility of further work is discussed. Possible improvements in the University’s information system are considered and the feasibility of introducing a planning programme budgeting system is discussed. The major conclusion to emerge from this study is that it proved possible to build a mathematical model of the University which can be usefully employed for planning and in particular for devising and testing quinquennial plans. This approach has the advantage that the implications of a given plan for all significant resources can be assessed. It also enables a wider range of plans to be investigated and full sensitivity analyses to be carried out.