<p>In this work we examine a state constrained resource allocation model a with finite time horizon. Therefore, we use the necessary conditions of the Pontrjagin's Maximum Principle to find candidates for the solution and verify them later on using the sufficient conditions given by the duality concept of Klötzler. Moreover, we proof that the solution of the corresponding infinite horizon model does not fulfill the overtaking criterion of Weizsäcker.</p>

In this work we examine a state constrained resource allocation model a with finite time horizon. Therefore, we use the necessary conditions of the Pontrjagin's Maximum Principle to find candidates for the solution and verify them later on using the sufficient conditions given by the duality concept of Klötzler. Moreover, we proof that the solution of the corresponding infinite horizon model does not fulfill the overtaking criterion of Weizsäcker.

Australian universities are multi-million dollar operations employing tens of thousands of people. They attract revenue from a variety of government and non-government sources, and yet, as non-profit organisations they are judged by governments, peers and their communities on their performance in teaching and research rather than on a financial bottom line. In order to achieve these results, university managers must make decisions on how to allocate available funding throughout the university. Faced with competing demands on scarce funds, how do university managers make these choices? One option is to use a resource allocation model to 'crunch the numbers'. Resource allocation models can incorporate a number of elements - student and staff numbers, weightings and performance data, for example - to allocate available funds. These allocation models are used in different ways in different universities, but serve the same basic purpose of assisting decision-making on how much to allocate to different sections of the organisation. Such models operate within a process and context that includes the strategic aims of the University, the organisation structure, its committees and culture. This thesis contains case studies of resource allocation models and processes used in three Australian universities. It examines the methods used for resource allocation at the first and second levels within each university; that is, from the Vice-Chancellor to Dean (or equivalent), and from Dean to Head of School (or equivalent). Observations and conclusions are drawn on the models used, the processes surrounding the models, and the continuity between the two layers of allocations. The research finds all the case-study universities operate models at multiple levels in their organisations, and that there is a concerning lack of consistency and flow-through at these different levels. The messages that the university leadership intends to send through the allocations may be lost to managers one-process removed from them. The research also concludes that transparency is the most important element of the resource allocation process. University staff dealing with allocation processes will accept the results, even if they are not ideal, if they can understand how and why decisions were made. As a professional doctorate thesis, the aim is to provide a practical aid to people with responsibility for resource allocation in universities.

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South African Air Quality Units are continuously undergoing changes, and improving their performance remains a constant endeavour. In addition, these units are also experiencing several challenges in terms of improving communication across the different spheres, accessing air quality data and using the information to support the decision-making required for efficient management of air quality in South Africa. This study investigated the concept of output efficiency within the South African air quality management context. Models that enable efficient resource allocation can be used to assist managers in understanding how to become efficient. There are, however, few models that focus on the output efficiency of the public sector and air quality management units. The primary purpose of the study was to develop a model to predict the extent to which organisational efficiency could be explained by the percentage of man-hours allocated to a range of management activities. In this study, the development of a model using the logistic regression technique is discussed. Data was collected for two financial years (2005/6 and 2006/7) from the air quality officers in the national, provincial and local spheres of government (N=228). The logistic regression model fitted indicates that the proportion of time spent on knowledge management activities contributes the most to the likelihood of an Air Quality Unit being efficient. The resource allocation model developed will ensure that air quality officers allocate resources appropriately and improve their output performance. / Graduate School for Business Leadership / D.B. L.

South African Air Quality Units are continuously undergoing changes, and improving their performance remains a constant endeavour. In addition, these units are also experiencing several challenges in terms of improving communication across the different spheres, accessing air quality data and using the information to support the decision-making required for efficient management of air quality in South Africa. This study investigated the concept of output efficiency within the South African air quality management context. Models that enable efficient resource allocation can be used to assist managers in understanding how to become efficient. There are, however, few models that focus on the output efficiency of the public sector and air quality management units. The primary purpose of the study was to develop a model to predict the extent to which organisational efficiency could be explained by the percentage of man-hours allocated to a range of management activities. In this study, the development of a model using the logistic regression technique is discussed. Data was collected for two financial years (2005/6 and 2006/7) from the air quality officers in the national, provincial and local spheres of government (N=228). The logistic regression model fitted indicates that the proportion of time spent on knowledge management activities contributes the most to the likelihood of an Air Quality Unit being efficient. The resource allocation model developed will ensure that air quality officers allocate resources appropriately and improve their output performance. / Graduate School for Business Leadership / D.B. L.