This thesis is concerned with donations of time and money to charitable institutions in Britain. The Charities Aid Foundation annual Charity Household Survey is statistically analysed and profiles of individuals likely to donate money to charity, and those likely to donate at different levels, are produced. A model of direct and indirect influences on charity donations is developed and the implications of the results for fundraising managers discussed. These analyses are then repeated for volunteers. Those most likely to volunteer and those who are likely to give at higher levels are profiled. A model of both direct and indirect influences on volunteering is developed and again the implications of the results for charity managers are discussed. In addition to the statistical analyses, interviews with fundraising managers from large British charities were conducted. These provided an additional check of the validity of the original findings and indicated areas where further research would be desirable.

Two machine shop computer models are developed to evaluate a set of heuristic decision rules. The first is of a small job shop where machine set up times can be either sequence-dependent or independent. Simple loading rules and combinations thereof are examined, together with a new heuristic rule which provides a 'look-ahead' capability. Results indicate firstly that in job shops with sequence dependent set-up times, the set-up time based loading rules give the best throughput performance, either when the ratio of set up time to processing time is high, or when there is a heavy work load. Secondly, the combining of loading rules, rather than using them separately, can produce better results for both throughput and delivery date criteria. The second model includes many characteristics of actual industrial machine shops, such as grouping of machines with similar capabilities, more complex job processes in the form of assembly networks, and the inclusion of manufacturing costs, inventory/work-in-progress costs, and penalty costs associated with late delivery. Using this model a set of cost-based decision rules is proposed and its performance compared with established loading rules. Results indicate, firstly, that relative performances of the loading rules used singly and combined are similar to those obtained in the smaller machine shop model. Secondly, the performance of the cost based decision rules generally equals or surpasses that of established loading rules, particularly with regard to the minimisation of inventory/work-in-progress costs. The results of the 'look ahead' heuristic rule tested in both models are disappointing, and did not appear to justify the extra computation required.

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In this thesis we consider the reliability, availability, uptime distribution and downtime distribution of R-out-of-N systems of identical components with components which have exponential operating times before break down. In particular, we are interested in systems where a finite number, M, of spares is available and a finite number of service facilities is available to install the spares into the system and to repair the failed items to a good-as-new state, and then to join the stock of spares which can be re-installed into the system at a later time. In chapter two we assume that repair times and installation times both have exponential distributions so that our system can be represented as a finite-state continuous-time Markov process. Two models are considered (a) with distinct repair and installation facilities and (b) with service facilities which carry out both repair and installation, with priority given to the installation activity. In chapter three we study a series system with 3 spares and a single service facility with arbitrary distributions for repair times and installation times. Installation takes pre-emptive priority over repairs, and we consider both 'resume' and 'restart' assumptions for interrupted repairs. We consider an approach based on Laplace transforms and the use of supplementary variables to make the process, Markovian. Chapter four generalises the results of chapter three to an arbitrary number, M, of spares. Here only the equilibrium results are obtained by probabilistic arguments. Chapter five deals with the uptime and downtime for both models of chapter four. We consider various distributions of repair times and of installation times. In chapter six we generalise the pre-emptive restart model with a single server and M spares for the series system, discussed in chapter four, to general R-out-of-N system (with single server). The pre-emptive resume case is rather more difficult, and is not dealt with in this thesis. Chapter seven dealt with the downtime distribution for this model. In chapter eight we study a standby system where installation and repair times are both constant. Although this is a special case of the models studied in chapter four, it can be approached differently with some interesting mathematics. Also some extra results about the number of failures over an interval are obtained. Throughout there are numerical examples which have been calculated using APL. We found that this was in some cases, particularly suitable for representing the mathematics of the problem, quite apart from actually computing answers. A large set of APL functions is included in the appendix.

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As early as the mid 1960's the production and scheduling systems at the Port Talbot and Llanwern sites of British Steel were computerised. This involved real-time shop floor data collection systems enabling material tracking and stock/order analysis. All orders were handled by computer systems. This enabled the scheduling sections to plan and schedule orders through the various processes aiming to meet delivery promises and control stocks. Each item of plant was scheduled individually, supplying adequate stock for the next process. Also, the planning and scheduling systems for Port Talbot were different and separate to Llanwern. In January 1995 work started on enhancing both works' planning and scheduling systems leading towards one common system. Initially the planning systems were developed to each site followed by the new scheduling systems. The most fundamental difference in the new system is that it plans the production activities for the whole plant, rather than just the individual units. This thesis describes the old planning and scheduling systems within Port Talbot and Llanwern Works and the difficulties associated with the old, manual methods used for scheduling the production units, particularly the steelmaking/continuous casting plant and the hot strip mills. Descriptions of the newly adopted systems are given with details of the implementations, plus information on the problems encountered. Associated systems are also described, in particular the manufacturing execution system (MES) and the plans for replacing it with a new system. There is also a comprehensive review of the literature pertaining to planning and scheduling in the metals, and more specifically, the steel industry.

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