Unmanned Vehicles (UVs) currently perform a variety of tasks critical to a military mission. In future, they are envisioned to have the ability to accomplish a mission co-operatively and effectively with limited fuel onboard. In particular, they must search for targets, classify the potential targets detected, attack the classified targets and perform an assessment of the damage done to the targets. In some cases, UVs are themselves munitions. The targets considered in this thesis are stationary. The problem considered in this thesis, referred to as the UV problem, is the allotment of tasks to each UV along with the sequence in which they must be performed so that a maximum number of tasks are accomplished collectively. The maneuverability constraints on the UV are accounted for by treating them as Dubin's vehicles. Since the UVs considered are disposable with life spans governed by their fuel capacity, it is imperative to use their life as efficiently as possible. Thus, we need to develop a fuel-optimal (equivalently, distance optimal) motion plan for the collection of UVs. As the number of tasks to be performed and the number of vehicles performing these tasks grow, the number of ways in which the set of tasks can be distributed among the UVs increases combinatorially. The tasks a UV is required to perform are also subject to timing constraints. A UV cannot perform certain tasks before completing others. We consider a simplified version of the UV problem and do not take into account the timing constraints on the tasks to be performed on targets. We use linear programming and graph theory to find a solution to this simplified UV problem; in the graph theory approach, we develop an algorithm which is a generalization of the solution procedures available to solve the Traveling Salesman Problem (TSP). We provide an example UV problem illustrating the solution procedure developed in this thesis.

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This dissertation analyses the determinants of demand for new passenger vehicles in South Africa over a ten-year period, between 1995 and 2005. The following investigation into the determinants of demand for new passenger cars, is based both on a statistical and empirical analysis of the performance of the South African new passenger car market. Firstly, in Chapter 2 a brief history of the South African motor in industry provides a background for the analysis which follows in this dissertation and gives some insight into the historical developments that created the structure of the industry during the period analysed by the study. The theoretical components of the thesis focus on the macro-economic theory of demand, which seeks to explain the influences which determine consumer demand when purchasing durable goods and more specifically new passenger cars. Chapter 3 explains how consumers trade off preferences and substitutes in their efforts to maximise their utility. When comparing the general theory of demand to the theory of demand for durable goods and more specifically the theory of demand for new passenger cars, it is demonstrated that the theory of demand for new passenger cars is inherently different to that of non-durable goods. New passenger cars and other durable goods require a relatively higher investment, last longer than non-durable goods and literally retain some of their value, as they get older. Chapter 3 creates a theoretical foundation upon which the determinants of demand for passenger cars will be analysed in Chapter 4. Chapter 4 forms the base upon which the South African New Passenger Car Market will to be analysed. In Chapter 4 the study statistically and graphically analyses the primary economic determinants of demand for new passenger cars. The analyses first present the relationship between price and new passenger car demand. It was found that demand for new passenger cars was price elastic. It was also identified that price elasticity of demand changed over the ten-year period analysed. Next, the impact of population growth and personal disposable income on new passenger car demand was analysed. It was discovered that should the population grow faster than the economy; relative prices unchanged, personal disposable income will decline and thereby affect desired stocks of new passenger cars negatively. The effect of disposable income on the sale of new passenger cars was found to be income inelastic. Income elasticity also, however displayed signs of change over the analysed period. The effect of the rate of interest on the demand for the new passenger cars was also analysed. The analysis indicated that changes in interest rates resulted in changes of various proportions in all rates of interest in the economy; such an effect filtered through to the new passenger car market. After this, the effect of GDP on the demand for new passenger cars was examined. The examination found that changes in the new passenger car market correlated very closely with GDP growth changes, hence GDP changes served as an important indicator of the new passenger car market. The result of changes in the price of fuel on new passenger car demand was also examined. The result showed that the structure of the market, i.e. the size of cars, etc. was more affected than the volume of sales. Finally, the effect of the level of confidence in new passenger car demand was analysed. Business and consumer confidence were found to be good indicators of the new passenger car market. Chapter 5 concluded and summarised the findings of the dissertation. The study also noted that the effects of South Africa’s upgraded public transport system in the form of the Bus Rapid Transport System (BRT) and the Gautrain on the demands of new passenger cars could be a case for future research. / Thesis (MCom (Economics))--North-West University, Vaal Triangle Campus, 2012