Submitted in fulfillment of the requirements of Doctor of Engineering, Durban University of Technology, Durban, South Africa, 2017. / The need to quantify and model transformations that have taken place in the cities of South Africa is one of the grand challenges linked to country’s transition to Democracy. Given the complexities associated with different stages of city transformation, it is imperative that models used to unpack processes of city transformation are novel. In this study it emerged that statistical methods alone are not adequate to fully present, in a comprehensible way, all facets of drivers of city transformation. As a result, statistical methods have been combined with mathematical and system dynamics models. Results revealed that city transformations derive from a number of triggers. Underlining these are income, migration and houses. The empirical data collected through questionnaire survey that was later incorporated into mathematical models demonstrated that income is a primary driver that fuels city migration. System Dynamic Models demonstrated that the availability of houses or accommodation serve as constraints that keep the city population within the limits of the carrying capacity of a city. In addition it was further confirmed, through mathematical models that income has varying effects on the attractiveness of cities. This was found to be linked to the shape of the distribution of income in the city. A normally distributed income with a peak in the middle results in a city being more attractive than an evenly distributed income that peaks either at very low or high income levels. This observation brought forth a need to test heterogeneity when analyzing city transformation using income as an index. Mathematical Models that incorporated heterogeneity demonstrated the usefulness of systems analysis in unpacking the mechanism of city transformation, a component of city management that requires serious consideration for planning, budgeting and provision of limited resources like houses in the cities. Success of methods used in this study led to a conclusion that these can be enhanced through other techniques like agent based models. With this call, improvements on this study that can be attained through these techniques are recommended. This will enrich the understanding of the transformation and dynamics of cities under different conditions than those that exist in South Africa. / D

South Africa provides a fascinating interface between the developed and the developing world and poses a multitude of opportunities for enhancing the sustainable development of local cities. The concept of City Logistics is concerned with the mobility of cities, and entails the process of optimizing urban logistics activities by considering the social, environmental, economic, financial, and energy impacts of urban freight movement. Vehicle routing and scheduling has the potential to address a number of these key focus areas. Applying optimization to vehicle routing and scheduling results in a reduced number of trips, better fleet utilization, and lower maintenance costs; thereby improving the financial situation of the fleet owner. Improved fleet utilization could have a positive environmental impact, while also improving the mobility of the city as a whole. Energy utilization is improved while customer satisfaction could also increase through on-time deliveries and reliability. The Vehicle Routing Problem (VRP) is a well-researched problem in Operations Research literature. The main objective of this type of problem is to minimize an objective function, typically distribution cost for individual carriers. The area of application is wide, and specific variants of the VRP transform the basic problem to conform to application specific requirements. It is the view of this dissertation that the various VRP variants have been researched in isolation, with little effort to integrate various problem variants into an instance that is more appropriate to the South African particularity with regards to logistics and vehicle routing. Finding a feasible, and integrated initial solution to a hard problem is the first step in addressing the scheduling issue. This dissertation attempts to integrate three specific variants: multiple time windows, a heterogeneous fleet, and double scheduling. As the problem is burdened with the added constraints, the computational effort required to find a solution increases. The dissertation therefore also contributes to reducing the computational burden by proposing a concept referred to as time window compatibility to intelligently evaluate the insertion of customers on positions within routes. The initial solution algorithm presented proved feasible for the integration of the variants, while the time window compatibility decreased the computational burden by 25%, and as much as 80% for specific customer configurations, when using benchmark data sets from literature. The dissertation also improved the quality of the initial solution, for example total distance traveled, by 13%. Finding an initial solution is the first step in solving vehicle routing problems. The second step is to improve the initial solution iteratively through an improvement heuristic in an attempt to find a global optimum. Although the improvement heuristic falls outside the scope of this dissertation, improvement of the initial solution has a significant impact on the quality of improvement heuristics, and is therefore a valuable contribution. / Dissertation (MEng)--University of Pretoria, 2007. / Industrial and Systems Engineering / MEng / Unrestricted