Masters Degrees (Logistics)

Permanent URI for this collection

https://scholar.sun.ac.za/handle/10019.1/727

Browse

Browsing Masters Degrees (Logistics) by browse.metadata.advisor "Hui, Cang"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    The development of a spatio-temporal model for water hyacinth, Eichhornia crassipes (Martius) Solms-Laubach (Pontederiaceae), biological control strategies
    (Stellenbosch : Stellenbosch University, 2016-12) Van Schalkwyk, Helene; Potgieter, Linke; Hui, Cang; Stellenbosch University. Faculty of Economic and Management Science. Dept. of Logistics.
    ENGLISH SUMMARY : The sustainable and cost-effective management of the notorious water hyacinth weed remains a challenge in South Africa. In this study, a reaction-diffusion model, consisting of a system of delayed partial differential equations, is developed to mathematically describe the population growth and dispersal of water hyacinth and the interacting populations of the various life stages of the Neochetina eichhorniae weevil as a biological control agent (BCA) in a temporally variable and spatially heterogeneous environment, subject to homogeneous Neumann boundary conditions on a bounded two-dimensional spatial domain. The primary objectives are to establish a spatio-temporal model which may be used to investigate the efficiency of different biological control release strategies, providing guidance towards the optimal magnitude, frequency, timing and distribution of BCA releases, and to evaluate the cost-effectiveness of local mass rearing programmes in biological control. Although previous studies have started to examine the influence of temperature on the population dynamics of the two species and the control of the weed under constant conditions, the model developed in this study is the first to evaluate the effect of introducing spatial dynamics. In addition, for the first time in research of water hyacinth management, different BCA release strategies are compared by means of mathematical modelling to provide practical recommendations for efficient and cost-effective biological control of water hyacinth in South Africa without having to conduct formal field experiments. Numerical solutions emphasize the benefit of frequent releases of Neichhorniae compared to a once-off release in the long term, as well as the advantage of more distributed releases along the edges of an infested water body. Furthermore, releases commencing in summer appear to be significantly more efficient and cost-effective than releases commencing in winter. The model is applied to a real-world release site in order to illustrate how the model may be utilized to provide guidance towards suitable BCA release strategies, which may minimize costs while maximizing the benefit for a specific site.
  • Thumbnail Image
    Item
    Non-cooperative games on networks
    (Stellenbosch : Stellenbosch University, 2013-03) Van der Merwe, Martijn; Van Vuuren, J. H.; Burger, A. P.; Hui, Cang; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Logistics.
    ENGLISH ABSTRACT: There are many examples of cooperation in action in society and in nature. In some cases cooperation leads to the increase of the overall welfare of those involved, and in other cases cooperation may be to the detriment of the larger society. The presence of cooperation seems natural if there is a direct bene t to individuals who choose to cooperate. However, in examples of cooperation this bene t is not always immediately obvious. The so called prisoner's dilemma is often used as an analogy to study cooperation and tease out the factors that lead to cooperation. In classical game theory, each player is assumed to be rational and hence typically seeks to select his strategy in such a way as to maximise his own expected pay-o . In the case of the classical prisoner's dilemma, this causes both players to defect. In evolutionary game theory, on the other hand, it is assumed that players have limited knowledge of the game and only bounded rationality. Games in evolutionary game theory are repeated in rounds and players are a orded the opportunity to adapt and learn as this repetition occurs. Past studies have revealed that cooperation may be a viable strategy if the prisoner's dilemma is placed in an evolutionary context, where the evolutionary tness of a strategy is directly related to the pay-o achieved by the player adopting the strategy. One of the mechanisms that promote the persistence of cooperation in the evolutionary prisoner's dilemma is structured interaction between players. A mathematical framework for representing the evolutionary prisoner's dilemma (ESPD) is developed in this thesis. The mathematical framework is used to undertake an analytical approach (i.e. avoiding the use of simulation) towards investigating the dynamics of the ESPD with a path, cycle, plane grid or toroidal grid as underlying graph. The objective of this investigation is to determine the likelihood of the emergence of persistent cooperation between players. The ESPD on a path or a cycle admits two fundamentally di erent parameter regions; large values of the temptation-to-defect parameter are not capable of inducing persistent cooperation, while small values of this parameter allow for the possibility of persistent cooperation. It is found that the likelihood of cooperation increases towards certainty as the order of the underlying graph increases if the underlying graph is a path or cycle. The state space of the ESPD with a plane or toroidal grid graph as underlying graph grows very quickly as a function of the graph order. The automorphism classes of game states are enumerated to determine exactly how fast the size of the state space of the game grows as a function of the order of the underlying graph. Finally, the dynamics of the ESPD is investigated for a grid graph as underlying graph (in cases where the state space is small enough) by means of constructing the corresponding state graphs of the ESPD.