Thesis (MSc (Logistics))--University of Stellenbosch, 2008. / The primary question considered in this study is whether a small population of a biological species introduced into a resource-heterogeneous environment, where it competes for these resources with an already established native species, will be able to invade successfully. A two-component autonomous system of reaction-diffusion equations with spatially inhomogeneous Lotka-Volterra competitive reaction terms and diffusion coefficients is derived as the governing equations of the competitive scenario. The model parameters for which the introduced species is able to invade describe the realized niche of that species. A linear stability analysis is performed for the model in the case where the resource heterogeneity is represented by, and the diffusion coefficients are, two-toned functions. In the case where the native species is not directly affected by the resource heterogeneity, necessary and sufficient conditions for successful invasion are derived. In the case where the native species is directly affected by the resource heterogeneity only sufficient conditions for successful invasion are derived. The reaction-diffusion equations employed in the model are deterministic. However, in reality biological species are subject to stochastic population perturbations. It is argued that the ability of the invading species to recover from a population perturbation is correlated with the persistence of the species in the niche that it occupies. Hence, invasion time is used as a relative measure to quantify the rate at which a species’ population distribution recovers from perturbation. Moreover, finite difference and spectral difference methods are employed to solve the model scenarios numerically and to corroborate the results of the linear stability analysis. Finally, a case study is performed. The model is instantiated with parameters that represent two different cultivars of barley in a hypothetical environment characterized by spatially varying water availability and the sufficient conditions for successful invasion are verified for this hypothetical scenario.

Thesis (MSc (Logistics))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: Technological advances made over the past century have had a major impact on traditional wineries. Software solutions for management issues are widely available and give rise to the prospect of computerized decision support systems assisting in various aspects of managing a winery. The most popular applications seem to be concerned with supply chain management or harvest scheduling. Such projects are under way all over the globe and great success has been achieved to this e ect. However, prior to this study no such project has been considered in South Africa. The phrase active cellar scheduling problem refers to the assignment of grape batches to processors inside the cellar where bottlenecks often occur during the busy harvesting period. The phrase harvest scheduling problem, on the other hand, refers to selecting the best possible dates to harvest the respective vineyard blocks in order to preserve grape quality. A mixed integer programming model for the active cellar scheduling problem is derived in this thesis, but proves to be too time consuming to solve exactly via the branch-and-bound method. A meta-heuristic tabu search approach is therefore designed to solve the problem approximately instead. When applied to a small, ctitious cellar, it is found that the tabu search method often solves the problem optimally. The computer processing time associated with the tabu search approach also constitutes a signi cant (often thousand-fold) improvement over that of the branch-and-bound approach for realistically sized problem instances. A generic tabu search is also designed to solve the over-arching harvest scheduling problem for a general winery. This schedule is found by referring to the smaller tabu search of the active cellar scheduling in order to verify the impact that harvesting moves have on activities in the cellar. One harvesting schedule is considered a better schedule than another when it has a lower harvest evaluation score, determined by the placement of the vineyard blocks in the harvesting schedule. The harvest evaluation score takes into account the combination of vineyard blocks selected for harvesting on the same day (and their e ect on the active cellar) as well as the ripeness and quality of the grapes. Both tabu searches are nally included in a exible, computerized decision support system, called VinDSS. This system is found to produce good harvesting schedules when compared to an actual ve day schedule during the 2009 harvesting period at Wamakersvallei, a winery serving as case study for this thesis. / AFRIKAANSE OPSOMMING: Tegnologiese vooruitgang oor die afgelope eeu het 'n groot invloed op tradisionele wynkelders gehad. Sagteware-oplossings wat besluitsteun tot bestuursaangeleenthede bied, is algemeen beskikbaar en het gelei tot die rekenaarmatige implementering van besluitsteunstelsels vir wynkelders. Dit blyk dat die mees popul^ere besluitsteuntoepassings in die wynindustrie te make het met besluite rakende van voorsieningskettings en oes-skedulering. Sulke besluitsteunprojekte is w^ereldwyd onderweg en het alreeds groot sukses behaal. Daar is egter tot dusver geen so 'n projek in Suid-Afrika onderneem nie. Die frase aktiewe kelderskeduleringsprobleem verwys na die toekenning van druifvragte aan masjiene binne die kelder waar bottelnekke algemeen tydens die besige parstydperk voorkom. Die frase oes-skeduleringsprobleem, daarenteen, verwys na die seleksie van bes moontlike oesdatums vir elk van die wingerdblokke om sodoende druifkwaliteit te verseker. 'n Gemengde heeltallige programmeringsmodel is vir die aktiewe kelderskeduleringsprobleem ontwikkel, maar die rekenaaroplossingstyd van hierdie benadering blyk te lank te wees om die probleem eksak deur middel van 'n vertak-en-begrens metode op te los. 'n Meta-heuristiese tabu soektog is dus ontwikkel om die probleem benaderd op te los. Wanneer hierdie benadering op 'n klein, ktiewe kelder toegepas word, word optimale oplossings dikwels verkry. Verder toon die rekenaaroplossingstyd van die tabu soektog 'n groot (in sommige gevalle byna 'n duisendvoudige) verbetering op di e van die eksakte oplossingsmetode. 'n Generiese tabu soektog is ook ontwikkel om die oorkoepelende oes-skeduleringsprobleem vir 'n algemene wynkelder op te los. So 'n oes-skedule word gevind deur na die kleiner tabu soektog vir die aktiewe kelderskedulering te verwys om sodoende die e ekte van veranderinge in die oesskedule op die prosesse binne die aktiewe kelder na te speur. Een oes-skedule word beter as 'n ander skedule beskou wanneer dit met 'n beter oes-evalueringswaarde gepaard gaan, soos deur die plasing van die wingerdblokke in die skedule bepaal. Die oes-evalueringswaarde neem die moontlike kombinasies van wingerblokke wat op dieselfde dag geoes word, in ag (en ook die e ek wat dit op aktiwiteite in die kelder het), asook die rypheid en kwaliteit van die druiwe. Beide tabu soektogte word in 'n plooibare, rekenaar-ge mplementeerde besluitsteunstelsel, bekend as VinDSS, ingesluit. Daar word gevind dat hierdie stelsel goeie oes-skedules lewer wanneer dit vergelyk word met 'n werklike vyf-dag skedule tydens die 2009 parsseisoen van Wamakersvallei, die kelder wat as gevallestudie vir hierdie tesis gedien het.

Thesis (MComm (Logistics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Suppose a lottery draw consists of forming a winning ticket by randomly choosing t m distinct numbers from a universal set Um = f1; : : : ;mg. Each lottery participant forms a set of tickets prior to the draw, each ticket consisting of n m distinct numbers from Um, and is awarded a prize if k minfn; tg or more numbers in at least one of his/her tickets matches those of the winning ticket. A lottery of this form is denoted by the quadruple hm; n; t; ki, and the prize is known as a k-prize. The participant's set of tickets is also known as a playing set. The participant may wish to form a playing set in such a way that the probability of winning a k-prize is at least 0 < 1. Naturally, the participant will want to minimise the cost of forming such a playing set, which means that the cardinality of the playing set should be as small as possible. This combinatorial minimisation problem is known as the incomplete lottery problem and was introduced by Gr undlingh [16], who also formulated a related problem called the resource utilisation problem. In this problem one attempts to select a playing set of pre-speci ed cardinality ` in such a way that the probability of winning a k-prize is maximised. Gr undlingh [16] studied the incomplete lottery problem and the resource utilisation problem in the special case where n = t. In this thesis both problems are considered in the general case where n 6= t. Exact and approximate solution methods are presented and compared to each other in terms of solution quality achieved, execution time and practical feasibility. The rst solution method involves a mathematical programming formulation of both problems. Using this solution method, both problems are solved for small lottery instances. An exhaustive enumeration solution method, which uses the concept of overlapping playing set structures [5, 16], is reviewed and used to solve both combinatorial optimisation problems for the same small lottery instances. The concept of an overlapping playing set structure is further explored and incorporated in an attempt to solve both combinatorial optimisation problems approximately by means of various metaheuristic solution approaches, including a simulated annealing algorithm, a tabu search and a genetic algorithm. The focus of the thesis nally shifts to a di erent problem involving lotteries. An investigation is conducted into the probability, P(N; ), of participants sharing a k-prize if a total of N tickets are purchased by participants of the lottery hm; n; t; ki. Special attention is a orded in this problem to the jackpot prize of the South African national lottery, Lotto, represented by the quadruple h49; 6; 6; 6i and how the value of P(N; ) is a ected by the way that participants select their playing sets. / AFRIKAANSE OPSOMMING: Gestel 'n lotery-trekking bestaan uit die ewekansige seleksie van 'n wenkaartjie bestaande uit t m verskillende getalle uit 'n universele versameling Um = f1; : : : ;mg. Elke lotery-deelnemer vorm 'n versameling kaartjies voor die trekking, wat elk uit n m verskillende getalle in Um bestaan, en wen 'n prys indien k minfn; tg of meer getalle in minstens een van sy/haar kaartjies ooreenstem met di e in die wenkaartjie. 'n Lotery van hierdie vorm word deur die viertal hm; n; t; ki aangedui, en die prys staan as 'n k-prys bekend. 'n Deelnemer se kaartjies staan ook as a spelversameling bekend. 'n Lotery-deelnemer mag poog om sy spelversameling s o te selekteer dat die waarskynlikheid om 'n k-prys te wen, minstens 0 < 1 is. Die deelnemer sal natuurlik die koste wat met so 'n spelversameling gepaard gaan, wil minimeer, wat beteken dat die kardinaliteit van sy spelversameling so klein as moontlik moet wees. Hierdie kombinatoriese minimeringsprobleem staan as die onvolledige lottery-probleem bekend en is vir die eerste keer deur Gr undlingh [16] bestudeer, wat ook die verwante hulpbronbenuttingsprobleem geformuleer het. In laasgenoemde probleem word daar gesoek na 'n spelversameling van vooraf-gespesi seerde kardinaliteit wat die waarskynlikheid om 'n k-prys te wen, maksimeer. Gr undlingh [16] het die onvolledige lottery-probleem en die hulpbronbenuttingsprobleem in die spesiale geval oorweeg waar n = t. In hierdie tesis word beide probleme in die algemeen oorweeg waar n 6= t. Eksakte en heuristiese oplossingstegnieke word vir beide probleme daargestel en met mekaar in terme van oplossingskwaliteit, oplossingstyd en praktiese haalbaarheid vergelyk. Die eerste oplossingstegniek behels 'n wiskundige programmeringsformulering van beide probleme. Die probleme word deur middel van hierdie benadering vir klein loterye opgelos. 'n Uitputtende enumerasietegniek, wat gebruik maak van die konsep van spelversameling oorvleuelingstrukture [5, 16], word daarna in o enskou geneem en beide kombinatoriese optimeringsprobleme word vir dieselfde klein loterye met behulp van hierdie tegniek opgelos. Die konsep van 'n spelversameling oorvleuelingstruktuur word verder ondersoek en in 'n benaderde oplossingstegniek vir beide kombinatoriese optimeringsprobleme ge nkorporeer deur gebruik te maak van verskeie metaheuristiese oplossingsbenaderings, insluitende 'n gesimuleerde afkoelingsalgoritme, 'n tabu-soektog en 'n genetiese algoritme. Die fokus in die tesis verskuif laastens na 'n ander probleem oor loterye. 'n Ondersoek word geloots na die waarskynlikheid, P(N; ), dat lottery-deelnemers 'n k-prys sal deel indien 'n totaal van N kaartjies in die lotery hm; n; t; ki gekoop word. Spesiale aandag word aan hierdie probleem geskenk in die geval van die boerpot-prys in die Suid-Afrikaanse nasionale lotery, Lotto, wat deur die viertal h49; 6; 6; 6i voorgestel word, en hoe die waarde van P(N; ) be nvloed word deur die manier waarop deelnmers hul spelversamelings selekteer.

Thesis (MPhil)--Stellenbosch University, 2000. / ENGLISH ABSTRACT: The increasing financial pressures exerted on ship owners in recent years due to cost inflation, overtonnage and low freight rates in many sectors, have forced ship owners to increase cost savings and contain costs. That induced certain shipowners to operate substandard ships. The cost advantages in substandard ships are through failing to maintain safety equipment and procedures, employing cheap and untrained crews, repairing only essential equipment on breakdown and register under flags that do not comply with all the international regulatory, economic and social requirements for ships. Those ships undercut the true costs of operating a ship and eventually drive the obedient shipowner out of the market at the cost of safe and clean seas. Because of the complex international environment in which shipping operates an international regulatory framework is needed to ensure safety at sea. This assignment gives a layout of that framework, which is co-ordinated by the International Maritime Organisation (!MO), as well as the ways in which it is implemented and regulated in individual countries, with reference to South Africa. The functioning of the South African Maritime Safety Agency (SAMSA), which has been established on 1 April 1998, is also discussed. The benefit of safe ports is highlighted and also the cost savings in marine insurance if ships are classified as safe. A brief description of the navigation instruments that SAMSA use to assist in achieving maritime safety is given. Finally, the diseconomies of substandard ships are debated against quality ships for cleaner seas. / AFRIKAANSE OPSOMMING: Die toenemende finansiële druk op skeepseienaars, as gevolg van koste inflasie, oortonnemaat en lae vragtariewe in verskeie sektore, het hulle gedwing om oor die laaste aantal jare hul kostes te beperk. Gedwonge kostebesparings gee aanleiding daartoe dat sekere skeepseienaars onveilige skepe bedryf. Kostevoordele in onveilige skepe word bereik deur veiligheidstoerusting en -prosedures nie in stand te hou nie, goedkoop en onopgeleide bemanning aan te stel, slegs die nodige herstelwerk aan toerusting te doen en deur te registreer onder vlae wat nie voldoen aan internasionale regulering, ekonomiese en sosiale vereistes vir skepe nie. Eienaars van sulke skepe, onderskruip die ware bedryfskoste van 'n skip en uiteindelik dryf dit die wetsgetroue skeepseienaars uit die mark ten koste van 'n veilige en skoon see. As gevolg van die komplekse internasionale omgewmg waann skeepvaart funksioneer, word 'n internasionale reguleringsraamwerk benodig om veiligheid ter see te verseker. Hierdie werkstuk gee 'n uitleg van daardie raamwerk, wat gekoordineer word deur die Internasionale Maritieme Organisasie (!MO), asook die manier waarop dit geïmplementeer en gereguleer word in individuele lande met verwysing tot Suid-Afrika. Die funksionering van die Suid-Afrikaanse Maritieme Veiligheids Agentskap (SAMSA), wat tot stand gebring is op 1 April 1998, word bespreek. Die voordele van veilige hawens word uitgelig, sowel as die besparings in maritieme versekeringskoste indien 'n skip as veilig geklassifiseer word. 'n Kort beskrywing van navigasie-instrumente wat SAMSA gebruik om maritieme veiligheid te bewerkstellig, word kortliks bespreek. Ten slotte, die dis-ekonomie van onveilige skepe word gedebateer teenoor die kwaliteit van skepe vir 'n skoner see.

Thesis (MComm (Logistics))--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: Mobile phone networks form an integral part of economic and social development globally. Mobile phones have become an everyday part of life and it is hard to imagine a competitive economy without the availability of mobile communications. Emerging markets benefit most from the implementation of mobile technology and growth trends are outperforming earlier predictions. The most popular and sustainable payment model used by mobile phone networks in emerging markets is the pre paid mechanism used for the distribution of airtime. This mechanism brings about unique challenges for networks in emerging markets. In this thesis the importance of the mobile phone network pre paid value channel is introduced through an analysis of pre paid revenue. A brief introduction is given to the systems and products that contribute to the functioning of the pre paid value channel. The revenue generation process is described with regards to the pre paid sector of the market and an in-depth explanation of the importance of deferred revenue is given, how it is recorded and what role it fulfils in the generation of revenue. The complexity of the network environment, both technical and operational makes the use of a business automation and support system (BSS) a necessary tool for effective execution of tasks and processes within the network environment. These systems record information from a wide spectrum of available technical network resources and use this information to automate the flow of network products. The use of such a system for the calculation of deferred revenue is suggested. Saaty‟s Analytical Hierarchy Process (AHP) algorithm and the Elimination and Choice Expressing Reality (ELECTRE) method are used to compare the newly proposed method for the calculation of deferred revenue using a BSS. Using Saaty's algorithm to estimate the effectiveness of deferred revenue as reported through the use of a BSS yields favourable results for the proposed method. This helps to bridge the gap in the poorly researched mobile telecommunications industry. ELECTRE is used to substantiate the findings of the model using AHP and meaningful tests are done to motivate correctness and accuracy of the results obtained throughout. Most importantly, the findings were shared with academic and industry experts, adding meaningful resemblance to the goals set out to achieve. / AFRIKAANSE OPSOMMING: Mobiele foon netwerke is wêreldwyd 'n onlosmaakbare deel van ekonomiese en sosiale ontwikkeling. Mobiele fone is deel van ons alledaagse lewe en dit is moeilik om 'n kompeterende ekonomie te bedink sonder die beskikbaarheid van mobiele kommunikasie. Ontluikende markte trek die meeste voordeel uit die implementering van mobiele tegnologie en groeitendense vertoon beter as wat vroeër voorspel is. Die mees gewilde en volhoubare betaalmetode wat deur mobiele foon netwerke in ontluikende markte gebruik word, is die voorafbetalingsmeganisme wat vir die verspreiding van lugtyd gebruik word. Hierdie meganisme bring unieke uitdagings vorendag in ontluikende markte. Die tesis beskryf die belangrikheid van die mobiele foon netwerk voorafbetalingswaardekanaal deur 'n analise te maak van vooruitbetalingsinkomste. 'n Kort oorsig oor die sisteme en produkte wat bydra tot die funksionering van die vooruitbetalingswaardekanaal word verskaf. 'n Beskrywing van die inkomste-genereringsproses vir die vooruitbetaling-sektor van die mark word verskaf en 'n in-diepte verduideliking van die belangrikheid van uitgestelde inkomste, hoe dit vasgelê word en watter rol dit speel in die generering van inkomste word verduidelik. Die kompleksiteit van die netwerkomgewing, beide op 'n tegniese en operasionele vlak, maak die gebruik van 'n besigheidsoutomatisering en ondersteuningsisteem (BSS) 'n noodsaaklike instrument vir die effektiewe uitvoer van take en prosesse binne die netwerkomgewing. Hierdie sisteme stoor informasie vanuit 'n wye spektrum van beskikbare tegniese netwerkbronne en gebruik die inligting om die vloei van netwerkprodukte te outomatiseer. Die gebruik van sodanige sisteem word voorgestel vir die berekening van uitgestelde inkomste. Saaty se Analitiese Hierargie Proses-algoritme (AHP) en die Eliminasie en Realiteit-Deur-Keuse Uitdrukkingsmetode (ELECTRE) word gebruik vir die vergelyking van die voorgestelde metode vir die berekening van uitgestelde inkomste deur middel van 'n BSS. Die gebruik van Saaty se algoritme om die effektiwiteit te bereken van uitgestelde inkomste soos gemeld deur die gebruik van 'n BSS, lewer gunstige resultate vir die voorgestelde metode. Dit vul 'n leemte in die swak nagevorsde mobiele telekommunikasie industrie. ELECTRE word gebruik om die bevindinge van die AHP-model te substansieer en betekenisvolle toetse word deurentyd gedoen om die korrektheid en akkuraatheid van die resultate te motiveer. Die belangrikste aspek van die navorsing is dat die bevindinge gedeel is met kenners binne die akademie sowel as die industrie, wat nou aansluit by die doelstellings wat aanvanklik beoog is.

Thesis (MSc)--Stellenbosch University, 2013. / 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. / AFRIKAANSE OPSOMMING: Daar is baie voorbeelde van samewerking in the gemeenskap en in die natuur. In sommige gevalle lei samewerking tot 'n toename in die algehele welvaart van die betrokkenes, terwyl samewerking in ander gevalle tot nadeel van die bre er gemeenskap mag wees. Die voorkoms van samewerking blyk natuurlik te wees indien daar 'n direkte voordeel vir die individue is wat kies om saam te werk. In voorbeelde van samewerking is s o 'n voordeel egter nie altyd voor-diehand- liggend nie. Die sogenaamde prisoniersdilemma word dikwels as voorbeeld in die studie van samewerking gebruik om die faktore wat na samewerking lei, te ontbloot. In klassieke speleteorie word daar aangeneem dat elke speler rasioneel is en dus poog om sy spelstrategie op s o 'n manier te kies dat sy eie verwagte uitbetaling gemaksimeer word. In die geval van die klassieke prisoniersdilemma veroorsaak dit dat beide spelers mekaar verraai. In evolusion^ere speleteorie, daarenteen, word daar slegs aangeneem dat elke speler oor beperkte kennis van die spel en begrensde rasionaliteit beskik. Spele in evolusion^ere speleteorie word in rondtes herhaal en spelers word die geleentheid gebied om gedurende hierdie herhalingsproses aan te pas en te leer. Vorige studies het getoon dat samewerking 'n lewensvatbare strategie is indien die prisoniersdilemma in 'n evolusion^ere konteks gespeel word, waar die evolusion^ere ksheid van 'n strategie direk afhang van die uitbetaling van 'n speler wat die strategie volg. Een van die meganismes wat volhoubare samewerking in die evolusion^ere prisoniersdilemma voortbring, is gestruktureerde interaksie tussen spelers. 'n Wiskundige raamwerk word vir die voorstelling van die evolusion^ere prisoniersdilemma in hierdie tesis ontwikkel. Hierdie wiskundige raamwerk word gebruik om 'n analitiese studie (met ander woorde sonder die gebruik van simulasie) van die dinamika van die prisoniersdilemma op 'n pad, siklus, rooster in die vlak, of rooster op die torus as onderliggende gra ek van stapel te stuur. Die doel van hierdie studie is om die waarskynlikheid vir die ontstaan van volhoubare samewerking tussen spelers te bepaal. Die prisoniersdilemma op 'n pad of siklus as onderliggende gra ek het twee fundamenteel verskillende parametergebiede tot gevolg; groot waardes van die versoeking-om-te-verraai parameter lei nie tot volhoubare samewerking nie, terwyl volhoubare samewerking wel vir klein waardes van hierdie parameter moontlik is. Daar word gevind dat die kans vir volhoubare samewerking toeneem tot sekerheid namate die orde van die onderliggende gra ek groei. Die toestandsruimte van die prisoniersdilemma met 'n rooster in die vlak of 'n rooster op die torus as onderliggende gra ek groei baie vinnig as 'n funksie van die orde van die gra ek. Die outomor smeklasse van die speltoestande word getel met die doel om te bepaal presies hoe vinnig die toestandsruimte van die spel as 'n funksie van die orde van die onderliggende gra ek groei. Die dinamika van die prisoniersdilemma met 'n rooster in die vlak of 'n rooster op die torus as onderliggende gra ek word laastens deur middel van konstruksies van die ooreenstemmende toestandsgra eke ondersoek (in gevalle waar die toestandsruimte klein genoeg is).

Thesis (MComm)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: This study explore how forecasting techniques can be combined in linear programming (LP) as a tool to optimise the parameters of forecasting methods in order to ensure sufficient capacity of logistic infrastructure exist for future growth. This study will use greenfield and brownfield projects from Sasol, a petrochemical company from South Africa, to test the methodology on. The methodology followed in the study was to firstly look at previous literature studies on logistical infrastructure and how to create sufficient capacity. Secondly, understandings of supply chain planning principles in general as well as supply chain planning in context of Sasol were investigated. Thirdly, different forecasting methods like; qualitative include judgemental, life cycle, Delphi method, market research etc. and quantitative methods including time series and causal methodologies had been investigated. Fourthly, decision making tools to incorporate multiple forecasts were investigated to understand why Sasol decided to use i2. Fifthly, the current capital project approach in Sasol had been investigated to fully understand where room for improvements would be possible. Finally the theory from the study was applied on two different projects in Sasol, one greenfield and one brownfield project. The results found that by using sound supply chain planning methodologies, sound supply chain design principles and multiple forecasts being combined by using LP decision making tools a better decision can be made with regards to logistical infrastructure investment as well as ensuring sufficient logistical infrastructure capacity. The two case studies have shown that this approach is flexible enough, apart from a few minor changes and can be adopted for both scenarios and that great results can be achieved. Logistical infrastructure could be optimised due to collaboration and the overall costs and performance of a supply chain improved. / AFRIKAANSE OPSOMMING: Hierdie studie ondersoek hoe lineêre programmering ( LP ), as n hulpmiddel, gebruik kan word om vooruitskattingstegnieke te kombineer om sodoende die vooruitskattingsmetodes te optimaliseer en te verseker dat voldoende kapasiteit van logistieke infrastruktuur bestaan vir toekomstige groei. Hierdie studie se metodes sal getoets word op groenveld- en bruinveldprojekte van Sasol , 'n petrochemiese maatskappy van Suid –Afrika. Die metode gevolg tydens die studie, was eerstens om te kyk na vorige literatuurstudies oor logistieke infrastruktuur en hoe om voldoende kapasiteit te skep. Tweedens, om ‘n breë oorsig van die beginsels van voorsieningsketting-beplanning te bekom sowel as voorsieningsketting-beplanning in die konteks van Sasol te ondersoek. Derdens, verskillende vootuitskattingsmetodes soos kwalitatiewe metodes (insluitend veroordelende-, lewensiklus- en Delphi-metode en marknavorsing) en kwantitatiewe metodes (insluitend die tydreeks- en oorsaaklike metodes) is geondersoek. In die vierde plek is besluitnemingshulpmiddels, wat verskeie vooruitskattings kombineer, geondersoek om te verstaan waarom Sasol besluit het om i2 aan te koop. In die vyfde plek is die metode van Sasol se kapitaalprojekte geondersoek om te verstaan of daar nie moontlik ruimte vir verbeterings sou wees nie. Laastens is die studie se metode op twee projekte van Sasol toegepas, een groenveld- en een bruinveldprojek. In die studie is gevind dat beter besluite geneem kan word aangaande beleggings in logistieke infrastruktuur en om te verskere daar is voldoende logistieke infrastruktuur kapasiteit - deur gebruik te maak van optimale metodes in voorsieningsketting-beplanning en voorsieningskettingontwerp. Die twee gevallestudies het getoon dat hierdie benadering buigsaam genoeg is, afgesien van 'n paar klein veranderinge, om vir beide moontlikhede gebruik te kan word en goeie resultate te behaal. Deur die samewerking van verskeie besigheidseenhede kon logistieke infrastruktuur geoptimaliseer word terwyl die kostes en algehele prestasie van voorsieningsketting verbeter kon word.

Thesis (MPhil)--Stellenbosch University, 2000. / ENGLISH ABSTRACT: The implementation of the Marketing of Agricultural Products Act of 1996 resulted in the deregulation of the South African fruit industry in October 1997. This led to independent decision-making regarding the marketing of export products by a host of deciduous fruit producers and exporters. No longer were the producers controlled by a monopoly. The deregulation challenged the inflexible single-channel fruit pooling marketing structure of the past and exposed domestic producers and exporters to the competitive global fruit market. By implication this translated into a need to become globally competitive in the interest of growing market share. The focus of this new marketing system is to give the producer the opportunity to export high quality fruit and earn an associated premium for his products, and to strengthen his brand and reputation through these efforts. The deregulation also provided the opportunity for independent fruit growers to influence the optimisation of the value chain, in the interest of lower costs and improved customer service. The market has since changed from supply (stock "push") to demand driven (stock "pull"). It is now imperative that the various producers and exporters provide an efficient supply chain in order to satisfy the end user demands. A consequence of this would be the increase in deciduous fruit quality as a determinant of decidU<;ms fruit demand. Market research was conducted to determine the impact that deregulation has had on South Africa's deciduous fruit industry and to establish the degree to which Portnet should transform to accommodate this changing and deregulated environment. In summary, deregulation has created many opportunities for South African fruit producers and exporters in the domestic and international markets. The only impediment is whether the new logistical structures will be able to reduce costs and improve profit margins, particularly now that economies of scale have been dissipated. Customer service may improve, but at what cost? / AFRIKAANSE OPSOMMING: Die implementering van die Bemarkingswet van Landbouprodukte in 1996 het gelei tot die deregulering van die Suid-Afrikaanse vrugtebedryf in Oktober 1997. Die gevolg hiervan was die onafhanklike besluitneming ten opsigte van die bemarking van uitvoerprodukte deur 'n groep sagtevrugteprodusente en -uitvoerders. Die produsente is nie langer deur 'n monopolie beheer nie. Die deregulering het die onbuigbare een-kanaal vrugtebemarkingstruktuur van die verlede opsy geskuif en binnelandse produsente en uitvoerders die geleentheid gebied om deel te word van die kompeterende intemasionale vrugtemark. Dit het by implikasie aanleiding gegee tot 'n behoefte om intemasionaal mededingend te wees in die belang van 'n groeiende markaandeel. Die fokus van hierdie nuwe bemarkingstelsel is om die produsent die geleentheid te gee om hoe kwaliteit vrugte uit te voer en die meegaande hoe premie vir sy produkte te verdien, asook om sy handelsmerk en reputasie sodoende te vestig. Die deregulasie het ook die onafhanklike vrugteprodusente die geleentheid gegee om seggenskap in die optimisering van die waardeketting te kry wat tot laer koste en verbeterde klientediens gelei het. Sedertdien het die mark verander vanaf 'n aanbodmark na 'n vraaggedrewe mark. Dit is nou uiters belangrik dat die verskillende produsente en uitvoerders 'n effektiewe voorsieningsnetwerk skep om in die eindverbruikers se behoeftes te voorsien. Die gevolg sou 'n toename in die gehalte van sagtevrugte wees, wat weer belangrike determinant van die sagtevrugte vraag is. Marknavorsing is gedoen om die impak van die deregulasie op die Suid-Afrikaanse sagtevrugtebedryfvas te stel. Wat ook vasgestel moes word, was die mate waartoe Portnet moet transformeer om in die veranderde en gedereguleerde omgewing te funksioneer. Om op te som, deregulering het verskeie geleenthede vir Suid-Afrika se vrugteprodusente en uitvoerders in die binnelandse en intemasionale markte geskep. Die enigste vraag is of die nuwe logistieke strukture wel koste sal verminder en winsmarges sal verhoog, veral noudat skaalvoordele nie meer van toepassing is nie. Klientediens sal verbeter, maar teen watter koste?

Thesis (PhD)--Stellenbosch University, 2011. / What factors influence the economic sustainability of local suppliers in emerging markets in the automotive value chain? The answer to this question is not only influenced by the direct and indirect customers of the automotive component suppliers, but it is also influenced by factors on the macro-, meso- and micro-levels of the supplier‟s environment. In order to investigate the research objective, the South African automotive industry is chosen as a case study in the global automotive value chain. The literature review indicates that variables that influence the economic sustainability of suppliers can be found on the global and regional levels of the automotive industry, as well as on the industry and corporate value chain levels. As the theory does not offer a holistic approach for a problem solution, the identified factors are assembled in a conceptual model that measures the economic sustainability of automotive component suppliers with respect to financial dimensions. The conceptual model is structured according to the macro-, meso- and micro-level influences, and also recognises the impact of governance structures on the government, market, industry and corporate levels. The suggested conceptual model is subsequently tested for totality and alignment with industry features using qualitative methods and is furthermore validated by using quantitative modelling data from primary research in the supplier component industry. The analysis of the quantitative data shows that the majority of factors influencing the economic sustainability of local component suppliers can be found on the micro- and meso-levels (corporate value chain and industry value chain), whereas the qualitative data implies that economic sustainability is mainly influenced by factors on the macro- and meso-levels (industrial policy and labour market). This finding shows that there is a discrepancy between the measurable influences and the automotive component suppliers‟ perception of the research problem. Nevertheless, it can be stated that the conceptual model, as supported by the stakeholder group, can be used for further research. Alongside the development of the conceptual model, the industry data is used for a discussion about the status of the South African automotive component supplier industry in order to point out strengths and issues as well as to identify factors that should change or improve to enable a viable future for suppliers.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Road Tra c legislation prescribes constraints on the forces/loads which vehicles may exert on the road at contact surfaces or load points. These constraints have bearing on speci c contact surfaces or groups of contact surfaces. The constraints are in the form of maximum force values and maximum ratios, which may exist between forces. The forces exerted by a vehicle on the road is determined by a combination of the vehicle's own mass, dimensional characteristics, and the mass and position of its cargo. The mass and position of the cargo can be modelled by only considering its centroid. The centroid's position is linked to a certain cargo arrangement. It is necessary, in terms of legal constraints, to distinguish between legally permissable- and non-permissable arrangements. Methods are proposed in this dissertation to determine the borders for the position of the centroid according to cargo-mass, for a variety of vehicle con gurations. The determination of borders for the position of the centroid is the result of a three part process. Firstly, the legal limits are translated to mathematical inequalities that must be satis ed for the forces at contact surfaces. Secondly, conservative parametric estimates for the forces, in terms of the position and the mass of the centroid of a given vehicle, must be derived. Finally these estimates are incorporated into the load constraints and an enclosed permissable area for the centroid is found. These position constraints are suitable inputs to solution methods of various cargo arrangement problems. Linear programmes which can solve certain general arrangement problems by utilising the position constraints on the centroid, were successfully developed. Solutions are presented for the arrangement of pallet-freight, as well as the arrangement of cargo units with asymetrical centroids over the length or width of a vehicle's cargo area. / AFRIKAANSE OPSOMMING: Padvervoerwetgewing skryf grense op kragte/laste voor wat voertuie by kontakoppervlakke of laspunte, op die pad mag uitoefen. Hierdie voorskrifte het betrekking op spesi eke laspunte en groepe van laspunte. Die voorskrifte is in die vorm van maksimum laswaardes by laspunte en maksimum ratio's wat tussen sekere laste mag bestaan. Die laste wat 'n voertuig op die pad uitvoer word bepaal deur 'n kombinasie van die voertuig se eie massa, dimensionele eienskappe, sowel as sy vrag se massa en posisie. Die vrag se massa en posisie kan gemodelleer word deur slegs die massamiddelpunt daarvan te beskou. Die massamiddelpunt se posisie word gekoppel aan 'n bepaalde vragrangskikking. Dit is nodig om, in terme van wetlike voorskrifte, te kan onderskei tussen wetlik toelaatbare en -ontoelaatbare rangskikkings. Metodes word in hierdie proefskrif voorgestel waarmee daar grense vir die posisie van die vragmassamiddelpunt bepaal kan word na gelang van die vragmassa, vir 'n verskeidenheid van voertuigkon gurasies. Die bepaling van grense vir die posisie van die vragmassamiddelpunt is die resultaat van 'n drieledige proses. Eerstens word die wetlike beperkings herlei na wiskundige ongelykhede waarbinne laste by kontakoppervlakke moet val. Tweedens word konserwatiewe parametriese beramings vir die laste verkry in terme van die ligging en massa van die vragmassamiddelpunt vir 'n gegewe voertuig. Laastens word hierdie beramings in die lasbeperkings opgeneem om 'n afgebakende toelaatbare gebied vir die vragmassamiddelpunt se posisie te verkry. Hierdie posisiebeperkings is geskik om as inset te dien in die oplossingmetodes van 'n verskeidenheid van vragrangskikkingsprobleme. Line^ere programme wat sekere algemene rangskikkingsprobleme kan oplos deur die aanwending van posisiebeperkings op die vragmassamiddelpunt, is suksesvol ontwikkel. Oplossings word aangebied vir die rangskikking van paletvrag, asook die rangskikking van vrageenhede met asimmetriese massamiddelpunte oor die lengte of breedte van 'n voertuig se vragarea.