Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Order picking is the most important activity in distribution centres. It involves the process of retrieving products from storage in response to a speci c customer request. The order picking system in a distribution centre used by Pep Stores Ltd. (Pep), located in Durban, South Africa, is considered. The order picking system in Pep utilises picking lines. The system requires that the pickers move in a clockwise direction around the picking line. The planning of picking lines may be divided into three tiers of decisions. The rst tier determines which Stock Keeping Units (SKUs) should be allocated to which picking line and is known as the SKU to Picking Line Assignment Problem (SPLAP). The second tier, the SKU Location Problem (SLP), considers the positioning of the various SKUs in a picking line. The nal tier considers the sequencing of the orders for pickers within a picking line and is referred to as the Order Sequencing Problem (OSP). Collectively, these three tiers aim to achieve the objective of picking all the SKUs for all the orders in the shortest possible time. The decisions associated with each tier are made sequentially during the planning of a picking line. Each problem therefore relies on the information generated by its predecessing tier(s). Initially the OSP is addressed. A number of heuristic and metaheuristic approaches are presented, together with an exact formulation to solve this tier. The size of the problem is reduced by using a relaxation of the problem that may be solved exactly. A number of greedy tour construction heuristics, a scope and ranking algorithm, methods based on awarding starting locations with respect to preference ratios and a modi ed assignment approach was used to solve the OSP. Furthermore, a tabu search, simulated annealing, genetic algorithm and a generalised extremal optimisation approach are used to solve the OSP. The solution quality and computational times of all the approaches are compared for the data provided by Pep, with the generalised extremal optimisation approach delivering the best solution quality. Two methods from the literature was used to model the SLP, whereafter an ant colony system was used to maximise the number of orders in common between adjacent SKUs. A number of agglomerative clustering algorithms were used from which dendrograms could be constructed. Two novel heuristic clustering algorithms were considered. The rst heuristic calculates a distance between two clusters as the set of orders that have to collect all the SKUs in both clusters, whereas the second method is based upon the frequency of SKUs within a cluster. Little or no improvement was achieved in most cases. The SPLAP was introduced by means of a number of possibilities of how to formulate objectives. A possible exact formulation is presented, followed by a nearest neighbour search, which was initially used to construct new picking lines based on all data sets. A di erent approach was then taken by means of a tabu search where the waves of two or three picking lines were altered. Signi cant savings may be incurred for large data sets. / AFRIKAANSE OPSOMMING: Die opmaak van bestellings is die belangrikste aktiwiteit in 'n distribusiesentrum. Dit behels dat geskikte hoeveelhede produkte uit stoorplekke opgespoor en herpak moet word om aan kleinhandeltakke gestuur te word. Die bedrywighede binne een van Pep Stores Ltd. (Pep) se distribusiesentrums in Durban, Suid-Afrika, word beskou. Die sisteem vereis dat die werkers in 'n kloksgewyse rigting om 'n uitsoeklyn beweeg. Die beplanning van die uitsoeklyne kan verdeel word in drie besluite/probleme. Die eerste besluit is watter voorraadeenhede (VEs) toegewys moet word aan watter uitsoeklyn. Die tweede besluit is in watter vakkies in die uitsoeklyn die VEs geplaas moet word, en word die VE-plasings probleem (VLP) genoem. Die nale besluit is in watter volgorde bestellings opgemaak moet word in 'n uitsoeklyn, en staan bekend as die volgorde-van-bestellings-probleem (VBP). Die doel van al drie hierdie probleme is om al die bestellings in 'n uitsoeklyn in die kortste moontlike tyd af te handel. Die besluite wat verband hou met elke vlak van besluit word opeenvolgend gedoen tydens die beplanning van 'n uitsoeklyn. Die oplossing van elke subprobleem berus op die inligting van die voorafgaande probleme. Aanvanlik word die VBP beskou. 'n Aantal heuristiese en metaheuristiese benaderings word aangebied saam met 'n eksakte formulering om die derde vlak op te los. Die grootte van die probleem is verminder deur die gebruik van 'n verslapping van 'n eksakte formulering. 'n Aantal toerkonstruksie heuristieke, 'n omvang en rangorde algoritme, metodes wat gebaseer is op die toekenning van beginpunte met betrekking tot voorkeurverhoudings en 'n veralgemeende toewysingsprobleem is gebruik om die VBP op te los. 'n Tabu-soektog, gesimuleerde tempering, genetiese algoritme en 'n veralgemeende-ekstreme-optimering-benadering word ook gebruik om die VBP op te los. Die oplossingsgehalte en berekeningstye van al die benaderings word vergelyk vir werklike data wat verskaf is deur Pep. Die veralgemeende-ekstreme-optimering-benadering lewer die beste oplossingsgehalte. Twee metodes uit die literatuur is gebruik om die VLP te modelleer, waarna 'n mier kolonie stelsel gebruik word om die aantal bestellings wat aangrensende VEs in gemeen het te maksimeer. 'n Aantal groeperingsalgoritmes word gebruik wat dendrogramme kan lewer. Twee heuristiese groeperingsalgoritmes word oorweeg. Die eerste heuristiek bereken die afstand tussen twee groepe as die aantal bestellings wat al die VEs in beide groepe moet versamel, terwyl die tweede metode gebaseer is op die frekwensie van VEs binne 'n groep. Min of geen verbeterings is in die meeste gevalle gevind. Die eerste besluit word bekend gestel na aanleiding van 'n aantal moontlike maniere om die doelwitte te formuleer. 'n Moontlike eksakte formulering word aangebied. 'n Alternatiewe benadering is geneem deur middel van 'n tabu-soektog waar die golwe van twee of drie uitsoeklyne gewysig word. Beduidende besparings word gerealiseer vir groot datastelle.

Thesis (MComm)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: PEP is a devision of Pepkor Retail Limited and is the biggest single brand store network in Southern Africa and also owns and runs the largest clothing factory in Southern Africa. It was founded in 1965 and has since grown to more than 1 400 stores in 9 African countries (there is a PEP store in almost every town and village in South Africa). Currently the warehouse management system (WMS) implemented by PEP only allows for a stock keeping unit (SKU) to be placed on one picking line in one location when the distribution list (DBN) is released. Because pickers are only allowed to walk clockwise around the conveyor belt, they are forced to pass a location at least the same number of times as the number of branches to which the SKU is to be distributed to. Therefore if the SKUs with the highest pick frequency can be assigned to 2 locations (it is duplicating the SKU), the number of times each of these locations must be passed may be reduced. In this study 4 questions are considered when 15 algorithms are constructed that will determine how an algorithm assign the SKUs to picking lines. Question 1 determines whether the original picking lines are to be treated separately (PS) or to combine them rst (PC). The second question is to decide if the SKUs are rst to be duplicated and then assigned to picking lines (DA) or if they are rst assigned to picking lines and then duplicated (AD). Question 3 determines whether the non-duplicate and duplicate SKUs are treated separately (ND) or simultaneously (S) when they are assigned to the picking lines. The nal question is to specify how the SKUs are assigned to the picking lines. Three assignment methods (cyclical, set length subset sequential assignment, remaining high, low cyclical assignment) and 6 clustering algorithms are introduced. The conclusion is made that the SKUs with the highest pick frequency is duplicated rst to yield the biggest saving in the number of cycles. Between 40{70% of the SKUs should be duplicated, dependant on the algorithm used. The only decision that has a major in uence on the number of cycles is the assignment method used. Algorithm 5 and 8 yielded the greatest saving in the number of cycles (40.7% and 39.8% respectively), both implementing set length subset sequential assignment, followed by the clustering algorithms. / AFRIKAANSE OPSOMMING: PEP is 'n afdeling van Pepkor Retail Limited en is die grootste enkel-handelsmerk winkelnetwerk in Suidelike Afrika. PEP besit en bestuur ook die grootste klerefabriek in Suidelike Afrika. PEP is gestig in 1965 en het sedertien gegroei tot meer as 1 400 winkels in 9 Afrika lande (daar is 'n PEP winkel in amper elke dorp in Suid-Afrika). Op die oomblik laat die pakhuisbestuurstelsel, wat deur PEP in sy distribusie sentrum ge mplementeer word, slegs toe dat voorraadeenhede (VEs) in 'n enkele vakkie langs 'n enkele uitsoeklyn geplaas word. Aangesien werkers slegs toegelaat word om kloksgewys om die vervoerband te beweeg, word hulle gedwing om ten minste soveel keer verby elke vakkie in die uitsoeklyn te loop as wat die aantal winkels is waarna die VEs in daardie vakkie versprei moet word. Dus indien die vakkies wat die VEs bevat wat na die meeste winkels versprei moet word, tussen 2 vakkies verdeel word (die VE word gedupliseer), verminder die aantal kere wat beide vakkies besoek moet word. In hierdie studie word 4 vrae beskou wat geantwoord moet word wanneer die 15 algoritmes opgestel word, wat sal bepaal hoe die algoritme die VEs hanteer. Vraag 1 bepaal of die oorspronklike uitsoeklyne wat deur PEP verskaf is apart hanteer word en of hulle eers gekombineer moet word. Die tweede vraag bepaal of die VEs eers gedupliseer word en dan aan die onderskeie uitsoeklyne toegedeel word en of die VEs eers aan die uitsoeklyne toegedeel word en dan gedupliseer word. Vraag 3 is slegs van toepassing wanneer die VEs eers gedupliseer word en dan toegedeel word aan die uitsoeklyne, en bepaal of die nie-gedupliseerde en gedupliseerde VEs apart of gelyktydig hanteer word. Die laaste vraag spesi seer met behulp van watter metode die VEs toegedeel word aan die onderskeie uitsoeklyne. Drie toedelingsmetodes (sikliese toedeling, vaste lengte subversameling opeenvolgende toedeling, oorblywende hoogste/laagste sikliese toedeling) en 6 bondelalgoritmes word voorgestel. Die gevolgtrekking word gemaak dat die VEs met die hoogste uitsoek frekwensie eerste gedupliseer moet word om die grootste besparing mee te bring in die aantal siklusse om al die VEs uit te soek. Tussen 40{70% van die VEs moet gedupliseer word afhangende van die algoritme wat gebruik word. Die enigste besluit wat 'n noemenswaardige invloed op die aantal siklusse het is die toedelingsmetode. Algoritme 5 en 8 lewer die grootste besparing in die aantal siklusse (40.7% en 39.8% onderskeidelik), beide implementeer die vaste lengte subversameling opeenvolgende toedeling, gevolg deur die bondelalgoritmes.

Thesis (PhD (Logistics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Computerised sugarcane harvest scheduling decision support is an active fi eld of research which ties in closely with the broader problem of automating and streamlining the various activities in the sugar supply chain. In this dissertation, the problem of providing decision support with respect to sugarcane harvesting decisions is defined within a number of contexts, each representing a typical kind of organisation of sugarcane farmers into a cohesive decision making unit with its speci fic requirements and limitations that exist in practice. A number of variations relevant to these contexts of an overarching tactical sugarcane harvest scheduling problem (THSP) are considered and solved in this dissertation. The THSP is the problem of providing objective, responsible decision support to persons charged with the task of determining optimal harvesting dates for a set of sugarcane fields across an entire season. Sugarcane fields typically diff er in terms of the age, variety, life-cycle stage and in many other properties of the cane grown on them. The growth of sugarcane crops may also be a ffected by environmental conditions such as accidental fires, frosts or storms which have a detrimental e ffect on crop-value. Since sugarcane is a living organism, its properties change over time, an so does the potential pro t associated with it. The practicalities of farming cause further complication of the problem (for example, seasonal changes alter the conditions under which the crop is harvested and transported). The rainy season carries with it the added cost of disallowing long-range vehicles to drive into the fields, forcing the unloading and reloading of cane at so-called loading zones. Other considerations, such as the early ploughing out of fields to allow them to fallow before being replanted, compounds the THSP into a multi-faceted difficult problem requiring efficient data management, mathematical modelling expertise and efficient computational work. In the literature the THSP has been viewed from many different standpoints and within many contexts, and a variety of operations research methodologies have been employed in solving the problem in part. There is, however, no description in the literature of a solution to the THSP that takes the negative e ffects of extreme environmental conditions on the quality of a harvesting schedule into account in a scienti fically justifi able manner; most models in the literature are based on optimising sucrose yield alone under normal conditions, rendering weak schedules in practice. The scope of the modelling and solution methodologies employed in this dissertation towards solving the THSP is restricted to integer programming formulations and approximate solution methods. The parameters associated with these models were determined empirically using historical data, as well as previous work on deterioration of sugarcane following environmental and other events. The THSP is solved in this dissertation by designing a generic architecture for a conceptual decision support system (DSS) for the THSP in the various contexts referred to above, which is capable of accommodating the e ects of extra-ordinary environmental conditions, as well as the introduction of a computer-implemented version of a real DSS for the THSP conforming to the framework of this generic architecture. The DSS building blocks include prediction models for sugarcane yield, sugarcane recoverable value under normal circumstances, the costs associated with a harvesting schedule and the negative e ects on sugarcane recoverable value of extraordinary environmental conditions. The working of the DSS is based on a combinatorial optimisation model resembling the well-known asymmetric traveling salesman problem with time-dependent costs which is solved approximately by means of an attribute-based tabu search in which both local and global moves have been incorporated. The DSS is also validated by experienced sugarcane industry experts in terms of the practicality and quality of the schedules that it produces. / AFRIKAANSE OPSOMMING: Gerekenariseerde besluitsteun vir die skedulering van suikerriet-oeste is 'n aktiewe navorsingsveld wat nou verwant is aan die bre ër probleem van die outomatisering en vaartbelyning van 'n verskeidenheid aktiwiteite in die suikervoorsieningsketting. Die probleem van die daarstelling van steun rakende suikkerriet oestingsbesluite word in hierdie proefskrif in 'n aantal kontekste oorweeg, elk met betrekking tot 'n tipiese soort organisasie van suikerrietboere in 'n samehorige besluitnemingseenheid met sy spesi eke vereistes en beperkings in die praktyk. Verskeie variasies van 'n oorkoepelende taktiese suikerriet-oesskeduleringsprobleem (TSOSP) wat in hierde kontekste relevant is, naamlik die probleem om objektiewe, verantwoordbare steun aan besluitnemers te bied wat verantwoordelik is vir die bepaling van optimale oesdatums vir 'n versameling suikerrietplantasies oor die bestek van 'n hele seisoen, word in hierdie proefskrif bestudeer en opgelos. Suikerrietplantasies verskil tipies in terme van ouderdom, gewastipe, posisie in die lewensiklus, en vele ander eienskappe van die suikerriet wat daar groei. Omgewingstoestande, soos onbeplande brande, ryp of storms, het verder ook 'n negatiewe impak op die waarde van suikerriet op sulke plantasies. Omdat suikerriet 'n lewende organisme is, verander die eienskappe daarvan oor tyd, en so ook die potensi ele wins wat daarmee geassosieer word. Boerderypraktyke bemoeilik verder die skeduleringsprobleem onder beskouing (seisoenale veranderings beïnvloed byvoorbeeld die wyse waarop suikerriet ge-oes en vervoer word). Addisionele koste gaan voorts met die re ënseisoen gepaard, omdat die plantasies dan nie toeganklik is vir langafstand transportvoertuie nie en suikerriet gevolglik na spesiale laaisones gekarwei moet word voordat dit op hierdie voertuie gelaai kan word. Ander oorwegings, soos die vroe ë uitploeg van plantasies sodat die grond kan rus voordat nuwe suikerriet aangeplant word, veroorsaak dat die TSOSP 'n moeilike multi-faset probleem is, wat goeie databestuur, wiskundige modelleringsvernuf en doeltreff ende rekenaarwerk vereis. Die TSOSP word in die literatuur vanuit verskillende standpunte en in verskeie kontekste oorweeg, en 'n aantal uiteenlopende operasionele navorsingsmetodologie ë is al ingespan om hierdie probleem ten dele op te los. Daar is egter geen poging in die literatuur om 'n oplossing vir die TSOSP daar te stel waarin daar op 'n wetenskaplik-verantwoordbare wyse voorsiening gemaak word vir die negatiewe e ffekte wat uitsonderlike omgewingstoestande op die kwaliteit van oesskedules het nie; die meeste modelle in die literatuure is op slegs sukrose-opbrengs onder normale omstandighede gebaseer, wat lei na swak skedules in die praktyk. Die bestek van die wiskundige modellerings- en gepaardgaande oplossings-metodologie ë word in hierdie proefskrif vir die TSOSP beperk tot onderskeidelik heeltallige programmeringsformulerings en die bepaling van benaderde oplossings deur lokale soekprosedures. Die parameters wat met hierdie modelle en soekmetodes geassosieer word, word empiries bepaal deur gebruikmaking van historiese data asook bestaande werk oor die degradering van suikerriet as gevolg van omgewings- en ander eksterne faktore. Die TSOSP word in hierdie proefskrif opgelos deur die ontwerp van 'n generiese argitektuur vir 'n konseptuele besluitsteunstelsel (BSS) vir die TSOSP in die onderskeie kontekste waarna hierbo verwys word en wat die e ekte van uitsonderlike omgewingsfaktore in ag neem, asook die daarstelling van 'n rekenaar-ge ïmplementeerde weergawe van 'n daadwerklike BSS vir die TSOSP wat in die raamwerk van hierdie generiese argitektuur pas. Die boustene van hierdie BSS sluit modelle in vir die voorspelling van suikerrietopbrengs, die herwinbare waarde van suikerriet onder normale omstandighede, die verwagte koste geassosieer met 'n oesskedule en die negatiewe e ekte van omgewingsfaktore op die herwinbare waarde van suikerriet. Die werking van die BSS is gebaseer op 'n kombinatoriese optimeringsprobleem wat aan die welbekende asimmetriese handelreisigersprobleem met tyd-afhanklike kostes herinner, en hierdie model word benaderd opgelos deur middel van 'n eienskap-gebaseerde tabu-soektog waarin beide lokale en globale skuiwe ge ïnkorporeer is. Die BSS word ook gevalideer in terme van die haalbaarheid en kwaliteit van die skedules wat dit oplewer, soos geassesseer deur ervare kundiges in die suikerrietbedryf.

Thesis (PhD (Logistics))--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: The design of a water distribution system (WDS) involves finding an acceptable trade-off between cost minimisation and the maximisation of numerous system benefits, such as hydraulic reliability and surplus capacity. The primary design problem involves cost-effective specifica- tion of a pipe network layout and pipe sizes (which are typically available in a discrete set of commercial diameters) in order to satisfy expected consumer water demands within required pressure limits. The problem may be extended to consider the design of additional WDS com- ponents, such as reservoirs, tanks, pumps and valves. Practical designs must also cater for the uncertainty of demand, the requirement of surplus capacity for future growth, and the hydraulic reliability of the system under different demand and potential failure conditions. A detailed literature review of exact and approximate approaches towards single-objective (minimum cost) WDS design optimisation is provided. Essential topics which have to be included in any modern WDS design paradigm (such as demand estimation, reliability quantification, tank design and pipe layout) are discussed. A number of formative concepts in multi-objective evo- lutionary optimisation are also reviewed (including a generic problem formulation, performance evaluation measures, comparative testing strategies, and suitable classes of metaheuristics). The two central themes of this dissertation are conducting multi-objective WDS design optimi- sation using metaheuristics, and a critical examination of surrogate measures used to quantify WDS reliability. The aim in the first theme is to compare numerous modern metaheuristics, in- cluding several multi-objective evolutionary algorithms, an estimation of distribution algorithm and a recent hyperheuristic named AMALGAM (an evolutionary framework for the simulta- neous incorporation of multiple metaheuristics applied here for the first time to a real-world problem), in order to determine which approach is most capable with respect to WDS design optimisation. Several novel metaheuristics are developed, as well as a number of new variants of existing algorithms, so that a total of twenty-three algorithms were compared. Testing with respect to eight small-to-large-sized WDS benchmarks from the literature reveals that the four top-performing algorithms are mutually non-dominated with respect to the vari- ous performance metrics. These algorithms are NSGA-II, TAMALGAMJndu, TAMALGAMndu and AMALGAMSndp (the last three being novel variants of AMALGAM). However, when these four algorithms are applied to the design of a very large real-world benchmark, the AMALGAM paradigm outperforms NSGA-II convincingly, with AMALGAMSndp exhibiting the best perfor- mance overall. As part of this study, a novel multi-objective greedy algorithm is developed by combining several heuristic design methods from the literature in order to mimic the design strategy of a human engineer. This algorithm functions as a powerful local search. However, it is shown that such an algorithm cannot compete with modern metaheuristics, which employ advanced strategies in order to uncover better solutions with less computational effort. The second central theme involves the comparison of several popular WDS reliability surro- gate measures (namely the Resilience Index, Network Resilience, Flow Entropy, and a novel mixed surrogate measure) in terms of their ability to produce designs that are robust against pipe failure and water demand variation. This is the first systematic study on a number of WDS benchmarks in which regression analysis is used to compare reliability surrogate measures with probabilistic reliability typically derived via simulation, and failure reliability calculated by considering all single-pipe failure events, with both reliability types quantified by means of average demand satisfaction. Although no single measure consistently outperforms the others, it is shown that using the Resilience Index and Network Resilience yields designs that achieve a better positive correlation with both probabilistic and failure reliability, and while the Mixed Surrogate measure shows some promise, using Flow Entropy on its own as a quantifier of re- liability should be avoided. Network Resilience is identified as being a superior predictor of failure reliability, and also having the desirable property of supplying designs with fewer and less severe size discontinuities between adjacent pipes. For this reason, it is recommended as the surrogate measure of choice for practical application towards design in the WDS industry. AMALGAMSndp is also applied to the design of a real South African WDS design case study in Gauteng Province, achieving savings of millions of Rands as well as significant reliability improvements on a preliminary engineered design by a consulting engineering firm. / AFRIKAANSE OPSOMMING: Die ontwerp van waterverspreidingsnetwerke (WVNe) behels die soeke na ’n aanvaarbare afruiling tussen koste-minimering en die maksimering van ’n aantal netwerkvoordele, soos hidroliese betroubaarheid en surpluskapasiteit. Die primere ontwerpsprobleem behels ’n koste-doeltreffende spesifikasie van ’n netwerkuitleg en pypgroottes (wat tipies in ’n diskrete aantal kommersiele deursnedes beskikbaar is) wat aan gebruikersaanvraag binne sekere drukspesifikasies voldoen. Die probleem kan uitgebrei word om die ontwerp van verdere WVN-komponente, soos op- gaardamme, opgaartenks, pompe en kleppe in ag te neem. Praktiese WVN-ontwerpe moet ook voorsiening maak vir onsekerheid van aanvraag, genoegsame surpluskapsiteit vir toekom- stige netwerkuitbreidings en die hidroliese betroubaarheid van die netwerk onder verskillende aanvraag- en potensiele falingsvoorwaardes. ’n Omvattende literatuurstudie word oor eksakte en benaderde oplossingsbenaderings tot enkel- doelwit (minimum koste) WVN-ontwerpsoptimering gedoen. Sentrale temas wat by heden- daagse WVN-ontwerpsparadigmas ingesluit behoort te word (soos aanvraagvooruitskatting, die kwantifisering van betroubaarheid, tenkontwerp en netwerkuitleg), word uitgelig. ’n Aantal basiese konsepte in meerdoelige evolusionˆere optimering (soos ’n generiese probleemformulering, werkverrigtingsmaatstawwe, vergelykende toetsingstrategie¨e, en sinvolle klasse metaheuristieke vir WVN-ontwerp) word ook aangeraak. Die twee sentrale temas in hierdie proefskrif is meerdoelige WVN-ontwerpsoptimering deur mid- del van metaheuristieke, en ’n kritiese evaluering van verskeie surrogaatmaatstawwe vir die kwantifisering van netwerkbetroubaarheid. Die doel in die eerste tema is om ’n aantal moderne metaheuristieke, insluitend verskeie meerdoelige evolusionere algoritmes en die onlangse hiper- heuristiek AMALGAM (’n evolusionere raamwerk vir die gelyktydige insluiting van ’n aantal metaheuristieke wat hier vir die eerste keer op ’n praktiese probleem toegepas word), met mekaar te vergelyk om sodoende ’n ideale benadering tot WVN-ontwerpoptimering te identi- fiseer. Verskeie nuwe metaheuristieke sowel as ’n aantal nuwe variasies op bestaande algoritmes word ontwikkel, sodat drie en twintig algoritmes in totaal met mekaar vergelyk word. Toetse aan die hand van agt klein- tot mediumgrootteWVN-toetsprobleme uit die literatuur dui daarop dat die vier top algoritmes mekaar onderling ten opsigte van verskeie werkverrigtings- maatstawwe domineer. Hierdie algoritmes is NSGA-II, TAMALGAMJndu, TAMALGAMndu en AMALGAMSndp, waarvan laasgenoemde drie nuwe variasies op AMALGAM is. Wanneer hierdie vier algoritmes egter vir die ontwerp van ’n groot WVN-toetsprobleem ingespan word, oortref die AMALGAM-paradigma die NSGA-II oortui-gend, en lewer AMALGAMSndp die beste resultate. As deel van hierdie studie is ’n nuwe meerdoelige gulsige algoritme ontwerp wat verskeie heuristiese ontwerpsmetodologiee uit die literatuur kombineer om sodoende die on- twerpstrategie van ’n ingenieur na te boots. Hierdie algoritme funksioneer as ’n kragtige lokale soekprosedure, maar daar word aangetoon dat die algoritme nie met moderne metaheuristieke, wat gevorderde soekstrategie¨e inspan om beter oplossings met minder berekeningsmoeite daar te stel, kan meeding nie. Die tweede sentrale tema behels die vergelyking van ’n aantal gewilde surrogaatmaatstawwe vir die kwantifisering van WVN-betroubaarheid (naamlik die elastisiteitsindeks, netwerkelastisiteit, vloei-entropie en ’n gemengde surrogaatmaatstaf ) in terme van die mate waartoe hul gebruik kan word om WVNe te identifiseer wat robuust is ten opsigte van pypfaling en variasie in aanvraag. Hierdie proefskrif bevat die eerste sistematiese vergelyking deur middel van regressie-analise van ’n aantal surrogaatmaatstawwe vir die kwantifisering van WVN-betroubaarheid en stogastiese betroubaarheid (wat tipies via simulasie bepaal word) in terme van ’n aantal toetsprobleme in die literatuur. Alhoewel geen enkele maatstaf as die beste na vore tree nie, word daar getoon dat gebruik van die elastisiteitsindeks en netwerkelastisiteit lei na WNV-ontwerpe met ’n groter positiewe korrelasie ten opsigte van beide stogastiese betroubaarheid en falingsbetroubaarheid. Verder toon die gebruik van die gemengde surrogaatmaatstaf potensiaal, maar die gebruik van vloei-entropie op sy eie as kwantifiseerder van betroubaarheid behoort vermy te word. Netwerkelastisiteit word as ’n hoe-gehalte indikator van falingsbetroubaarheid geidentifiseer en het ook die eienskap dat dit daartoe instaat is om ontwerpe met ’n kleiner aantal diskontinuiteite sowel as van ’n minder ekstreme graad van diskontinuiteite tussen deursnedes van aangrensende pype daar te stel. Om hierdie rede word netwerkelastisiteit as die surogaatmaatstaf van voorkeur aanbeveel vir toepassings van WVN-ontwerpe in die praktyk. AMALGAM word ook ten opsigte van ’n werklike Suid-Afrikaanse WVN-ontwerp gevallestudie in Gauteng toegepas. Hierdie toepassing lei na die besparing van miljoene rande asook noe- menswaardige verbeterings in terme van netwerkbetroubaarheid in vergeleke met ’n aanvanklike ingenieursontwerp deur ’n konsultasiefirma.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: see item for full text / AFRIKAANSE OPSOMMING: sien item vir volteks

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 (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 (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: An order picking operation in a distribution centre (DC) owned by Pep Stores Ltd, located in Durban, South Africa was considered. The order picking operation utilises picking lines and the concept of wave picking. A picking line is a central area with storage locations for pallet loads of stock keeping units (SKUs) around a conveyor belt. The system shows many similarities to unidirectional carousel systems found in literature, however, the unidirectional carousel system is not common. Sets of SKUs must be assigned to pick waves. The SKUs associated with a single wave are then arranged on a picking line after which pickers move in a clockwise direction around the conveyor belt to pick the orders. The entire order picking operation was broken into three tiers of decision making and three corresponding subproblems were identi ed. The rst two subproblems were investigated which focused on a single picking line. The rst subproblem called the order sequencing problem (OSP) considered the sequencing of orders for pickers and the second called the SKU location problem (SLP) the assignment of SKUs to locations in the picking line for a given wave. A tight lower bound was established for the OSP using the concept of a maximal cut. This lower bound was transformed into a feasible solution within 1 pick cycle of the lower bound. The solution was also shown to be robust and dynamic for use in practice. Faster solution times, however, were required for use in solution techniques for the SLP. Four variations of a greedy heuristic as well as two metaheuristic methods were therefore developed to solve the problem in shorter times. An ant colony approach was developed to solve the SLP. Furthermore, four variations of a hierarchical clustering algorithm were developed to cluster SKUs together on a picking line and three metaheuristic methods were developed to sequence these clusters. All the proposed approaches outperformed known methods for assigning locations to SKUs on a carousel. To test the validity of assumptions and assess the practicality of the proposed solutions an agent based simulation model was built. All proposed solutions were shown to be applicable in practice and the proposed solutions to both subporblems outperformed the current approaches by Pep. Furthermore, it was established that the OSP is a more important problem, in comparison to the SLP, for Pep to solve as limited savings can be achieved when solving the SLP. / AFRIKAANSE OPSOMMING: 'n Stelsel vir die opmaak van bestellings in 'n distribusiesentrum van Pep Stores Bpk. in Durban, Suid-Afrika word beskou. Hierdie stelsel gebruik uitsoeklyne waarop bestellings in golwe opgemaak word. 'n Uitsoeklyn is 'n area met vakkies waarop pallette met voorraadeenhede gestoor kan word. Hierdie vakkies is rondom 'n voerband gerangskik. Die stelsel het ooreenkomste met die eenrigting carrousselstelsels wat in die literatuur voorkom, maar hierdie eenrigtingstelsels is nie algemeen nie. Voorraadeenhede moet aan 'n golf toegewys word wat in 'n uitsoeklyn gerangskik word, waarna werkers dan die bestellings in die betrokke golf opmaak. Die hele operasie van bestellings opmaak kan opgebreek word in drie vlakke van besluite met gepaardgaande subprobleme. Die eerste twee subprobleme wat 'n enkele uitsoeklyn beskou, word aangespreek. Die eerste subprobleem, naamlik die volgorde-van-bestellings-probleem (VBP) beskou die volgorde waarin bestellings opgemaak word. Die tweede probeem is die voorraadeenheidaan- vakkie-toewysingsprobleem (VVTP) en beskou die toewysings van voorraadeenhede aan vakkies in 'n uitsoeklyn vir 'n gegewe golf. 'n Sterk ondergrens vir die VBP is bepaal met behulp van die konsep van 'n maksimum snit. Hierdie ondergrens kan gebruik word om 'n toelaatbare oplossing te bepaal wat hoogstens 1 carrousselsiklus meer as die ondergrens het. Hierdie oplossings kan dinamies gebruik word en kan dus net so in die praktyk aangewend word. Vinniger oplossingstegnieke is egter nodig indien die VVTP opgelos moet word. Twee metaheuristiese metodes word dus voorgestel waarmee oplossings vir die VBP vinniger bepaal kan word. 'n Mierkolonie benadering is ontwikkel om die VVTP op te los. Verder is vier variasies van 'n hi erargiese groeperingsalgoritme ontwikkel om voorraadeenhede saam te groepeer op 'n uitsoeklyn. Drie metaheuristieke is aangewend om hierdie groepe in volgorde te rangskik. Al hierdie benaderings vaar beter as bekende metodes om voorraadeenhede op 'n carroussel te rankskik. Om die geldigheid van die aannames en die praktiese uitvoerbaarheid van die oplossings te toets, is 'n agent gebaseerde simulasie model gebou. Daar is bevind dat al die voorgestelde oplossings prakties implementeerbaar is en dat al die metodes verbeter op die huidige werkswyse in Pep. Verder kon vasgestel word die VBP belangriker as die VVTP vir Pep is omdat veel kleiner potensiele besparings met die VVTP moontlik is as met die VBP.

Thesis (MComm)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: FoodBank South Africa is an non-profit organisation formed to establish a national network of community foodbanks in urban and rural areas of South Africa, with all participants working towards the common goal of eliminating hunger and food insecurity. FoodBank Cape Town was the first of these community foodbanks launched in South Africa on 2 March 2009. The operations of FoodBank Cape Town include sourcing food and redistributing it to agencies (social services organisations running feeding programmes). Currently the majority of the food is sourced from the retail sector and then redistributed to approximately two hundred agencies. The logistics involved in both sourcing and distributing food are vital to the efficient functioning of FoodBank Cape Town. Since the costs associated with these logistics operations are very high, streamlining these operations has been identified as a priority area for efficiency improvement. The focus in this thesis is on the distribution logistics involved, specifically focussing on a facility location problem according to which FoodBank Cape Town can establish local distribution depots to which it delivers food and from which the agencies collect food assigned to them. A mixed-integer programming model is formulated for the above facility location problem and small test instances of the problem are solved using different exact and approximate solution methods in order to identify a suitable solution methodology for the full (large-scale) FoodBank Cape Town facility location problem. The full facility location problem is solved approximately by means of a meta-heuristic solution method in the more highly constrained instances, while an exact method is selected for solving the lesser constrained instances. The problem is first solved based on the distances between the warehouse and the depots as well as the distances between the agencies and the depots, for the twenty four instances where 17 to 40 depots are located. The model is then developed further to incorporate the cost of distribution. This cost-based facility location model is solved with a view to minimise the cost of food distribution from the warehouse to the depots and the cost of food distribution incurred by each agency to collect food from its assigned depot. A basic vehicle routing technique is applied to the cost-based facility location solution and the associated costs of the distribution are updated. This cost-based solution updating process is performed iteratively until the solution converges. Since the cost of food distribution depends on the vehicle fleet composition used, a vehicle fleet composition comparison of possible FoodBank Cape Town vehicles is performed to determine the most desirable vehicle fleet composition to be used for the distribution of food to depots. The results of the FoodBank Cape Town facility location problem and vehicle fleet composition comparison are presented and recommendations are made to FoodBank Cape Town regarding the preferred number of depots, the location of these depots and the preferred vehicle fleet composition. / AFRIKAANSE OPSOMMING: FoodBank South Africa is ’n nie-winsgewende organisasie wat ten doel het om ’n nasionale netwerk van gemeenskapsvoedselbanke in stedelike en landelike gebiede van Suid-Afrika op die been te bring, waarin al die deelnemers die gemeenskaplike doel nastreef om honger en voedselonsekerheid te elimineer. Foodbank Cape Town was die eerste van hierdie gemeenskapsvoedselbanke in Suid-Afrika en is op 2 Maart 2009 gestig. Die take van Foodbank Cape Town sluit in die versameling van voedsel en die verspreiding daarvan aan agentskappe (gemeenskapsorganisasies wat voedingsprogramme bestuur). Die oorgrote meerderheid voedsel is tans uit die kleinhandelsektor afkomstig en word aan ongeveer tweehonderd agentskappe versprei. Die logistiek wat met hierdie versamelings- en verspreidingsprosesse gepaard gaan, is sentraal tot die doeltreffende funksionering van FoodBank Cape Town. Aangesien die kostes verbonde aan hierdie logistieke prosesse baie hoog is, is hierdie aktiwiteite as ’n prioriteitsarea vir verbetering geidentifiseer. Die fokus in hierdie tesis val op die logistiek verbonde aan die verspreiding van voedsel deur FoodBank Cape Town, en meer spesifiek op die probleem van die plasing van ’n aantal lokale verspreidingsdepots waar FoodBank Cape Town voedsel kan aflewer en waar die agentskappe dan voedsel wat aan hulle toegeken is, kan gaan afhaal. ’n Gemengde heeltallige-programmeringsmodel word vir die bogenoemde plasingsprobleem geformuleer en klein gevalle van die model word deur middel van beide eksakte en benadere oplossingstegnieke opgelos om sodoende ’n geskikte oplossingsmetode vir die volle (grootskaalse) Food- Bank Cape Town plasingsmodel te identifiseer. Die volle plasingsmodel word aan die hand van ’n metaheuristiese oplossingstegniek benaderd opgelos vir hoogsbeperkte gevalle van die model, terwyl minder beperkte gevalle van die model eksak opgelos word. Die plasingsmodel word eers met die oog op die minimering van afstande tussen die pakhuis en verspreidingsdepots sowel as tussen die verspreidingsdepots en agentskappe vir die vier-en-twintig gevalle van die plasing van 17 tot 40 verspreidingsdepots opgelos. Die model word dan verder ontwikkel om ook die koste van die verspreiding van voedsel in ag te neem. Die koste-gebaseerde plasingsmodel word opgelos met die doel om die voedselbankkoste van voedselverspreiding vanaf die pakhuis na die lokale verspreidingsdepots sowel as die agentskapkoste van die afhaal van voedsel vanaf verspreidingsdepots te minimeer. ’n Basiese voertuigroeteringstegniek word op die koste-gebaseerde plasingsmodel toegepas en die verspreidingskoste word dienooreenkomstig aangepas. Hierdie aanpassingsproses van die koste-gebaseerde oplossing word herhaal totdat die oplossing konvergeer. Aangesien die koste van voedselverspreiding afhang van die voertuigvlootsamestelling, word ’n vergelyking tussen moontlike vlootsamestellings vir FoodBank Cape Town getref om die mees geskikte samestelling van voertuie vir die verspreiding van voedsel te vind. Die resultate van die FoodBank Cape Town verspreidingsdepot-plasingsprobleem en vlootsamestellingsvergelyking word aangebied en ’n aanbeveling word aan FoodBank Cape Town gemaak in terme van ’n geskikte aantal verspreidingsdepots, waar hierdie depots geleë behoort te wees, en ’n geskikte voertuigvlootsamestelling vir die verspreiding van voedsel.