Department of Logistics

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Aanpassing van grootte-mengsels tydens voorraadtoewysing in 'n kettingwinkel
(LitNet, 2014-12) Thom, Elmien; Visagie, Stephan; Matthews, Jason
Die toewysing van voorraad aan winkels is een van die belangrike prosesse in die bestuur van ’n kettingwinkel. In die klerebedryf behels toewysingsbesluite onder andere die bepaling van hoeveelhede van elke grootte (byvoorbeeld klein, medium en groot) wat aan elke winkel gestuur moet word. ’n Gevallestudie van hierdie probleem in Pep Stores Bpk. (PEP), een van die vernaamste kleinhandelaars in Suid-Afrika, word in hierdie artikel beskou. In PEP word produkte by fabrieke bestel maande voordat dit in die takke beskikbaar is. Vanaf die fabrieke word die produkte na hul distribusiesentra verskeep, van waar dit per pad na die onderskeie takke versprei word. Onderliggend aan die verspreidingsnetwerk is ’n beplanningsproses en ’n toewysingsproses. Tydens die beplanningsproses word daar voorlopige toewysingsbesluite geneem. Tydens die toewysingsproses, wanneer daar meer onlangse verkoopsdata beskikbaar is, word die aanvanklike beplanning aangepas en word daar finaal besluit hoeveel van elke produk en grootte aan elke tak gestuur sal word. In hierdie artikel word modelle ontwikkel wat gebruik kan word wanneer hierdie finale toewysingsbesluite geneem word. Die doelwit van die modelle poog om voorraad só toe te wys dat geen winkel te min of te veel voorraad van enige grootte ontvang nie. Vier modelle word aangebied waarin die verwagte voorraad-tekorte en -surplusse by die takke geminimeer word. Twee van die modelle is doelwitprogrammeringsmodelle. Die eerste doelwitprogrammeringsmodel word nie aanbeveel nie, aangesien die tweede model beter resultate lewer in ’n korter oplossingstyd. Die tweede doelwitprogrammeringsmodel lewer goeie resultate, maar die oplossingstyd is in party gevalle te lank. Daarom is twee verslappings van hierdie model ontwikkel met die oog op die vermindering van oplossingstyd. Hierdie twee modelle lewer bevredigende oplossingstye en toon ’n gemiddelde verbetering van tot 27% op PEP se huidige oplossing volgens die verskillende maatstawwe.
Added sugar, macro- and micronutrient intakes and anthropometry of children in a developing world context
(Public Library of Science, 2015) Maunder, Eleni M. W.; Nel, Johanna H.; Steyn, Nelia P.; Kruger, H. Salome; Labadarios, Demetre
Objective: The objective of this study was to determine the relationship between added sugar and dietary diversity, micronutrient intakes and anthropometric status in a nationally representative study of children, 1–8.9 years of age in South Africa. Methods: Secondary analysis of a national survey of children (weighted n = 2,200; non weighted n = 2818) was undertaken. Validated 24-hour recalls of children were collected from mothers/ caregivers and stratified into quartiles of percentage energy from added sugar (% EAS). A dietary diversity score (DDS) using 9 food groups, a food variety score (FVS) of individual food items, and a mean adequacy ratio (MAR) based on 11 micronutrients were calculated. The prevalence of stunting and overweight/obesity was also determined. Results: Added sugar intake varied from 7.5–10.3%of energy intake for rural and urban areas, respectively. Mean added sugar intake ranged from 1.0% of energy intake in Quartile 1 (1– 3 years) (Q1) to 19.3% in Q4 (4–8 years). Main sources of added sugar were white sugar (60.1%), cool drinks (squash type) (10.4%) and carbonated cool drinks (6.0%). Added sugar intake, correlated positively with most micronutrient intakes, DDS, FVS, and MAR. Significant negative partial correlations, adjusted for energy intake, were found between added sugar intake and intakes of protein, fibre, thiamin, pantothenic acid, biotin, vitamin E, calcium (1–3 years), phosphorus, iron (4–8 years), magnesium and zinc. The prevalence of overweight/obesity was higher in children aged 4–8 years in Q4 of %EAS than in other quartiles [mean (95%CI) %prevalence overweight 23.0 (16.2–29.8)% in Q4 compared to 13.0 (8.7–17.3)% in Q1, p = 0.0063]. Conclusion: Although DDS, FVS, MAR and micronutrient intakes were positively correlated with added sugar intakes, overall negative associations between micronutrients and added sugar intakes, adjusted for dietary energy, indicate micronutrient dilution. Overweight/obesity was increased with higher added sugar intakes in the 4–8 year old children.
Allocating epidemic response teams and vaccine deliveries by drone in generic network structures, according to expected prevented exposures
(Public Library of Science, 2021) Matter, Dean; Potgieter, Linke
The tumultuous inception of an epidemic is usually accompanied by difficulty in determining how to respond best. In developing nations, this can be compounded by logistical challenges, such as vaccine shortages and poor road infrastructure. To provide guidance towards improved epidemic response, various resource allocation models, in conjunction with a network-based SEIRVD epidemic model, are proposed in this article. Further, the feasibility of using drones for vaccine delivery is evaluated, and assorted relevant parameters are discussed. For the sake of generality, these results are presented for multiple network structures, representing interconnected populations—upon which repeated epidemic simulations are performed. The resource allocation models formulated maximise expected prevented exposures on each day of a simulated epidemic, by allocating response teams and vaccine deliveries according to the solutions of two respective integer programming problems—thereby influencing the simulated epidemic through the SEIRVD model. These models, when compared with a range of alternative resource allocation strategies, were found to reduce both the number of cases per epidemic, and the number of vaccines required. Consequently, the recommendation is made that such models be used as decision support tools in epidemic response. In the absence thereof, prioritizing locations for vaccinations according to susceptible population, rather than total population or number of infections, is most effective for the majority of network types. In other results, fixed-wing drones are demonstrated to be a viable delivery method for vaccines in the context of an epidemic, if sufficient drones can be promptly procured; the detrimental effect of intervention delay was discovered to be significant. In addition, the importance of well-documented routine vaccination activities is highlighted, due to the benefits of increased pre-epidemic immunity rates, and targeted vaccination.
An analysis of the influence of logistics activities on the export cold chain of temperature sensitive fruit through the Port of Cape Town
(AOSIS Publishing, 2015-09) Goedhals-Gerber, Leila L.; Haasbroek, Laura; Freiboth, Heinrich W.; Van Dyk, Esbeth
Background: South Africa exports a large variety of different fruit types and cultivars worldwide. Yet, there is concern in the South African fruit industry that too much fruit and money is lost each year due to breaks along the fresh fruit export cold chain. Objective: The objective of this article was to identify the influence of logistics activities on breaks along the South African fruit export cold chain. The focus is specifically on temperature sensitive fruit, exported in refrigerated containers to Europe and the United Kingdom through the Port of Cape Town. This supply chain was selected as this was the most accessible supply chain in terms of retrieving the necessary temperature data. Method: The cold chain was investigated from the cold store, through all segments, until the Port of Cape Town. Temperature data collected with temperature monitoring devices from different fruit export supply chains of grapes, plums and pome fruit (apples and pears) were analysed to identify the percentage of temperature breaks and the length of temperature breaks that occur at each segment of the cold chain. Results: The results show that a large number of breaks are experienced along South Africa’s fruit export cold chain, specifically at the interface between the cold store and the truck. In addition, the findings also show that there has been an improvement in the number of breaks experienced in the Port of Cape Town following the implementation of the NAVIS and Refcon systems. Conclusion: This article concludes by providing the fruit industry with areas that require addressing to improve operational procedures along the fruit export cold chain to help ensure that the fruit arrives at its final destination at optimal quality.
The application of a computerised decision support system for generator maintenance scheduling : a South African case study
(Southern African Institute for Industrial Engineering, 2012-11) Schlunz, E. B.; Van Vuuren, J. H.
In the generator maintenance scheduling (GMS) problem, a schedule is sought for the planned maintenance outages of generating units in a power system. The GMS model considered in this paper is formulated as a mixed-integer quadratic program assuming a reliability objective, subject to certain constraints. A generic GMS solution methodology is derived, capable of solving general GMS problem instances that conform to this model structure, and implemented in a computerised decision support system. The decision support system is then used to solve a real-life case study in the South African national power system.
Assignment of stock keeping units to parallel unidirectional picking
(SAIIE, 2015-05) Matthews, Jason; Visagie, Stephan E.
An order picking system consisting of a number of parallel unidirectional picking lines is investigated. Stock keeping units (SKUs) that are grouped by product type into distributions (DBNs) are assigned daily to available picking lines. A mathematical programming formulation and its relaxations is presented. A greedy insertion and a greedy phased insertion are further introduced to obtain feasible results within usable computation times for all test cases. The walking distance of the pickers was shown to decrease by about 22 per cent compared with the current assignment approach. However, product handling and operational risk increases.
Die beraming van verhoogde streeksinkome wat uit ekonomies geregverdigde padbouprojekte spruit
(AOSIS OpenJournal, 2005) Pienaar, W. J.
This article identifies the possible development benefits than can emanate from economically justified road construction projects. It shows how the once-off increase in regional income resulting from investment in road construction projects, and the recurring additional regional income resulting from the use of new or improved roads can be estimated. The difference is shown that exists between a cost-benefit analysis (to determine how economically justified a project is) and a regional economic income analysis (to estimate the general economic benefits that will be developed by investment in and usage of a road). Procedures are proposed through which the once-off and recurring increases in regional income can be estimated by using multiplier and accelerator analyses respectively. Finally guidelines are supplied on the appropriate usage of input variables in the calculation of the regional income multiplier.
Calculation of freight externality costs for South Africa
(AOSIS OpenJournals, 2012-11) Swarts, Stefaan; King, David; Simpson, Zane P.; Havenga, Jan H.; Goedhals-Gerber, Leila L.
The purpose of this study is to quantify the marginal external costs associated with freight transport in South Africa. Six cost elements are included as externality cost items, namely, costs related to accidents, emissions, roadway land availability, policing, noise and congestion. Inputs in the calculations were a gravity-oriented freight flow model, a road transport cost model, actual transport costs for other modes, a warehousing cost survey, an inventory delay calculation and various national sources of information such as accident statistics and government budgets. Estimation techniques resulted in advances for externality cost measurement in South Africa. The quantification of the cost elements will be used to update the South African Freight Demand Model. The results show that the cost of transportation would have been 20% more if external factors were taken into account. The marginal rates of externalities can be used to develop scenarios based on alternative choices for South Africa’s freight transport infrastructure configuration.
The composite supply chain efficiency model : a case study of the Sishen-Saldanha supply chain
(AOSIS Publishing, 2016) Goedhals-Gerber, Leila L.
ENGLISH SUMMARY : As South Africa strives to be a major force in global markets, it is essential that South African supply chains achieve and maintain a competitive advantage. One approach to achieving this is to ensure that South African supply chains maximise their levels of efficiency. Consequently, the efficiency levels of South Africa’s supply chains must be evaluated. The objective of this article is to propose a model that can assist South African industries in becoming internationally competitive by providing them with a tool for evaluating their levels of efficiency both as individual firms and as a component in an overall supply chain. The Composite Supply Chain Efficiency Model (CSCEM) was developed to measure supply chain efficiency across supply chains using variables identified as problem areas experienced by South African supply chains. The CSCEM is tested in this article using the Sishen-Saldanda iron ore supply chain as a case study. The results indicate that all three links or nodes along the Sishen-Saldanha iron ore supply chain performed well. The average efficiency of the rail leg was 97.34%, while the average efficiency of the mine and the port were 97% and 95.44%, respectively. The results also show that the CSCEM can be used by South African firms to measure their levels of supply chain efficiency. This article concludes with the benefits of the CSCEM.
Container terminal spatial planning : a 2041 paradigm for the Western Cape Province in South Africa
(AOSIS OpenJournals, 2012-11) Havenga, Jan H.; King, David; Simpson, Zane P.; Goedhals-Gerber, Leila L.; De Bod, Anneke
This paper investigates the suitable location for an intermodal inland container terminal (IICT) in the city of Cape Town. A container market segmentation approach is used to project growth for container volumes over a 30-year period for all origin and destination pairings on a geographical district level in an identified catchment area. The segmentation guides the decision on what type of facility is necessary to fulfil capacity requirements in the catchment area and will be used to determine the maximum space requirements for a future IICT. Alternative sites are ranked from most suitable to least suitable using multi-criteria analysis, and preferred locations are identified. Currently, South Africa’s freight movement is dominated by the road sector. Heavy road congestion is thus prevalent at the Cape Town Container Terminal (CTCT). The paper proposes three possible alternative sites for an IICT that will focus on a hub-and-spoke system of transporting freight.
The decarbonisation of transport logistics : a South African case study
(Unisa Press, 2018-10-09) Goedhals-Gerber, Leila L.; Freiboth, Heinrich W.; Havenga, Jan H.
South Africa is currently one of the "dirtiest" economies in the world in terms of carbon emissions. The South African economy is heavily dependent on energy-intensive industries, such as mining and primary minerals beneficiation, which in turn rely on fossil fuels as a source of energy. Sustainability is still a relatively new concept in South Africa, but awareness is growing, and there are several on-going initiatives aimed at reducing the country's total energy consumption. The objective of this paper is to apply the TIMBER framework to assess current transport decarbonisation activities in South Africa. The article discusses a limited field survey of ten important logistics experts in South Africa to establish whether the findings of the researchers are similar to the perceptions within the logistics sector of major industries in South Africa. This paper concludes by providing possible solutions for reducing carbon emissions in South Africa's logistics industry.
Dietary intake of the urban Black population of Cape Town : the cardiovascular risk in black South Africans (CRIBSA) study
(MDPI, 2016) Steyn, Nelia P.; Jaffer, Nasreen; Nel, Johanna; Levitt, Naomi; Steyn, Krisela; Lombard, Carl; Peer, Nasheeta
Introduction: To determine dietary intake of 19 to 64 years old urban Africans in Cape Town in 2009 and examine the changes between 1990 and 2009. Methods: A representative cross-sectional sample (n = 544), stratified by gender and age was randomly selected in 2009 from the same areas sampled in 1990. Socio-demographic data and a 24-h dietary recall were obtained by trained field workers. The associations of dietary data with an asset index and degree of urbanization were assessed. Results: Fat intakes were higher in 19–44-year-old men (32% energy (E)) and women (33.4%E) in 2009 compared with 1990 (men: 25.9%E, women: 27.0%E) while carbohydrate intakes were lower in 2009 (men 53.2%E, women: 55.5%E) than in 1990 (men: 61.3%E; women: 62%E) while sugar intake increased significantly (p < 0.01) in women. There were significant positive correlations between urbanization and total fat (p = 0.016), saturated fat (p = 0.001), monounsaturated fat (p = 0.002) and fat as a %E intake (p = 0.046). Urbanization was inversely associated with intake of carbohydrate %E (p < 0.001). Overall micronutrient intakes improved significantly compared with 1990. It should also be noted that energy and macronutrient intakes were all significant in a linear regression model using mean adequacy ratio (MAR) as a measure of dietary quality in 2009, as was duration of urbanization. Discussion: The higher fat and lower carbohydrate %E intakes in this population demonstrate a transition to a more urbanized diet over last two decades. These dietary changes reflect the nutrition transitions that typically occur as a longer time is spent in urban centers.
Dietary practices and adolescent obesity in secondary school learners at disadvantaged schools in South Africa : urban–rural and gender differences
(MDPI, 2020-08) Okeyo, Alice P.; Seekoe, Eunice; de Villiers, Anniza; Faber, Mieke; Nel, Johanna H.; Steyn, Nelia P.
South Africa has a high prevalence of obesity in black female adolescents and a paucity of knowledge regarding contributing dietary practices. The aim of this study was to assess the dietary practices and weight status of male and female adolescents at secondary schools in the Eastern Cape province in urban and rural areas. Sixteen schools and grade 8–12 learners (N = 1360) were randomly selected from three health districts comprising poor disadvantaged communities. A short unquantified food frequency questionnaire was used to collect data on learners’ usual eating practices with regards to weekly meal pattern, breakfast consumption, foods taken to school, takeaways, and snacks eaten while watching television (TV). Body mass index measurements were determined for each learner. Prevalence of combined overweight and obesity differed significantly between genders, 9.9% in males versus 36.1% in females (p < 0.001). Significant gender differences were noted regarding eating practices. Females had a higher frequency of eating sugary snacks (p < 0.001) and a lower frequency of eating breakfast (p < 0.01) than males. Females ate significantly more fried fish (p < 0.05), pizza (p < 0.05) fat cakes (fried dough balls) (p < 0.05), hotdogs (p < 0.01), candy (p < 0.001), cake (p < 0.01), and crisps (p < 0.001). Compared to urban areas, the frequency of eating breakfast (p < 0.01) and sugary snacks (p < 0.05) was significantly higher in rural areas. Significantly more learners in urban areas consumed boerewors (beef sausage) rolls (p = 0.027), hamburgers (p = 0.004), and soft drinks (p = 0.019), while more learners in the rural areas consumed cordial (p = 0.001). In conclusion, a high prevalence of combined overweight and obesity was found in black female adolescents and a high prevalence of poor dietary practices was observed, with significant gender and urban–rural differences.
The effects of incorporating vehicle acceleration explicitly into a microscopic traffic simulation model
(Southern African Institute for Industrial Engineering, 2013-08) Burger, A. P.; Einhorn, M. D.; Van Vuuren, J. H.
Explicitly incorporating individual vehicle acceleration into a traffic simulation model is not a trivial task, and typically results in a considerable increase in model complexity. For this reason, alternative implicit techniques have been introduced in the literature to compensate for the delay times associated with acceleration. In this paper, the claim is investigated that these implicit modelling techniques adequately account for the time delays due to vehicle acceleration; the modelling techniques are implemented in a simulated environment, and compared with models in which vehicle acceleration has been incorporated explicitly for a number of traffic network topologies and traffic densities. It is found that considerable discrepancies may result between the two approaches.
Ekonomiese aspekte van pypleidingvervoer : 'n Suid-Afrikaanse perspektief
(AOSIS, 2009) Pienaar, Wessel J.
Economic aspects of pipeline transport: a South African perspective Pipeline transport is unique among modes of transport in that the pipe, which facilitates freight movement, is both the way and the vehicle, and it is permanently connected to terminals, which facilitate freight storage. This feature makes it the only mode of transport that does not require any materials or goods handling. In view of the facts that pipeline infrastructure is extremely capital intensive and that it has an unprecedented longevity, pipeline transport enjoys the highest level of economies of scale of all modes of transport. This economy is subject to steady and enduring high levels of demand. It is also the only mode of freight transport of which the operations do not require a return journey, whereby joint cost due to empty running is avoided. The commercial transport of crude oil and petroleum products by pipeline and the envisaged new investment in this mode of transport are receiving increased attention in South Africa. Transnet Pipelines recently obtained permission from the National Energy Regulator of South Africa (Nersa) to construct and operate a new 60-cm petroleum products pipeline 704 kilometres in length from Durban to Gauteng. In addition, the newly-formed Petroline consortium recently obtained permission to construct and operate a 30 cm petroleum products pipeline 199 kilometres in length from Maputo to Nelspruit, with an extension of 249 kilometres in length eventually to Kendal, where it can be linked up with the present Transnet pipeline network. The disadvantages of pipeline transport lie mainly in its extreme functional speciali sation and dependence upon sustained high-volume trafﬁc. The initial cost of installation is high and justiﬁed only when both the demand and supply are guaranteed to continue for an indeﬁ nite period. Despite the fact that tank ships run empty during return trips, pipeline transport can only compete with sea transport between the same origin and destination if the pipeline route is considerably shorter than the sea route, or where sea transport is subject to exceptional charges, such as heavy canal dues. The economic assessment of a pipeline necessitates the investigation of several alternatives in order to determine whether the project is justiﬁable in terms of the economic resources its commercial existence will require. Firstly, alternative locations of the pipeline may have to be compared. A second consideration is the size of the pipeline, since one with a larger diameter, and capable of handling a greater trafﬁc volume, involves higher initial investment cost but lower costs for pumps and energy to propel the pumps. A third decision concerns the choice of pump technology. Most pumps are driven by electric motors, although diesel engines or gas turbines can also be used. A fourth important consideration is whether the reﬁnery should be located at the beginning of the line (upstream, close to the oil ﬁeld or the port of entry) or at the end of the line (downstream, close to the market). The ﬁfth step in the economic evaluation is to compare the pipeline cost with the cost of the next best transport alternative, which is usually rail transport. If these investigations indicate that a pipeline promises to be technically feasible, ﬁnancially viable and economically justiﬁed, detailed design of the pipeline may commence. In terms of market participants the supply of pipeline transport is the most highly concentrated of all freight transport modes. With a few exceptions, there is but one crude oil, one products and one natural gas pipeline connecting producing areas or reﬁneries and areas of consumption. This high degree of monopoly results from declining unit costs with increases in capacity, so that the lowest costs are achieved by a concentration of output in a single pipeline. Therefore, pipeline operations that can fulﬁl entire market demands are pure natural monopolies. Where the distance between supply points (such as geographically separated oil ﬁelds or ports of entry) is far in relation to the delivery distance to the market area, such an area’s fuel demand can often be most efﬁciently fulﬁlled by two or more different pipeline operations. The clients of a common carrier are direct competitors in the wholesale fuel market, therefore they should bear full cost responsibility for the service rendered by the pipeline. Service below total cost to a client implies that it is subsidized by its competitors. The only instance when delivery can take place below total cost is when:the necessary spare capacity exists to accommodate the consignment (i.e. that the opportunity for another consignment to be delivered at full cost is not jeopardized);all the avoidable (i.e. short-run) costs are covered and some contribution to unavoidable (i.e. ﬁ xed or long-run) costs is made; and the consignment delivery would not have taken place at a price covering full costs.
Enumerasie van self-ortogonale Latynse vierkante met simmetriese ortogonale maats
(LitNet Academic, 2012-04) Burger, Alewyn P.; Kidd, Martin P.; Van Vuuren, Jan H.
OPSOMMING: vierkante met simmetriese, ortogonale maats (SOLVSOMs), ’n probleem wat nog nie in die literatuur oor kombinatoriese ontwerpe aangespreek is nie. In die besonder bepaal ons die getal (ry, kolom)-paratoopklasse van SOLVSOMs van orde n ≤ 10 deur inligting in bestaande, uitputtende databasisse van self-ortogonale Latynse vierkante en simmetriese Latynse vierkante met behulp van ’n boomsoektog met terugkering (Eng: backtracking) te kombineer. Ons bepaal ook die getal verskillende SOLVSOMs, SOLVSOMs in standaardvorm en transponentisomorfismeklasse van SOLVSOMs van ordes n ≤ 10 deur gebruikmaking van standaard tegnieke uit abstrakte algebra. In die proses beantwoord ons ’n 34 jaar-oue oop bestaansvraag oor SOLVSOMs van orde 10 deur aan te toon dat geen so ’n ontwerp bestaan nie. Aangesien ’n SOLVSOM van orde n in standaardvorm ekwivalent is aan ’n spelskedule vir ’n gadevermydende gemengde-dubbels rondomtalie-tennistoernooi vir n getroude pare, dui hierdie resultaat daarop dat geen so ’n toernooi vir 10 getroude pare geskeduleer kan word nie.
An evaluation of the effectiveness of observation camera placement within the meerkat radio telescope project
(SAIIE, 2015) Heyns, A. M.; Van Vuuren, J. H.
A recent development within the MeerKAT sub-project of the Square Kilometre Array radio telescope network was the placement of a network of three observation cameras in pursuit of two specific visibility objectives. In this paper, we evaluate the effectiveness of the locations of the MeerKAT observation camera network according to a novel multi-objective geographic information systems-based facility location framework. We find that the configuration chosen and implemented by the MeerKAT decision-makers is of very high quality, although we are able to uncover slightly superior alternative placement configurations. A significant amount of time and effort could, however, have been saved in the process of choosing the appropriate camera sites, had our solutions been available to the decision-makers.
The evolutionary spatial prisoner's dilemma on a cycle
(Operations Research Society of South Africa (ORSSA), 2013) Burger, A. P.; Van der Merwe, M.; Van Vuuren, J. H.
In this paper we consider the Evolutionary Spatial Prisoner's Dilemma (ESPD) in which players are modelled by the vertices of a cycle representing a spatial or organisational structure amongst the players. During each round of the ESPD every pair of adjacent players in the cycle play a classical prisoner's dilemma against each other, and they update their strategies from one round to the next based on the perceived success achieved by the strategies of neighbouring players during the previous round. In this way players are able to adapt and learn from each other's strategies as the game progresses without being able to rationalise good strategies. We characterise all steady states of the game as well as the structures of those initial states that lead to the emergence of persistent substates of cooperation over time. We finally determine analytically (i.e. without using simulation) the probability that the game's states will evolve from a randomly generated initial state towards a steady state which accommodates some form of persistent cooperation. More specifically, we show that there exists a range of game parameter values for which the likelihood of the emergence of persistent cooperation increases to almost certainty as the length of the cycle increases.
The existence of planar hypotraceable oriented graphs
(Discrete Mathematics & amp; Theoretical Computer Science, 2017) Van Aardt, Susan A.; Burger, Alewyn Petrus; Frick, Marietjie
A digraph is \emph{traceable} if it has a path that visits every vertex. A digraph D is \emph{hypotraceable} if D is not traceable but D−v is traceable for every vertex v∈V(D). It is known that there exists a planar hypotraceable digraph of order n for every n≥7, but no examples of planar hypotraceable oriented graphs (digraphs without 2-cycles) have yet appeared in the literature. We show that there exists a planar hypotraceable oriented graph of order n for every even n≥10, with the possible exception of n=14.
Extending freight flow modelling to Sub-Saharan Africa to inform infrastructure investments : trade data issues
(AOSIS OpenJournals, 2012-11) Havenga, Jan H.; Simpson, Zane P.; King, David; Lanz, E. J.; Goedhals-Gerber, Leila L.; De Bod, Anneke
This paper highlights the first attempt by researchers at Stellenbosch University to model freight flows between and for 17 countries in sub-Saharan Africa (SSA). The model will be informed by and linked to the South African surface Freight Demand Model (FDM) given these dimensions. By analysing and collating available datasets and developing a freight flow model, a better understanding of freight movements between countries can be obtained and then used for long-term planning efforts. A simple methodology is envisaged that will entail a high-level corridor classification that links a major district in the country with a similar district in another country. Existing trade data will be used to corroborate new base-year economic demand and supply volumetric data that will be generated from social accounting matrices for each country. The trade data will also provide initial flow dynamics between countries that will be refined according to the new volumes. The model can then generate commodity-level corridor flows between SSA countries, and between SSA countries and the rest of the world, as well as intra-country rural and metropolitan flows, using a gravity-based modelling approach. This article outlines efforts to harmonise trade data between the 17 countries identified, as well as between these countries and the rest of the world as a first step towards developing a freight demand model for sub-Saharan Africa.

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