|
Mariza M Goosen (Fulltime Hons BSc, 1997). Honours
year project in applied mathematics (operations research) entitled
Optimale beheerstrategieë vir besproeiingsreservoirs involved
mathematical modelling in order to find good release strategies for medium
scale open air irrigation reservoirs. The project also included a case
study on Keerom Dam (the second largest privately owned open air reservoir
in South Africa) near Worcester during which close co-operation between the
Department of Applied Mathematics and the farmers' Board of Management at
Keerom, Nuy was achieved.
|
 |
|
Grant E Huddlestone (Fulltime Hons
BSc, 1997). Honours year project in applied mathematics (operations
research) entitled An optimal control strategy for the production of
fruit juice concentrates involved mathematical modelling in order to
find good pulping schedules at fruit pulping plants which minimise fruit
losses due to unacceptable grade deterioration. The project also included a
case study at a large well-known pulping plant in the Western Cape during
which close co-operation between the Department of Applied Mathematics and
the chief plant engineer was achieved. The results of this project were
presented at the annual conference of the Operations Research Society of
South Africa (ORSSA) held in Durban (August 1997) and was published in
ORiON, the journal of ORSSA. |
 |
|
Werner R Gründingh (Fulltime BSc, 1998-1999).
Special research project in
applied mathematics (operations research) involved the development of an
active decision support system for managers of medium scale open air
reservoirs. This user-friendly Microsoft Windows personal computer
implemented system, called ORMADSS (for Optimal Reservoir Management Active
Decision Support System) was based on the theoretical model developed in
the 1997 honours year project by Mariza Goosen. The system was installed at
various work stations in the Nuy Valley near Worcester where it is
currently being used and validated in conjunction with decisions regarding
the release of water from Keerom Dam. The general system was launched at
the 15th triennial conference of the International Federation
of Operations Research Societies (IFORS) held in Beijing, Peoples'
Republic of China (August 1999), where the project was first selected as one of
the finalists and later as runner-up in the International OR in Development Prize
competition. The decision support system was also published in
International Transactions of Operations Research, the journal of
IFORS. |
 |
|
Elmien A Wagenaar (Fulltime Hons BSc, 1999).
Honours year project in applied mathematics (operations research)
entitled Kwantifisering van die invloed van bestuurseienskappe op die
sukses van beleggingsportefeuljes involved the use of mathematical
techniques in order to define an index which may be used to quantify those
characteristics of a portfolio investment manager that might have a bearing
on the success of his/her portfolios. Close co-operation between the
Department of Applied Mathematics and investment managers and analysts at
GENSEC (an asset allocation company within the SANLAM group) was achieved.
Work eminating from this project was published in ORiON, the journal
of ORSSA. Elmien Wagenaar was awarded the annual student prize for
the best graduate year project in operations research by ORSSA for the year
1999. |
 |
|
Tharine Louw (Part time Hons BSc, 1999-2000). Honours
year project in applied mathematics (cryptology & number theory)
entitled The safety and security of data in an object-orientated
environment involved the use of mathematical cryptology in order to
protect the integrity, confidentiality and authenticity of data extracted
form an object-orientated database by legitimate users via the internet.
This project formed part of a larger project in collaboration with the
Department of Computer Science at Stellenbosch University and a well-known
database development firm in Cape Town. |
 |
|
Werner R Gründlingh (Fulltime Hons BSc, 2000).
Honours year project in applied mathematics (cryptology & number
theory) entitled Genetic crypt-analysis of two basic block ciphers
involved the use of genetic algorithms to achieve convergence towards
probable keys during crypt-analytic attacks upon substitution and columnar
transposition cryptographic ciphers. Close co-operation between the Department of Applied
Mathematics and a government agency was achieved during this project, and
the work was submitted for publication in ORiON. |
|
|
Desmond Coetzer (Fulltime Hons BSc, 2000). Honours
year project in applied mathematics (operations research) entitled
Contrasting average client waiting time against cost minimisation in bank
queues involved the use of simulation to determine to optimal number of
(heterogeneous) tellers at a bank or micro-lender in order to ensure client
satisfaction while simultaneously attempting to minimise salaries and
training costs incurred by maintaining these tellers. Close co-operation
between the Department of Applied Mathematics and the Nu-Era micro-lender
group was achieved during this project. |
 |
|
Stephen Benecke (Fulltime Hons BSc, 2001). Honours
year project in applied mathematics (numerical modelling) entitled Die
modellering van torsie in kabels
onderhewig aan aksiale wringkragte involved the use of systems of
differential equations to model the tension forces in and 3D shape of a
cable subjected to axial twist at its endpoints. The models were solved
numerically via MATLAB. (Co-supervisor: Prof JAC Weideman, Department of
Applied Mathematics, Stellenbosch University) |
 |
|
Cindy A Lloyd (Fulltime Hons BSc, 2001). Honours year
project in applied mathematics (cryptology & number theory) entitled
The strengths & weaknesses of public key cryptography involved a study
of the impact that a variety of (improbable) number theoretic breakthroughs
might have on information security and integrity of the internet. |
 |
|
Margarete J Louw (Fulltime Hons BSc, 2001).
Honours year project in applied mathematics (operations research)
entitled Finding good nursing schedules involved the use of tabu-searches
and genetic algorithms to construct cost-efficient duty rosters for nursing
staff at a hospital. Close co-operation between the Department of Applied
Mathematics and Stikland Hospital was achieved during this project.
(Co-supervisor: Ms I Nieuwoudt, Department of Applied Mathematics,
Stellenbosch University). |
 |
|
Hendri J Botha (Fulltime Hons BSc, 2002).
Honours project in applied mathematics (cryptology) entitled 'n Kripto-analitiese aanval op die GOBOS-sisteem involved
the design of an automated ciphertext-only attack on a cryptographic cipher consisting of a matrix-coordinate phrase substitution,
followed by a periodic Vigenčre-type addition substitution. This system is often used as a building block within more
sophisticated hand-implemented block ciphers, and although not secure when used by itself, it is surprisingly robust,
and time consuming to break manually. Hence the need for an automated approach toward breaking the system. Close
cooperation was achieved during this project between the Department of Applied Mathematics and the National Communication Centre.
|
 |
|
Rickus Jooste (Fulltime Hons BSc, 2005).
Honours project in applied mathematics (number theory) entitled Spouse Avoiding Mixed Doubles Tennis Tournaments involved
the design of a computer-implemented decison support tool for the design of a playing schedule for n married couples competing in
a mixed doubles round-robin tennis tournament, so that (i) every player opposes every other player of the same sex exactly once,
(ii) every player opposes every player of the opposite sex (except his/her spouse) exactly once, and (iii) every player
is partnered with every player of the opposite sex (except his/her spouse) exactly once. An exact (optimal) schedule for such a
tournament may be constructed by means of self-orthogonal latin square together with a symmetric latin square partner which is
orthogonal with respect to the first (self-orthogonal) square. Such latin square pairs exist when n is coprime to 6 or when
n is a prime power. For other cases slightly sub-optimal tournament schedules may still be found. The project topic was
suggested by Prof DP Laurie of the Mathematics Department at the University of Stellenbosch.
|
 |
|
Francois du Toit (Fulltime Hons BSc, 2006).
Honours project in operational analysis entitled The scheduled weapon assignment problem involved the formulation of a weapon
assignment model capable of temporal decision support with respect to the assignment of available weapons to engage observed fixed
wing enemy aircraft in the context of a Ground Based Air Defense environment. During the course of the modelling process special care
was given to the estimation of a number of model parameters, including the priorities of eliminating the various enemy aircraft,
which was based on both the level of threatening behaviour of these aircraft with respect to the defended (own force) assets and the
priorities of the own force assets regarding their anticipated roles with respect to mission success. In order to derive an index
capable of representing the priorities of own force assets an indepth asset analysis was undertaken in conjunction with a number of
military experts. Close cooperation was achieved during this project between the Department of Mathematical Sciences and Reutech Radar Systems.
|
 |
|
Grant van Dieman (Fulltime Hons BSc, 2006).
Honours project in operational analysis entitled The assignment problem involved a survey of literature on the lassical assignment
problem and its variations (including the assignment problem with assignee qualifications, the k-cardinality assignment problem, the
bottleneck assignment problem, the balanced assignment problem, the lexicographic assignment problem, the semi-assignment problem, the
catagorized assignment problem, the multi-criteria assignment problem and the quadratic assignment problem). A number of exact techniques
for solving these problems (such as the successive shortest path algorithm for maximum flows in a graph, the maximum weight graph matching
algorithm and a branch and bound technique) were also investigated. Close cooperation was achieved during this project
between the Department of Mathematical Sciences and Reutech Radar Systems.
|
 |
|
|
|
Eugene H Stipp (Fulltime MSc, 1999-2000).
Masters project in applied mathematics (graph theory and combinatorics)
entitled Bounds for Ramsey numbers in multipartite graphs involved
an extension of classical graph theoretic Ramsey theory in that the class of complete, balanced multipartite
graphs were considered instead of the usual class of complete graphs and that
an attempt was made to answer the question: What is the smallest
edge-bicoloured multipartite graph that will necessarily contain a
monochromatic copy of a multipartite graph of (pre-specified) specific
size? Weak theoretical bounds as well as sharper bounds for small
multipartite graphs were found by using computer searches as well as
probabilistic (statistical) approaches. |
 |
|
Elmien Wagenaar (Part time MSc, 2000-2002). Masters
project in applied mathematics (operations research) entitled Asset
allocation strategies for financial
investments involved the use of ranking techniques and quadratic
programming to investigate whether sound asset allocation strategies might
exist in various market conditions. Close co-operation between the
Department of Applied Mathematics and SP2 (a member of the
SANLAM Group) was achieved during this project. (Advisor: Ms H Conradie,
GENSEC Asset Management) |
|
|
George Groves (Fulltime MIng, 2001-2001). Masters
project in industrial engineering (graph theory & combinatorics)
entitled Network service scheduling & routing involved the use
of tabu-search procedures to find near-optimal routings for service
vehicles in a transportation network where different types of links have
to be serviced with different frequencies during the service schedule. Two
objectives were set for these routes: to minimise total travel distance and
simultaneously to spread out (in time) consecutive services of any
particular link in the network. (Co-supervisor: Mr J Bekker, Department
of Industrial Engineering, Stellenbosch University) |
 |
|
Werner Gründlingh (Fulltime MSc, 2001-2002).
Masters project in applied mathematics (graph theory &
combinatorics) entitled A combinatorial problem concerning lotteries
involved the use of combinatorial arguments and computer searches to
estimate bounds on the smallest number of lottery tickets that have to be
bought on order to win a minor prize in a variety of national and state
operated lottery schemes world wide. (Advisor: Dr AP Burger, Department of
Mathematics, Applied Mathematics & Astronomy, UNISA) |
|
|
Catherine Black (Part time MEngSci, 2001-2003).
Masters project in engineering sciences
(operations research) entitled Optimisation techniques in the context of
cutting problems & inventory control in cardboard box producing
factories involved the use of inventory models and cutting strategies
in order to streamline storage and production at cardboard producing
factories. The methods were computerised and applied in the special case
study of Click-a-Box (a firm from whom cardboard boxes may ordered at short
notice via the internet). Close co-operation between the Department of
Applied Mathematics and the Click-a-Box factory was achieved during this
project. |
 |
|
Eric Herrmann (Part time MFor, 2001-2003). Masters
project in forestry & conservation (operations research) entitled
Population dynamics of lions in the Kgalagadi Transfrontier Park:
Modelling the effect of human-caused mortality involved the use of
spread sheet models to determine the robustness of the border lion prides
population in the partially fenced Kgalagadi Transfrontier Park.
These lions are being persecuted by neighbouring farmers who experience
substantial cattle losses due to lion transgression into their farmlands, and the
following question was considered: Will these lions be able to survive the
onslaught? (Co-supervisor: Prof S Milton, Department of Conservation &
Forestry, Stellenbosch University and Dr PJ Funston, Kgalagadi Transfrontier Park). |
 |
|
David J Coleman (Fulltime MSc, 2002-2003).
Masters project in operations research entitled Heuristic scheduling of tasks on a factory floor using computer
simulation involved the use of simulation techniques to develop good heuristic schedules for the production
process of wood products at Infinite Woods, a factory in the Western Cape. The objective of the study was
to design a computerised decision support system that could be used to resolve frequently observed bottlenecks on
the factory floor, as an alternative to the system developed by Margarete Louw (which was based on optimisation
techniques). (Co-supervisor: Ms I Nieuwoudt; Advisor: Ms J le Roux) |
 |
|
Margarete J Louw (Fulltime MSc, 2002-2003).
Masters project in operations research entitled Die ontwerp van 'n ge-outomatiseerde besluitnemingsondersteuning stelsel
vir die optimale skedulering van take op 'n fabrieksvloer involved the use of job-shop scheduling techniques to develop
optimal schedules for the production process of wood products at Infinite Woods, a factory in the Western Cape. The
objective of the study was to design a computerised decision support system that could be used to resolve frequently observed
bottlenecks on the factory floor, as an alternative to the system developed by David Coleman (which was based on heuristic
simulation techniques). (Co-supervisor: Ms I Nieuwoudt)
|
|
|
Nicky A Pantland (Part time MSc, 2002-2004).
Masters project in applied mathematics (numerical modelling) entitled 3D numerical techniques for determining the foot of
a continental slope involved the use of numerical differentiation shemes and data smoothing techniques in determining the seaward
foot of a contentental shelf. The objective determination of the foot of a continental slope is one of the essential criteria in
claiming an extended continental shelf by any coastal state as part of its commitment to the United Nations Convention on The Law
of the Sea (UNCLOS). Many coastal states (including South Africa) are signatories to UNCLOS and are thus bound by the
articles contained therein. A time limit of 10 years from signing of the agreement is currently in place and Suth Africa is required
to submit a once-off, professional and scientifically substantiated claim on an extended continental shelf - bringing with it increased
mineral rights. In the case of South Africa, a significant area of seafloor estate has been identified as potential claim material, and
this masters study formed part of the realisation of this potential. Close co-operation was achieved between the Department of
Applied Mathematics
and IMT.
|
 |
|
Johan H van Heerden (Part time MSc, 2002-2004).
Masters project in operations research entitled Detecting fraud in cellular telephone networks involved the use of
real-time statistical and data mining techniques to design an automated decision support system capable of warning cellular
telephone service providers early on of possible fraudulently placed calls, based on abnormal call destinations, call frequencies,
call durations and times at which calls are placed. Close co-operation was achieved between the Department of Applied Mathematics
and the cellular provider via the IT company ISIS.
|
 |
|
Wynand Winterbach (Fulltime MSc, 2002-2003).
Masters project in applied mathematics (graph theory) entitled The crossing number of a graph in the plane
involved the use of analytical arguments and computer algorithms to determine the minimal number of edge crossings with which a plane
drawing of a multipartite graph can be realised. The objectives of the study were (1) to determine crossing numbers for all complete
multipartite graphs of order less than 10, (2) to establish as tight as possible upper and lower bounds for crossing numbers of larger
multipartite graphs, and (3) to characterise forbidden sub-graph structures for crossing number 1, such as the two forbidden
sub-graphs K5 and K3,3 for planar graphs (crossing number 0) according to Kuratowski's theorem.
|
 |
|
Stephen Benecke (Fulltime MSc, 2003-2004). Masters project in applied mathematics (graph
theory) entitled Higher order domination in graphs involved the investigation of
various domination parameters (protection strategies) for different graph classes.
In this investigation the classical domination parameter was generalised in order to incorporate the notions of weak Roman and secure
domination, thereby introducing a dynamic aspect to the (static) classical domination problem. Higher orders of these
parameters (safe configurations after a finite number of moves) were examined. The limiting cases when the
number of moves becomes infinite were also considered. |
 |
|
Frank G Ortmann (Fulltime MSc, 2003-2004). Masters project in applied mathematics (optimisation) entitled A logistics supply
chain management model for fresh fruit produce exported from South Africa involved the use of mixed linear and integer
programming techniques to find (a) the maximum flow (throughput) and (b) minimum cost flow of fresh fruit, earmarked for export,
from the point of local cold storage (just after picking) through a large national infrastructure grid (comprising road & rail
links as well as a number of intermediate storage facilities at, for example, stations) to harbours and airports, from which
export takes place. This project was conducted in close co-operation with Transportek, a division of the CSIR, as well
as various players in the South African fresh fruit industry. The aim of the project was twofold: to model the complete
national fresh fruit produce supply chain with a view to (i) determine in which ways it would be possible to achieve cost
savings during the process of exporting fruit, and (ii) to identify suitable extensions to and improvements of the existing
export infrastructure in order to be able to meet expected increases in future demand. (Advisor: Dr Esbeth van Dyk, CSIR)
|
 |
|
Hendri Botha (Fulltime MSc, 2003-2005).
Masters project in applied mathematics (cryptology) entitled Crypt-analysis of an Advanced Operational Stream Cipher involved
the cryptanalysis of a widely used stream cipher, in terms of well-known design principles such as confusion and diffusion, as well
as period and other statistical properties (balance, non-linearity, correlation immunity) of the output and key streams. This was
followed by the design of an automated and computer-implemented ciphertext-only (partial) attack on the stream cipher, and statistical
and case testing of the practicality and accuracy of the designed attack. It was found that the attack is capable of reducing the key
space to such a degree that a brute-force key search completion would be possible with computing technology of the near future - thereby
placing the cipher within reach of a break. Close cooperation was achieved during this project between the Department of
Applied Mathematics and the National Communication Centre. (Co-supervisor: Dr SG Berjak)
|
|
|
Jaco N Roux (Part time MScEng, 2004-2005).
Masters project in engineering sciences (operations research) entitled Threat Evaluation of Fixed Wing Aircraft in a
Ground Based Air Defense Environment involved the development of threat evaluation algorithms for a Ground Based Air Defense System.
This system supports the command team in their assessment of the tactical situation, i.e. it provides a means to exercise tactical
control of effector- and sensor-systems to fulfill engagement operations within the area of responsibility. Close cooperation
was achieved during this project between the Department of Applied Mathematics and Reutech Radar Systems. (Co-supervisor: Mr P-J
Wolfaardt, Reutech Radar Systems) |
 |
|
Adriaan Janse van Vuuren (Fulltime MSc, 2004-2007).
Masters project in operational analysis entitled Niche Occupation in Biological Species Competition involved the modeling
and analysis of the dynamics of competing biological species. In the investigation a system of partial differential equations
(PDE’s) in space and time were used to model the species densities. The PDE’s in the system were a generalization of the
reaction-diffusion type PDE’s formulated by Fisher in 1937 to model gene diffusion in population genetics. The generalizations
accounted for inhomogeneous in space and time diffusion rates and environmental carrying capacities. The model was used to gain
qualitative insight into geographical regions of species dominance or survival.
|
 |
|
Francois Binneman (Fulltime MSc, 2005-2006).
Masters project in operations research entitled Network Reliability as a result of Redundant Connectivity involved the development of algorithms to aid in the
decision making of construction of networks, with an emphasis on the reliability and stability of the networks. Concepts developed from the graph theoretic literature
were used to extend existing theory regarding the connectivity of graphs. These concepts may be used to define certain properties that a graph should have in order to
achieve a certain level of reliability within the graph. The aim of the algorithms developed was to return a subgraph of a graph (given as input) by removing as many
edges of the original graph as possible, hence reducing the total cost of the graph, without compromising a certain specified level of connectivity.
The theory developed here may be applied in the development of electrical, communications, transportation and computer networks.
|
 |
|
Jacques du Toit (Fulltime MScEng, 2006-).
Masters project in engineering sciences (operations research) entitled The Probability of Attack of Fixed Wing Aircraft in a
Ground Based Air Defense Environment involved the development of detailed algorithms capable of measuring the probability of attack
of a friendly asset by an enemy fixed wing aircraft, based on the real-time behaviour of the aircraft (as observed by radar sensors).
These algorithms were designed for use as sub-procedures in the general threat evalution system developed by Jaco Roux in his masters
thesis. The objectives of the project were (i) to determine a set of critical aircraft profile
attributes which allow for sufficient estimation of probability of attack values under certain circumstances, (ii) to investigate the
relationships and dependencies of these profiles so as to establish relevant multi-dimensional attack probability density functions,
(iii) to develop a support tool for aiding an expert when estimating initial values for these probabilities, and (iv) to develop
mathematical models for updating these probability values as real-time radar sensor data become available. Close cooperation
was achieved during this project between the Department of Applied Mathematics and Reutech Radar Systems.
(Co-supervisor: Mr JN Roux, Reutech Radar Systems) |
 |
|
Andries M Heyns (Fulltime MScEng, 2006-).
Masters project in engineering sciences (operations research) entitled Measuring the Threat Value of Fixed Wing Aircraft in a
Ground Based Air Defense Environment involved the development of detailed threat evaluation algorithms for use as sub-procedures
in the general threat evalution sustem developed by Jaco Roux in his masters thesis. The objectives of the project were (i) to
investigate factors that influence probabilities of attack, of a hit and of a kill by enemy fixed wing aircraft, (ii) to develop a support
tool for aiding an expert when estimating initial values for these probabilities, (iii) to develop detailed mathematical models for
updating these probability values as real-time radar sensor data become available, and (iv) to investigate the possibility and
desirability of measuring threat by means of alternative probabilities than those mentioned above. Close cooperation was achieved during
this project between the Department of Applied Mathematics and Reutech Radar Systems. (Co-supervisor: Mr JN Roux, Reutech Radar
Systems) |
 |
|
Willa Lotz (Fulltime MScEng, 2006-).
Masters project in engineering sciences (operations research) entitled Probability of Attack Stage of Fixed Wing Aircraft in a
Ground Based Air Defense Environment involved the development of detailed attack stage classification algorithms for use as subroutines
in the general threat evalution system developed by Jaco Roux in his masters thesis. The objectives of the project were (i) to develop
mathematical models capable of classifying an enemy fixed wing aircraft into one of a number of progressive stages of attack against a
friendly asset based on real-time measurable and/or derived aircraft attributes, (ii) to investigate the dependencies and relationships
between these attributes in the context of attack stage classification, and (iii) to test the model accuracies against real aircraft
flight data. Close cooperation was achieved during this project between the Department of Applied Mathematics and Reutech Radar
Systems. (Co-supervisor: Mr JN Roux, Reutech Radar Systems) |
 |
|
Cobus Potgieter (Fulltime MScEng, 2006-).
Masters project in engineering sciences (operations research) entitled Real-time Weapons Assignment in a
Ground Based Air Defense Environment involved the development of real-time weapons engagement protocols with respect to enemy fixed
wing aircraft for a Ground Based Air Defense System. This system provides the command team with a means to exercise tactical
control of effector- and sensor-systems in order to fulfill defense engagement operations within the area of responsibility. The objectives of
the project were (i) to introduce a transparant, elementary framework in which the weapons assignment problem may be investigated, (ii)
to establish preliminary decisions required for the development of a mathematical model for weapons assignment, and (iii) to develop and
implement a simple mathematical model for weapons assignment in the military domain. Close cooperation was achieved during this
project between the Department of Applied Mathematics and Reutech Radar Systems. (Co-supervisor: Mr JN Roux, Reutech Radar Systems) |
 |
|
Darian Raad (Fulltime MSc, 2006-).
Masters project in operational analysis entitled A Mathematical Model of Water Supply and Demand in Southern Africa
involved modelling natural water resources, water delivery infrastructure, and water demand patterns in South Africa. These models
were used as a predictive tool to determine the future status of water resources in the country. The models were complemented by
computer-implemented decision support software to determine the optimal placement of new infrastructure such as dams, reservoirs
and pipelines, and identify regions where water shortage is likely to occur. Factors fuch as demand, landforms, environmental
and human impact, cost and efficiency were considered during the optimization process. The objectives of this project were (i) to
construct an accurate mathematical model of the country’s natural water system, (ii) to perform a scientific investigation of the
national water crisis, and (iii) to provide a practical decision support tool for the effective management of water supply
infrastructure.
|
 |
|
Francois du Toit (Fulltime MSc, 2007-).
Masters project in operational analysis entitled A mathematical model for scheduling weapon assignment in a ground based
air defense environment involved the derivation and formulation of a mathematical model capable of providing temporal decision support
to a commander or operator with respect to the assignment of weapons to engage observed fixed wing enemy aircraft in a ground based air
defense environment. The model takes as input quantities parameters such as single shot hit probabilities of the various weapons and the priorities of
eliminating enemy aircraft based on their threatening kinematic behavious with respect to the assets, and suggests and updates a weapon-aircraft
engagement list at each time step, based on an appraisal of predictions of the tactical environment over a moving future time window.
Close cooperation was achieved during this project between the Department of Mathematical Sciences and Reutech Radar Systems.
(Co-supervisor: Mr JN Roux, Reutech Radar Systems) |
|
|
Basie Kok (Fulltime MSc, 2007-).
Masters project in operational analysis entitled A simulation-based evaluation of a threat evaluation and weapon assignment system
in a ground based air defense environment involved the computerized implementation of a threat evaluation and weapon assignment decision
support system (DSS). The threat evaluation (TE) part of the DSS estimates values associated with the threatening behaviour of fixed wing
enemy aircraft with respect to defended (own force) assets by means of both conventional kinematic models and probability based models. The
weapon assignment (WA) part of the DSS suggets weapon-target engagement pairs to a military operator or commander in real time. The simulation-based
implementation of the DSS in this project was capable of evaluating the effectiveness of various TE, WA and flight path prediction models
developed by Jacques du Toit, Andries Heyns, Willa Lotz, Cobus Potgieter and Francois du Toit. Close cooperation was achieved during this
project between the Department of Mathematical Sciences and Reutech Radar Systems. (Co-supervisor: Mr JN Roux, Reutech Radar Systems) |
 |
|
Adri van der Merwe (Fulltime MSc, 2007-).
Masters project in operational analysis entitled Decision support with respect to the scheduling of vinyard block harvesting involved
the development of a computerized decision support system capable of suggesting a schedule for vinyard block harvesting on 160 farms on the
Wellington wine route and the subsequent allocation of the resulting grape juice batches to bins in three wine cellars. The model is based on
a variation of the assignment problem in conjunction with various task scheduling methodologies and takes as input parameters data such as the
slopes and amounts of sun-time of each vine block, measurements of sugar and alcohol content from grape samples, climatic data and
the availability of cellar bins. Close cooperation was achieved during this project between the Department of Mathematical Sciences and a number
of cellars on the Wellington Wine Route. (Co-supervisor: Dr FE van Dyk, CSIR) |
 |
|
Grant van Dieman (Fulltime MSc, 2007-).
Masters project in operational analysis entitled A comparison of exact and heuristic solution methodologies for the classical assignment
problem and its variations involved, as the title suggests, an indepth analysis, implementation and comparison of a number of solution
methodologies for the classical assignment problem and variations thereof, such as the assignment problem with assignee qualifications, the
k-cardinality assignment problem, the bottleneck assignment problem, the balanced assignment problem, the lexicographic assignment problem,
the semi-assignment problem, the catagorized assignment problem, the multi-criteria assignment problem and the quadratic assignment problem).
The exact solution techniques considered included the successive shortest path algorithm for maximum flows in a graph, the maximum weight graph matching
algorithm and a branch and bound technique, whilst the heuristic methdologies included a tabu search approach and a genetic algorithmic
implementation. The techniques were compared both in terms of their execution times and solution qualities. (Co-supervisor: Mr JN Roux, Reutech
Radar Systems) |
|
|
Elmari du Toit (Part time PhD, 2000-2001). Doctoral
project in applied mathematics (operations research) entitled A
quantitative
bio-economic investigation of inshore fisheries involved the
mathematical modelling of harvesting policies for the South African Cape
Rock Lobster (Jasus lalandii) which is both biologically sustainable
and economically viable during the long term. Close co-operation between
the Department of Applied Mathematics and the Department of Sea Fisheries
was achieved during this project. (Co-supervisors: Dr GC Cruywagen, Prof
TP Dreyer & Prof JP du Plessis) |
 |
|
Stephen G Berjak (Fulltime PhD, 2000-2003). Doctoral
project in applied mathematics (cryptology & number theory) entitled
A crypt-analytic attack design against a block-oriented streamcipher
with a 160-bit secret key involved the use of group and number
theoretic arguments as well as computer searches to attack a widely used cryptographic cipher.
Close co-operation between the Department of Applied Mathematics and a
government agency was achieved during this project. (Advisor: Mr N van
Greunen) |
 |
|
Isabelle Nieuwoudt (Part time PhD, 2002-2006). Doctoral project in applied mathematics (graph theory) entitled Maximal
Degree Chromatic Numbers for Graphs involved the development of algorithms capable of determining the smallest number of colours
that could possibly be used to colour the vertices of a graph G such that no monochromatically induced sub-graph of G
has maximal degree larger than some specified number n. This way of colouring has an application in, for example, the
scheduling problem where users of a computer system are in conflict if they require access to one or more of the same files. These
users have to be scheduled for file access efficiently in a minimum number of access groupings, where some threshold of conflict
may be tolerated. The objectives of this study were: (i) to resolve the above NP-complete problem for complete balanced multipartite
graphs, (ii) to establish as tight as possible upper and lower bounds for the maximal degree chromatic number of complete
unbalanced multipartite graphs, and (iii) to characterise the sequence of maximal degree chromatic numbers for all graphs as the
parameter n increases.
|
 |
|
Nthabiseng Ntene (Fulltime PhD, 2003-2006). Doctoral project in operations research entitled A Decision Support System
for the 2D Strip Packing Problem involved the use of meta-heuristics and a combination of various heuristics to come up with
efficient packing arrangements of a number of smaller 2D shapes into some larger 2D shape, so as to minimise the total packing
height. The aim of the project was: (i) to develop new heuristics for this hard problem, (ii) to modify known heuristics and
meta-heuristic procedures so as to improve their solution qualities and (iii) to design a user-friendly computerised decision
support system containing implementations of the known and new heuristics, as well as modified heuristics and meta-heuristics,
which could aid production planners in various industries in which the packing problem is prevalent.
|
 |
|
George W Groves (Part time PhD, 2003-2004, upgrade from MScEng). Doctoral
project in industrial engineering (graph theory) entitled The scheduled multiple traversal postman problem involved the use
of tabu-search and other heuristic procedures to find near-optimal routings for a service
vehicles in a transportation network where different types of links have
to be serviced with different frequencies during the service schedule. Two
objectives were set for these routes: to minimise total travel distance and
simultaneously to spread out (in time) consecutive services of any
particular link in the network. (Co-promoter: Prof W van Wijk, Department
of Industrial Engineering, Stellenbosch University) |
|
|
Jeanne le Roux (Part time PhD, 2004-). Doctoral project in operations reserach entitled |
 |
|
Johan Janse van Rensburg (Part time PhD, 2004-). Doctoral project in operations reserach entitled |
 |
|
Werner R Gründlingh (Fulltime PhD, 2003-2004, upgrade from MSc).
Doctoral project in applied mathematics (graph theory &
combinatorics) entitled Two new problems on dominating sets in lottery schemes
involved the use of combinatorial arguments and computer searches to
estimate bounds on answers to the following two questions: (i) What is the smallest number of lottery tickets that have to be
bought on order to be at least a% sure of winning a minor prize in one of a variety of national and state
operated lottery schemes world wide? (ii) If only b lottery tickets can be afforded in one of a variety of national and state
operated lottery schemes world wide, how should they be constructed so as to maximise the player's chances of winning a minor prize?
(Co-promoter: Dr AP Burger, Department of Mathematics and Statistics, University of Victoria, Canada) |
 |
|
Jaco N Roux (Part time PhD, 2006-).
Doctoral project in engineering sciences (operations research) entitled the Design of a Real-time Threat Evaluation and
Weapon Assignment (TEWA) involved the integreation and implementation of threat evaluation and weapon assignment algorithms
for a Ground Based Air Defense System into a fully fledged operational TEWA system, and was a direct consequence of Mr Roux's work on
master's level. Close cooperation was achieved during this project between the Department of Applied Mathematics and Reutech Radar
Systems. (Co-promoter: Mr P-J Wolfaardt, Reutech Radar Systems) |
|
|
Frank G Ortmann (Fulltime PhD, 2006-). Doctoral project in operations research entitled Stochastic cascading inventory
decision support involved the combined use of inventory models and cutting strategies in order to streamline storage and
production at cardboard box producing factories. In order to minimise costs, board sizes were determined in order to allow for a
cutting strategy that minimises waste. This, in turn, must be compared to the cost of keeping inventory so as to find a solution
that minimises the costs of both waste and inventory. This called for iterative refinements to board sizes, cutting strategies
and inventory models. The methods were computerised and applied in the special case study of Click-a-Box, a cardboard
box producing factory in the South African Western Cape. This was an evolution of the masters project written by Catherine
Black, in which the inventory models and cutting strategies were considered as separate problems, and the question of board
sizes was not addressed.
|
|
