Study Group Problems
Problems
There will be about five problems. So far the following problems have been selected.
- Coal mine pillar extraction
Industry: Mining
Industry representatives: Professor Nielen Van Der Merwe and Dr Halil Yilmaz
Moderator:
Description:
While it is common practice in coal mining to leave large unmined pillars in situ to support the overburden, many South African coal mines are considering to mine those pillars on the retreat in a secondary operation in order to improve resource utilization. Pillar extraction is not a new mining method and few problems arise when it is planned from the beginning, when it is possible to design pillars to a size that will facilitate safe secondary mining.
The challenge is to extract the older, smaller pillars that were left in situ several decades ago and were not specifically designed to be extracted. In any pillar extraction operation, the pillars are never extracted completely. Small pillar remnants, called snooks, are left for safety reasons. The requirements for successful pillar extraction are that the overburden has to fail in order to prevent undue build-up of abutment stresses on the as yet unmined pillars, implying that some distance behind the working area, the snooks have to fail while they have to be stable in the immediate vicinity of the working area.
The overburden rock mass is layered and can be treated as a series of beams of different thickness with known tensile strength and elastic modulus. The snooks underneath the beams can be treated as point support that have finite strength and quantifiable compression characteristics.
The challenge is to quantify the interaction between the snooks and the overlying rock mass and predict under which conditions the snooks and the overlying rock beams will fail.
pillarpbmisg2011repv2.pdf - Rising water table and seismicity
Industry: Mining
Industry representatives: Professor Nielen Van Der Merwe and Dr Halil Yilmaz
Moderator:
Description:
The old, now closed gold mines in the Witwatersrand are in the process of flooding. While most of the attention is on the environmental aspect with the possibility of the contaminated water decanting out of the mines, there is another, lesser known aspect that deserves attention.
The mine workings are intersected by numerous geological faults that are stable by virtue of the frictional resistance to movement and the clamping effect of stresses normal to the fault plane. It is possible that the rising water table, resulting in elevated levels of water pressure at depth, will cause water in the deeper areas of the mines to ingress into the fault planes. This will reduce the frictional resistance to movement across the faults as well as the effective normal stress to the fault plane, increasing the lilelihood of movement. If the faults move, there will be seismic events (small to medium earthquakes).
If this happens, a city like Johannesburg could experience small earthquakes. There is at least a suspicion that it may already have happened on a small scale.
The challenge is to quantify the relationship between water pressure and the frictional resistance to movement across the fault planes so that the likelihood of seismic events can be estimated. -
Optimization model for campus parking space allocation
Industry: University and industry in general
Industry representative: Dr. Aderemi Adewumi
Moderator: Professor Montaz Ali
Description:
The uncertain nature of the demand for parking in many organizations has led to some major planning problems. Parking facilities, allocation and conflicts are among the most common problems facing traffic managers. The problem can be in terms of scarcity (few available spaces compared to demand) or management (inefficient usage of available facilities). Specifically, parking is considered a major land use problem in campus planning. The surge in the number of non-resident, staff and visitor car owners coupled with the limited parking space makes parking space allocation (PSA) a difficult one. Planners and Managers tend to proffer a “blind” solution to the problem without proper understanding of its nature and best solution technique. Shortage of parking space near activity centers is worsened as car ownership and registration on campus increase especially on campuses located in urban centres. Given the administrative rules, regulations and restrictions regarding campus parking, there is an urgent need to find an optimal way of allocating parking space based on specific constraints and requirements.Many people have looked at the problem from the administrative and management point of view. However, it is believed that mathematical modelling and perhaps optimization can provide a substantial guide to its solution. The challenge is to develop a model of the problem that determines how best to use existing land in the competitive and policy-driven university campus environment. Major constraints and parameters that traffic managers consider essential to optimal parking need to be investigated. The ultimate goal is to come up with practical solutions that will assist in proper planning, design and allocation of campus parking space and facilities.
parking.pdf -
Optimal assignment of blood in blood banking system
Industry: Hospital and National Blood Bank
Industry representative: Dr Aderemi Adewumi
Moderator:
Description:
Blood compatibility has many aspects, and is determined not only by the blood types (O, A, B, AB), but also by blood factors, (Rh, Kell, etc). The risk of a serious transfusion reaction can be minimized if the donor unit is both ABO-compatible and Rhesus (Rh)-compatible. Type O and Rh negative blood can be given if the recipient’s blood group is not known, as may happen in an emergency. However, the scarcity of type O and Rh negative blood types requires that available blood has to be properly assigned among potential recipients depending on their own blood type and group. It is believed that the number of possible ways assignment can be done essentially gives rise to an NP-Hard problem. This classification of blood and the natural restriction in the blood donation/transfusion system makes it mandatory to determine the best way to assign available blood resources in the blood bank to recipients so as to minimize the quantity of blood imported from outside the system and stabilize the quantities assigned on a daily basis. The challenge is to model the problem and find an optimal way of blood assignment that will guarantee efficient usage of available blood types. This will contribute to the good management of a blood donation-transfusion system. It will determine the best assignment of blood resources to demand, which minimize the quantity of blood imported from outside the system and stabilizes the quantities assigned daily.
blood_final_presentation.pdf -
Mathematical combination problem pertaining to bio-refineries
Industry: Sugar Milling Research Institute
Industry representatives: Professor Steve Davis
Moderator: Dr Aderemic Adewumi
Description:
Rising oil prices and climate change are increasing the viability and necessity to produce plant based, as opposed to fossil based products, such as bio-plastics, bio-polymers, bio-fuels and other renewable energies. When it comes to converting radiation and water into biomass, sugarcane is one of the two most productive plants known to man. Also, sugarcane is already a commercially cultivated crop and is therefore a good bio refinery feedstock candidate. Worldwide there has been a significant drive within the sugar industries to research and develop bio refinery technologies. There are now more bio refinery technologies available than what we can install at any single sugarcane factory. Sugarcane comprise of various compounds, such as fibre, sucrose, glucose, fructose and starch. These compounds make up the feedstock for different bio products and it is therefore most viable that more than one bioprocess will be installed at a single sugarcane factory. A suitable combination of processes hence needs to be selected for a specific sugarcane producing area. This selection should ideally be based on economics, the typical composition of cane in the region, exposure to risk and the existing infrastructure on the ground. The purpose of this project will be to demonstrate how mathematical optimisation methods (and perhaps other approaches) could assist the sugar industry with this combinatorial problem. Biorefineries.pdf.
sugar_overall_report.pdf -
Mobile Device Detection Based on User Agent Strings
Industry: Mobile Web: ZyeLabs
Industry representative: Ismail Dhorat
Moderator:
Description:
Every browser, web crawler and mobile device when requesting a web page, sends its "user-agent". Within the context of the HTTP protocol, the User-Agent is simply a string passed in the request header that is used as a means to identify itself. The user-agent can be used for a variety of purposes such as formatting content appropriately for the device requesting the content.It’s often much simpler to detect desktop browsers and render content appropriately since the features available are pretty well known. In addition the list of possible UA’s are few when compared to mobile device user agents. A simple string matching algorithm could be used to detect desktop browsers without affecting performance of you website or service.
The problem is that there are thousands of different mobile devices, each with their own screen sizes, features and versions of browsers. Even devices that share the same core operating system may often have different features. This makes detecting and rendering content specific to a mobile device difficult.
One of the solutions is to make use of the WURFL (Wireless Universal Resource File) which is a big repository that catalogues these mobile device UA's. The WURFL can be used to detect the device of the user and serve the appropriate content. The query however needs to be optimized, and return a response within a reasonable time frame. Currently Heuristics, Levenshtein distance and reduction of the string has been used to reduce the query time.
The challenge is to detect mobile devices and their relevant properties such as screen size, in an optimized manner based on the User Agent. This can be achieved by either optimizing the existing algorithms or introducing a hybrid of newer, faster algorithms.
cellphone.pdf -
Soccer match ball
Industry: Wits Soccer Club
Industry representative: Dennis Tshabalala
Moderator: Professor Tim Myers
Student Moderator: Gideon Fareo
Description:
In a Cup match all teams use the ball given to them by the South African Football Association but in a League match the home team chooses the soccer ball. Nike supplies three different types of soccer balls to Wits Soccer Club all within the required specifications of circumference, weight and material. The three soccer balls given to the Wits Soccer Team are: T90, Tracer and Omni.The Study Group is asked to recommend which of the three soccer balls Wits Soccer Team should use for its home matches.
The criteria for a good soccer ball are that it must behave predictably, it must not swerve and it must be stable while moving through the air. The Study Group is asked to take into account the types of grass used in South Africa (rye and kikuyu), the effect of high and low altitude on the trajectory of the ball, on the drag and on the transition from turbulent to laminar flow and to consider the flight of the soccer ball at corner kicks, free kicks and goal kicks.
jabulani.pdf.
foottex.pdf.