Open-pit block sequencing optimization: A mathematical model and solution technique

This study presents a comprehensive mathematical formulation model for a short-term open-pit mine block sequencing problem, which considers nearly all relevant technical aspects in open-pit mining. The proposed model aims to obtain the optimum extraction sequences of the original-size (smallest) blocks over short time intervals and in the presence of real-life constraints, including precedence relationship, machine capacity, grade requirements, processing demands and stockpile management. A hybrid branch-and-bound and simulated annealing algorithm is developed to solve the problem. Computational experiments show that the proposed methodology is a promising way to provide quantitative recommendations for mine planning and scheduling engineers.

A new multi-objective model to optimise rail transport scheduler

The sugarcane transport system plays a critical role in the overall performance of Australia’s sugarcane industry. An inefficient sugarcane transport system interrupts the raw sugarcane harvesting process, delays the delivery of sugarcane to the mill, deteriorates the sugar quality, increases the usage of empty bins, and leads to the additional sugarcane production costs. Due to these negative effects, there is an urgent need for an efficient sugarcane transport schedule that should be developed by the rail schedulers. In this study, a multi-objective model using mixed integer programming (MIP) is developed to produce an industry-oriented scheduling optimiser for sugarcane rail transport system. The exact MIP solver (IBM ILOG-CPLEX) is applied to minimise the makespan and the total operating time as multi-objective functions. Moreover, the so-called Siding neighbourhood search (SNS) algorithm is developed and integrated with Sidings Satisfaction Priorities (SSP) and Rail Conflict Elimination (RCE) algorithms to solve the problem in a more efficient way. In implementation, the sugarcane transport system of Kalamia Sugar Mill that is a coastal locality about 1050 km northwest of Brisbane city is investigated as a real case study. Computational experiments indicate that high-quality solutions are obtainable in industry-scale applications.

Mathematical modelling and numerical simulation of phosphine flow during grain fumigation in leaky cylindrical silos

The phosphine distribution in a cylindrical silo containing grain is predicted. A three-dimensional mathematical model, which accounts for multicomponent gas phase transport and the sorption of phosphine into the grain kernel is developed. In addition, a simple model is presented to describe the death of insects within the grain as a function of their exposure to phosphine gas. The proposed model is solved using the commercially available computational fluid dynamics (CFD) software, FLUENT, together with our own C code to customize the solver in order to incorporate the models for sorption and insect extinction. Two types of fumigation delivery are studied, namely, fan- forced from the base of the silo and tablet from the top of the silo. An analysis of the predicted phosphine distribution shows that during fan forced fumigation, the position of the leaky area is very important to the development of the gas flow field and the phosphine distribution in the silo. If the leak is in the lower section of the silo, insects that exist near the top of the silo may not be eradicated. However, the position of a leak does not affect phosphine distribution during tablet fumigation. For such fumigation in a typical silo configuration, phosphine concentrations remain low near the base of the silo. Furthermore, we find that half-life pressure test readings are not an indicator of phosphine distribution during tablet fumigation.

An operational-level multi-stage mine production timetabling model for optimally synchronising drilling, blasting and excavating operations

This paper proposes a new multi-stage mine production timetabling (MMPT) model to optimise open-pit mine production operations including drilling, blasting and excavating under real-time mining constraints. The MMPT problem is formulated as a mixed integer programming model and can be optimally solved for small-size MMPT instances by IBM ILOG-CPLEX. Due to NP-hardness, an improved shifting-bottleneck-procedure algorithm based on the extended disjunctive graph is developed to solve large-size MMPT instances in an effective and efficient way. Extensive computational experiments are presented to validate the proposed algorithm that is able to efficiently obtain the near-optimal operational timetable of mining equipment units. The advantages are indicated by sensitivity analysis under various real-life scenarios. The proposed MMPT methodology is promising to be implemented as a tool for mining industry because it is straightforwardly modelled as a standard scheduling model, efficiently solved by the heuristic algorithm, and flexibly expanded by adopting additional industrial constraints.

A multi-criteria approach for hospital capacity analysis

Hospitals are critical elements of health care systems and analysing their capacity to do work is a very important topic. To perform a system wide analysis of public hospital resources and capacity, a multi-objective optimization (MOO) approach has been proposed. This approach identifies the theoretical capacity of the entire hospital and facilitates a sensitivity analysis, for example of the patient case mix. It is necessary because the competition for hospital resources, for example between different entities, is highly influential on what work can be done. The MOO approach has been extensively tested on a real life case study and significant worth is shown. In this MOO approach, the epsilon constraint method has been utilized. However, for solving real life applications, with a large number of competing objectives, it was necessary to devise new and improved algorithms. In addition, to identify the best solution, a separable programming approach was developed. Multiple optimal solutions are also obtained via the iterative refinement and re-solution of the model.

A model eliciting framework for integrating mathematics and robotics learning

Robotics is taught in many Australian ICT classrooms, in both primary and secondary schools. Robotics activities, including those developed using the LEGO Mindstorms NXT technology, are mathematics-rich and provide a fertile round for learners to develop and extend their mathematical thinking. However, this context for learning mathematics is often under-exploited. In this paper a variant of the model construction sequence (Lesh, Cramer, Doerr, Post, & Zawojewski, 2003) is proposed, with the purpose of explicitly integrating robotics and mathematics teaching and learning. Lesh et al.’s model construction sequence and the model eliciting activities it embeds were initially researched in primary mathematics classrooms and more recently in university engineering courses. The model construction sequence involves learners working collaboratively upon product-focussed tasks, through which they develop and expose their conceptual understanding. The integrating model proposed in this paper has been used to design and analyse a sequence of activities in an Australian Year 4 classroom. In that sequence more traditional classroom learning was complemented by the programming of LEGO-based robots to ‘act out’ the addition and subtraction of simple fractions (tenths) on a number-line. The framework was found to be useful for planning the sequence of learning and, more importantly, provided the participating teacher with the ability to critically reflect upon robotics technology as a tool to scaffold the learning of mathematics.

Mathematical modelling of rock-bed solar thermal storage tank

An important application of thermal storage is solar energy for power generation or process heating. Low temperature thermal storage in a packed rock bed is considered best option for thermal storage for solar drying applications. In this paper, mathematical formulations for conical and cylindrical rock bed storage tanks have been developed. The model equations are solved numerically for charging/discharging cycles. From the simulated results, it was observed that for the same aspect ratio between the diameter and the length of the thermal storages, the conical thermal storage had better performance. The temperature distribution was found to be more uniform in the truncated conical shape rock bed storage. Also, the pressure drop over long period of time in the conical thermal storage was lower than that of the cylindrical thermal storage. Hence, the amount of power required from a centrifugal fan was lower.

Combining unsupervised and invigilated assessment of introductory programming

We compared student performance on large-scale take-home assignments and small-scale invigilated tests that require competency with exactly the same programming concepts. The purpose of the tests, which were carried out soon after the take home assignments were submitted, was to validate the students' assignments as individual work. We found widespread discrepancies between the marks achieved by students between the two types of tasks. Many students were able to achieve a much higher grade on the take-home assignments than the invigilated tests. We conclude that these paired assessments are an effective way to quickly identify students who are still struggling with programming concepts that we might otherwise assume they understand, given their ability to complete similar, yet more complicated, tasks in their own time. We classify these students as not yet being at the neo-Piagetian stage of concrete operational reasoning.

Optimising the operational energy efficiency of an open-pit coal mine system

This thesis investigates factors that impact the energy efficiency of a mining operation. An innovative mathematical framework and solution approach are developed to model, solve and analyse an open-pit coal mine. A case study in South East Queensland is investigated to validate the approach and explore the opportunities for using it to aid long, medium and short term decision makers.