An interactive planning and scheduling framework for optimising pits-to-crushers operations

In this paper, an interactive planning and scheduling framework are proposed for optimising operations from pits to crushers in ore mining industry. Series of theoretical and practical operations research techniques are investigated to improve the overall efficiency of mining systems due to the facts that mining managers need to tackle optimisation problems within different horizons and with different levels of detail. Under this framework, mine design planning,mine production sequencing and mine transportation scheduling models are integrated and interacted within a whole optimisation system. The proposed integrated framework could be used by mining industry for reducing equipment costs, improving the production efficiency and maximising the net present value.

A short-term production scheduling methodology for open-pit mines

A multi-resource multi-stage scheduling methodology is developed to solve short-term open-pit mine production scheduling problems as a generic multi-resource multi-stage scheduling problem. It is modelled using essential characteristics of short-term mining production operations such as drilling, sampling, blasting and excavating under the capacity constraints of mining equipment at each processing stage. Based on an extended disjunctive graph model, a shifting-bottleneck-procedure algorithm is enhanced and applied to obtain feasible short-term open-pit mine production schedules and near-optimal solutions. The proposed methodology and its solution quality are verified and validated using a real mining case study.

Existence of travelling wave solutions for a model of tumour invasion

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al. (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analysed using geometric singular perturbation theory. We prove the existence of three types of physically realistic travelling wave solutions in the case of small diffusion. These solutions reduce to the no diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth travelling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the travelling wave solutions is also discussed.

A geometric construction of travelling wave solutions to the Keller–Segel model

We study a version of the Keller–Segel model for bacterial chemotaxis, for which exact travelling wave solutions are explicitly known in the zero attractant diffusion limit. Using geometric singular perturbation theory, we construct travelling wave solutions in the small diffusion case that converge to these exact solutions in the singular limit.