Yashar Pourrahimian

Mixed integer linear programming formulations for open pit production scheduling

One of the main obstacles in using mixed integer linear programming (MILP) formulations for large-scale open pit production scheduling is the size of the problem. The objective of this work is to develop, implement, and verify deterministic MILP formulations for long-term large-scale open pit production scheduling problems. The objective of the model is to maximize the net present value, while meeting grade blending, mining and processing capacities, and the precedence of block extraction constraints. We present four MILP formulations; the first two models are modifications of available models; we also propose, test and validate two new MILP formulations. To reduce the number of binary integer variables in the formulation, we aggregate blocks into larger units referred to as mining-cuts. We compare the performances of the proposed models based on net present value generated, practical mining production constraints, size of the mathematical programming formulations, the number of integer variables required in formulation, and the computational time required for convergence. An iron ore mine case study is represented to illustrate the practicality of the models as well.

Mixed–Integer Linear Programming formulation for block–cave sequence optimisation

Relying only on manual planning methods or computer software based on heuristic algorithms will lead to mine schedules that are not the optimal global solution. The objective of this paper is to develop a practical optimisation framework to schedule production for caving operations. We present two Mixed–Integer Linear Programming (MILP) formulations for the long–term production scheduling of block caving. First, we solve the problem at the drawpoint level. Then, we aggregate drawpoints into larger units referred to as clusters. The formulations are developed, implemented and verified in the TOMLAB/CPLEX environment. The production scheduler aims to maximise the Net Present Value (NPV) of the mining operation while the mine planner has control over the development rate, vertical mining rate, lateral mining rate, mining capacity, maximum number of active drawpoints and advancement direction. Application and comparison of the models for production scheduling using real mine data over 15 periods are presented.

Hierarchical mine production scheduling using discrete-event simulation

Mine planning involves different levels of decision-making depending on the time horizon under consideration. The main goal of this study is to develop a discrete-event simulation model to link long-term predictive mine plans with short-term production schedules in the presence of uncertainty. We have developed, verified and validated a discrete-event simulation model for open pit production scheduling using the SLAM simulation language. The simulation model takes into consideration constraints and uncertainties associated with mining and processing capacities, crusher availability, stockpiling strategy and blending requirements. Application of the simulation model is presented by an iron ore open pit mine case study.

An application of mathematical programming to determine the best height of draw in block-cave sequence optimisation

Abstract Planning block-caving operations poses complexities in different areas such as safety, environment, ground control and production scheduling. The objective of this paper is to develop a practical optimisation framework for production scheduling of block-caving operations. A mixed-integer linear programming (MILP) formulation is developed, implemented and verified in the TOMLAB/CPLEX environment. In this formulation, the slices within each draw column are aggregated into selective units using a hierarchical clustering algorithm and the mining reserve is computed as a result of the optimal production schedule for each advancement direction. This paper presents a model application of a production schedule for 102 drawpoints with 3457 slices over 14 periods. The results show in order to obtain the maximum net present value (NPV), only 88% of the reserve is extracted. Also, the solving time for the presented method is 78 times faster than method without slice aggregation.

Conditional draw control system in block-cave production scheduling using mathematical programming

Abstract Block caving is a complex and large-scale mining method. The application of block caving is for low-grade, caveable and massive ore-bodies. Among the underground mining methods available, caving methods are favoured because of their low cost and high level of production. Generating a production schedule that will provide optimal operating strategies without geotechnical constraints is not practical in block caving. Establishing relationships among draw columns to consider depletion rates of other draw columns is complex but essential to provide a reasonable solution for real block-caving mines. This paper presents a mixed-integer linear programming (MILP) model to optimise the extraction sequence of drawpoints over multiple time horizons of block-cave mines with respect to the draw control systems. Four resolutions are formulated in this paper to guarantee practical solutions with respect to draw control managing in mined areas according to the draw rate and conditional draw rate constraints. Application and comparison of the four resolutions for production scheduling based on the draw control systems are presented using 325 drawpoints over 15 periods. The performance was analysed based on maximising the net present value (NPV) at a discount rate of 12%. The maximum obtained NPV from of the proposed MILP models is

Optimizing block caving drawpoints over multiple geostatistical models

451.07M.

Development of a new classification system for assessing of rock mass drillability index (RDi)

ABSTRACT Large-scale mining methods are commonplace in the mining industry, and caving has become the preferred underground mining technique. The use of block caving has increased worldwide and is expected to grow because of high production rates, low mining costs, and low waste production. One key engineering consideration in block caving is the drawpoint spacing layout, which must be selected prior to production based on widely spaced exploration data; uncertainty is highest during this stage of mining; and selecting an appropriate extraction level and layout is important for economic and safety considerations. In the proposed methodology, uncertainty in the grade block model is assessed with sequential Gaussian simulation and an optimisation procedure is developed to maximise net present value over many realisations while being constrained by mining considerations. This novel approach generates one layout that is optimal over all realisations rather than consider optimisation on a single kriged model which is standard practice; in this way risk can be assessed and mitigated by selecting the layout that maximises profit but also minimises the variance of profit over all realisations. The methodology is demonstrated using a case study, and the proposed technique outperforms traditional optimisation based on a kriged model.