Mathematical programming applications in block-caving scheduling: a review of models and algorithms

Khodayari, Firouz; Pourrahimian, Yashar

doi:10.1504/ijmme.2015.071174

Cited by 21 publications

(12 citation statements)

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“…Most of the studies consider only the upper and lower boundary for draw rate in their modelling. Khodayari and Pourrahimian (2015b) presented a comprehensive review of operations research in block caving. They summarised several authors' attempts to use different methods to develop methodologies for optimising production scheduling in block caving operations.…”

Section: Literature Reviewmentioning

confidence: 99%

Draw rate optimisation in block cave production scheduling using mathematical programming

Nezhadshahmohammad¹,

Khodayari²,

Pourrahimian³

2017

Proceedings of the First International Conference on Underground Mining Technology

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Among the underground mining methods available, caving methods are favoured because of their low cost and high production rates. Block caving operations offer a much smaller environmental footprint compared to equivalent open pit operations due to the much smaller volume of waste to be moved and handled. In general, draw control is fundamental to success or failure of any block cave operation. 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 draw control systems. A mathematical draw rate strategy is formulated in this paper to guarantee exact solutions. Draw control management provides optimal operating strategies while meeting practical, technical and environmental constraints. Furthermore, dilution and caving are improved indirectly, because the method considers the draw rate strategy according to geotechnical properties of the rock mass. Surface displacements are controlled by using the draw rate in all drawpoints during the life of the mine. Application and verification of the presented model for production scheduling based on the draw control system are presented using a case study.

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Section: Literature Reviewmentioning

confidence: 99%

Draw rate optimisation in block cave production scheduling using mathematical programming

Nezhadshahmohammad¹,

Khodayari²,

Pourrahimian³

2017

Proceedings of the First International Conference on Underground Mining Technology

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“…The proposed model in this paper also determines the BHOD as a result of the optimisation. Khodayari and Pourrahimian [7] discuss most of the recent approaches to block cave scheduling using operations research methods. Diering et al [8] present a deterministic approach called PCBC, which is the industry standard programme for block cave scheduling.…”

Section: Introductionmentioning

confidence: 99%

Stochastic optimisation of long-term block cave scheduling with hang-up and grade uncertainty

Dirkx

Kazakidis

Dimitrakopoulos

2018

International Journal of Mining, Reclamation and Environment

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Mass mining methods provide alternatives in developing deeper and lower-grade mineral deposits. Consequently, block cave mining has been increasingly popular mass mining method, especially for large copper deposits currently being mined by open pit methods. This study adopts similar concepts as in stochastic open pit production planning to the planning of block cave mines, to evaluate their effectiveness in a different approach to mass mining. The main contribution of this study is the incorporation of the uncertainty of delays from hang-ups and grades directly into the production scheduling process of a cave mining operation. Hang-up uncertainty relates to the uncertainty linked to the occurrence of ore that clogs the production draw points. This clogging causes time delays in the production cycle leading to tonnage losses and additional costs. Grade uncertainty is incorporated by means of stochastic orebody simulations. Both uncertainty sources are directly linked to the extraction decisions and influence the optimized schedules. The proposed stochastic integer programming model is applied to the optimization of the long-term schedule of a large-scale, low-grade copper deposit by taking into account hang-up delays in block caving. The results of the optimization maximizing net present value clearly show the capability of the formulation to mitigate the effects of both grade and hang-up uncertainty.

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“…Khodayari and Pourrahimian (2014) included the calculation of best height of draw (BHOD) in the production scheduling optimisation model to be an output of the mine plan and not an input. A more detailed review of the mathematical models and their applications in block cave mining production scheduling was presented by Khodayari and Pourrahimian (2015b).…”

Section: Introductionmentioning

confidence: 99%

Application of mathematical modelling for draw control under material flow uncertainty

Khodayari¹,

Pourrahimian²,

Ben-Awuah³

2018

Proceedings of the Fourth International Symposium on Block and Sublevel Caving

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Production scheduling is one of the key steps in the decision-making process of any mining operation. In block caving, it is the choice of the amount of caved rock to extract from drawpoints in different periods. One of the main differences between block caving and other mining methods is the influence of the material flow on production, and draw control in general. Achieving an optimum production schedule without consideration of the cave rate and material flow could be unrealistic and impractical as the movements of material between drawpoints will result in unexpected production grades and tonnages. In this paper, a stochastic mixed integer optimisation model is proposed to optimise the production schedule during the life of the mine. The uncertainties of production grades and tonnages are captured by defining a number of scenarios that represent the probable movements of fragmented rock between drawpoints in the same neighbourhood. The decision variables in the formulation are based on the slice model, which means that the mathematical solution determines which slices are extracted from drawpoints in each period of production. The goal is to maximise the net present value of the project during the life of the mine and minimise the deviations of production grades and tonnages from the defined goals in all probable scenarios resulting from the movements of the fragmented rock between drawpoints. Application of the proposed model in caving operations can not only improve the profitability of the project, but also increase the confidence of the production schedule. MATLAB was used for programming and CPLEX for solving the model. The designed graphical user interface, with the capability of adding different technical and operational constraints, will be a flexible tool for mine planners to control the draw based on the company's goals during the life of the mine.

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Mathematical programming applications in block-caving scheduling: a review of models and algorithms

Cited by 21 publications

References 0 publications

Draw rate optimisation in block cave production scheduling using mathematical programming

Draw rate optimisation in block cave production scheduling using mathematical programming

Stochastic optimisation of long-term block cave scheduling with hang-up and grade uncertainty

Application of mathematical modelling for draw control under material flow uncertainty

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