Mixed integer linear programming formulations for open pit production scheduling

Askari–Nasab, Hooman; Pourrahimian, Yashar; Ben-Awuah, Eugene; Kalantari, Samira

doi:10.1134/s1062739147030117

Cited by 54 publications

(17 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Note thatp bt is computed as (4) require that each block can be extracted no more than once. Constraints (5) ensure that the minimum and maximum operational resource constraints are satisfied each period. We assume here that q br > 0, which is a commonly used in practice and permits feasible solutions more readily than without it; as such, the formulation only contains lower and upper bounds but omits constructs that would lend themselves to blending.…”

Section: The Constrained Pit Limit Problemmentioning

confidence: 99%

“…Here, we define the coefficients q br andq brd , corresponding to constraints (5) and (10) in (CPIT ) and (PCPSP ). This entry consists of n lines, where n is at most the total number of non-zero coefficients in the aforementioned constraints.…”

Section: D110 Resource Constraint Coefficientsmentioning

confidence: 99%

“…The units, sometimes termed "smallest mining units," that are used for scheduling purposes, must be representative of the mining operation being modeled. (See, for example, [5] who present descriptions of and formulations for suitable block sizes.) For production scheduling at the tactical level, one may more realistically use aggregated blocks to fit the geology of the operation and the time fidelity of the model; [47] present a clustering algorithm based on a similarity index to aggregate blocks into these smallest mining units.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

MineLib: a library of open pit mining problems

et al. 2012

View full text Add to dashboard Cite

Similar to the mixed-integer programming library (MIPLIB), we present a library of publicly available test problem instances for three classical types of open pit mining problems: the ultimate pit limit problem and two variants of open pit production scheduling problems. The ultimate pit limit problem determines a set of notional three-dimensional blocks containing ore and/or waste material to extract to maximize value subject to geospatial precedence constraints. Open pit production scheduling problems seek to determine when, if ever, a block is extracted from an open pit mine. A typical objective is to maximize the net present value of the extracted ore; constraints include precedence and upper bounds on operational resource usage. Extensions of this problem can include (i) lower bounds on operational resource usage, (ii) the determination of whether a block is sent to a waste dump, i.e., discarded, or to a processing plant, i.e., to a facility that derives salable mineral from the block, (iii) average grade constraints at the processing plant, and (iv) inventories of extracted but unprocessed material. Although open pit mining problems have appeared in academic literature dating back to the 1960s, no standard representations exist, and there are no commonly available corresponding data sets. We describe some representative open pit mining problems, briefly mention related literature, and provide a library consisting of mathematical models and sets of instances, available on the Internet. We conclude with directions for use of this newly established mining library. The library serves not only as a suggestion of standard expressions of and available data for open pit mining problems, but also as encouragement for the development of increasingly sophisticated algorithms.

show abstract

Section: The Constrained Pit Limit Problemmentioning

confidence: 99%

Section: D110 Resource Constraint Coefficientsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

MineLib: a library of open pit mining problems

et al. 2012

View full text Add to dashboard Cite

show abstract

“…Mixed-integer linear programming (MILP) is a powerful tool extensively used in the literature for mine planning optimization. Typical mine planning models maximize the NPV over the mine-life, with respect to the mining and processing capacities, ore blending constraints, and spatial precedence among mining blocks (Johnson, 1969;Askari-Nasab and Awuah-Offei, 2009;Askari-Nasab et al, 2011). Further than the pure long-term mine planning models, few works are published addressing the linkage between mine planning and tailings production (Kalantari et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Mixed Integer Linear Programming for Oil Sands Production Planning and Tailings Management

Badiozamani¹,

Ben-Awuah²,

Askari–Nasab³

2019

J ENVIRON INFORM

Self Cite

View full text Add to dashboard Cite

In oil sands open-pit mining, further processing of the extracted oil sands generates massive volumes of tailings. To save space, the tailings are deposited in in-pit tailings containments constructed by internal dykes using mine waste material. In this paper, an integrated mine planning framework is proposed and implemented using mixed-integer linear programming to optimize the production schedule with respect to dyke construction and in-pit tailings deposition. A case study is carried out to verify the performance of the proposed optimization model. The results demonstrate how the produced tailings are deposited in the excavated mining pits as the mining operation proceeds and the in-pit dykes are constructed using mine waste material. The framework facilitates sustainable oil sands mining through a reduced environmental footprint.

show abstract

“…The use of mixed integer linear programming (MILP) is a modelling approach well suited to formulate the mine scheduling optimisation problem. Compared to open pit applications (for example [1,2,3,21]), the research published on underground mine scheduling problems is limited. Earlier references to the use of MILP formulations can be found in the publications by Carlyle & Eaves [4], Rahal et al [14] and Smith et al [19], although no model formulations were provided in these papers.…”

Section: Introductionmentioning

confidence: 99%

An improved formulation of the underground mine scheduling optimisation problem when considering selective mining

Terblanché

Bley

2015

ORiON

View full text Add to dashboard Cite

The use of mixed integer programming is a modelling approach well suited to formulate the mine scheduling optimisation problem for both open pit and underground mining. The resolution applied for discretising the problem, however, has a direct effect on both the level of selectivity that can be applied to improve profitability, as well as the computational feasibility. The proposed model allows for a balance in reducing the resolution used in discretising the underground mine scheduling problem, while maintaining enough detail that will allow the generation of mine production schedules that improve profitability through selective mining. As a secondary contribution, an improved formulation set within a resource production/consumption framework is presented, which can potentially simplify notation used in formulating underground mine scheduling optimisation problems.

show abstract

Mixed integer linear programming formulations for open pit production scheduling

Cited by 54 publications

References 13 publications

MineLib: a library of open pit mining problems

MineLib: a library of open pit mining problems

Mixed Integer Linear Programming for Oil Sands Production Planning and Tailings Management

An improved formulation of the underground mine scheduling optimisation problem when considering selective mining

Contact Info

Product

Resources

About