Mojtaba Rezakhah - Academia.edu (original) (raw)
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Papers by Mojtaba Rezakhah
This dissertation consists of three papers; the first is published in European Journal of Operati... more This dissertation consists of three papers; the first is published in European Journal of Operational Research, the second is nearing submission to Optimization and Engineering, and the third is nearing submission to International Journal of Mining, Reclamation and Environment. These papers apply operations research techniques to open pit mine production scheduling with stockpiling (OPMPS+S). The first paper, “Linear Models for Stockpiling in Open-pit Mine Production Scheduling Problems,” reviews existing models to solve OPMPS+S and shows that a nonlinear-integer model provides an exact solution but is intractable even for medium-size data sets. Then, we present an approximation to that nonlinear-integer model, solve the nonlinear-integer and proposed models for multiple data sets and show that the latter model provides solutions very close to those provided by the nonlinear-integer model. By pairing this novel formulation with recently developed linear programming algorithms and he...
Stockpiles are a crucial part of mine planning. However, they are often ignored in longterm plann... more Stockpiles are a crucial part of mine planning. However, they are often ignored in longterm planning due to the difficulty of correctly evaluating their impact in mine scheduling. This difficulty arises mainly because materials of different grades are mixed in a stockpile, and the final grade of the material leaving the stockpile is a complex non-linear function of the material inside the stockpile. In practice, computational software uses different (usually linear) approximations for estimating this grade, but it is not clear how good these approximations are. In this paper, we discuss different optimization models to approximate the real impact of a stockpile on long-term mine planning. We discuss the properties of these models and compare the quality of the approximations computationally. We show that it is possible to obtain good upper and lower bounds on the resulting grade of the stockpile, and realistic and accurate estimations of the behavior of the stockpile. We also discus...
Open pit mine production scheduling (OPMPS) is a decision problem which maximizes net present val... more Open pit mine production scheduling (OPMPS) is a decision problem which maximizes net present value (NPV) by determining the extraction time and destination of each block of ore and/or waste in a deposit. Stockpiles can be used to maintain low-grade ore for future processing, to store extracted material until processing capacity is available, or to blend material based on single or multiple block characteristics (i.e., metal grade and/or contaminant).
Natural Resources Research
It is of a high importance to introduce intelligent systems for estimation and optimization of bl... more It is of a high importance to introduce intelligent systems for estimation and optimization of blasting-induced ground vibration because it is one the most unwanted phenomena of blasting and it can damage surrounding structures. Hence, in this paper, estimation and minimization of blast-induced peak particle velocity (PPV) were conducted in two separate phases, namely prediction and optimization. In the prediction phase, an artificial neural network (ANN) model was developed to forecast PPV using as model inputs burden, spacing, distance from blast face, and charge per delay. The results of prediction phase showed that the ANN model, with coefficient of determinations of 0.938 and 0.977 for training and testing stages, respectively, can provide a high level of accuracy. In the optimization phase, the developed ANN model was used as an objective function of firefly algorithm (FA) in order to minimize the PPV. Many FA models were constructed to see the effects of FA parameters on the optimization results. Eventually, it was found that the FA-based optimization was able to decrease PPV to 17 mm/s (or 60% reduction). In addition, burden of 3.1 m, spacing of 3.9 m, and charge per delay of 247 kg were obtained as the values optimized by FA. The results confirmed that both developed techniques of ANN and FA are powerful, accurate, and applicable in estimating and minimizing blasting-induced ground vibration and they can be used with caution in similar fields.
Computers & Operations Research
Abstract The open pit mine production scheduling with stockpiling (OPMPS+S) problem decides when ... more Abstract The open pit mine production scheduling with stockpiling (OPMPS+S) problem decides when to extract each notional, three-dimensional block of ore and/or waste in a deposit. In addition, this problem determines whether to send each block to a processing plant, to a stockpile, or to a waste dump. The objective function maximizes net present value, subject to constraints such as precedence, and capacities for mining and processing. Because the material within the stockpile is exposed to the environment, time-dependent changes may occur in the material’s properties, which results in increased processing costs or, equivalently, a net loss of value. We extend a linear-integer mine-planning model that considers stockpiling to account for degradation within the stockpile(s). We compare results from this model on a data set from an operational mine to more commonly used, yet less detailed, models that provide lower and upper bounds on the net present value. We show that the material degradation within a stockpile has an impact on the value that a stockpile provides. Specifically, by considering 5% and 10% annual degradation for our instances, we observe that the value that a stockpile provides decreases by 37% and 69%, respectively, relative to the computed value of a stockpile without degradation.
European Journal of Operational Research
The open pit mine production scheduling (OPMPS) problem seeks to determine when, if ever, to extr... more The open pit mine production scheduling (OPMPS) problem seeks to determine when, if ever, to extract each notional, three-dimensional block of ore and/or waste in a deposit and what to do with each, e.g., send it to a particular processing plant or to the waste dump. This scheduling model maximizes net present value subject to spatial precedence constraints, and resource capacities. Certain mines use stockpiles for blending different grades of extracted material, storing excess until processing capacity is available, or keeping low-grade ore for possible future processing. Common models assume that material in these stockpiles, or “buckets,” is theoretically immediately mixed and becomes homogeneous.
Computers & Operations Research
Abstract Open pit mine production scheduling (OPMPS) is a decision problem which seeks to maximiz... more Abstract Open pit mine production scheduling (OPMPS) is a decision problem which seeks to maximize net present value (NPV) by determining the extraction time of each block of ore and/or waste in a deposit and the destination to which this block is sent, e.g., a processing plant or waste dump. Spatial precedence constraints are imposed, as are resource capacities. Stockpiles can be used to maintain low-grade ore for future processing, to store extracted material until processing capacity is available, and/or to blend material based on single or multiple block characteristics (i.e., metal grade and/or contaminant). We adapt an existing integer-linear program to an operational polymetallic (gold and copper) open pit mine, in which the stockpile is used to blend materials based on multiple block characteristics, and call it ( P ^ l a ) . We observe that the linear programming relaxation of our objective function is unimodal for different grade combinations (metals and contaminants) in the stockpile, which allows us to search systematically for an optimal grade combination while exploiting the linear structure of our optimization model. We compare the schedule of ( P ^ l a ) with that produced by ( P n s ) which does not consider stockpiling, and with ( P ˜ l a ) , which controls only the metal content in the stockpile and ignores the contaminant level at the mill and in the stockpile. Our proposed solution technique provides schedules for large instances in a few seconds up to a few minutes with significantly different stockpiling and material flow strategies depending on the model. We show that our model improves the NPV of the project while satisfying operational constraints.
This dissertation consists of three papers; the first is published in European Journal of Operati... more This dissertation consists of three papers; the first is published in European Journal of Operational Research, the second is nearing submission to Optimization and Engineering, and the third is nearing submission to International Journal of Mining, Reclamation and Environment. These papers apply operations research techniques to open pit mine production scheduling with stockpiling (OPMPS+S). The first paper, “Linear Models for Stockpiling in Open-pit Mine Production Scheduling Problems,” reviews existing models to solve OPMPS+S and shows that a nonlinear-integer model provides an exact solution but is intractable even for medium-size data sets. Then, we present an approximation to that nonlinear-integer model, solve the nonlinear-integer and proposed models for multiple data sets and show that the latter model provides solutions very close to those provided by the nonlinear-integer model. By pairing this novel formulation with recently developed linear programming algorithms and he...
Stockpiles are a crucial part of mine planning. However, they are often ignored in longterm plann... more Stockpiles are a crucial part of mine planning. However, they are often ignored in longterm planning due to the difficulty of correctly evaluating their impact in mine scheduling. This difficulty arises mainly because materials of different grades are mixed in a stockpile, and the final grade of the material leaving the stockpile is a complex non-linear function of the material inside the stockpile. In practice, computational software uses different (usually linear) approximations for estimating this grade, but it is not clear how good these approximations are. In this paper, we discuss different optimization models to approximate the real impact of a stockpile on long-term mine planning. We discuss the properties of these models and compare the quality of the approximations computationally. We show that it is possible to obtain good upper and lower bounds on the resulting grade of the stockpile, and realistic and accurate estimations of the behavior of the stockpile. We also discus...
Open pit mine production scheduling (OPMPS) is a decision problem which maximizes net present val... more Open pit mine production scheduling (OPMPS) is a decision problem which maximizes net present value (NPV) by determining the extraction time and destination of each block of ore and/or waste in a deposit. Stockpiles can be used to maintain low-grade ore for future processing, to store extracted material until processing capacity is available, or to blend material based on single or multiple block characteristics (i.e., metal grade and/or contaminant).
Natural Resources Research
It is of a high importance to introduce intelligent systems for estimation and optimization of bl... more It is of a high importance to introduce intelligent systems for estimation and optimization of blasting-induced ground vibration because it is one the most unwanted phenomena of blasting and it can damage surrounding structures. Hence, in this paper, estimation and minimization of blast-induced peak particle velocity (PPV) were conducted in two separate phases, namely prediction and optimization. In the prediction phase, an artificial neural network (ANN) model was developed to forecast PPV using as model inputs burden, spacing, distance from blast face, and charge per delay. The results of prediction phase showed that the ANN model, with coefficient of determinations of 0.938 and 0.977 for training and testing stages, respectively, can provide a high level of accuracy. In the optimization phase, the developed ANN model was used as an objective function of firefly algorithm (FA) in order to minimize the PPV. Many FA models were constructed to see the effects of FA parameters on the optimization results. Eventually, it was found that the FA-based optimization was able to decrease PPV to 17 mm/s (or 60% reduction). In addition, burden of 3.1 m, spacing of 3.9 m, and charge per delay of 247 kg were obtained as the values optimized by FA. The results confirmed that both developed techniques of ANN and FA are powerful, accurate, and applicable in estimating and minimizing blasting-induced ground vibration and they can be used with caution in similar fields.
Computers & Operations Research
Abstract The open pit mine production scheduling with stockpiling (OPMPS+S) problem decides when ... more Abstract The open pit mine production scheduling with stockpiling (OPMPS+S) problem decides when to extract each notional, three-dimensional block of ore and/or waste in a deposit. In addition, this problem determines whether to send each block to a processing plant, to a stockpile, or to a waste dump. The objective function maximizes net present value, subject to constraints such as precedence, and capacities for mining and processing. Because the material within the stockpile is exposed to the environment, time-dependent changes may occur in the material’s properties, which results in increased processing costs or, equivalently, a net loss of value. We extend a linear-integer mine-planning model that considers stockpiling to account for degradation within the stockpile(s). We compare results from this model on a data set from an operational mine to more commonly used, yet less detailed, models that provide lower and upper bounds on the net present value. We show that the material degradation within a stockpile has an impact on the value that a stockpile provides. Specifically, by considering 5% and 10% annual degradation for our instances, we observe that the value that a stockpile provides decreases by 37% and 69%, respectively, relative to the computed value of a stockpile without degradation.
European Journal of Operational Research
The open pit mine production scheduling (OPMPS) problem seeks to determine when, if ever, to extr... more The open pit mine production scheduling (OPMPS) problem seeks to determine when, if ever, to extract each notional, three-dimensional block of ore and/or waste in a deposit and what to do with each, e.g., send it to a particular processing plant or to the waste dump. This scheduling model maximizes net present value subject to spatial precedence constraints, and resource capacities. Certain mines use stockpiles for blending different grades of extracted material, storing excess until processing capacity is available, or keeping low-grade ore for possible future processing. Common models assume that material in these stockpiles, or “buckets,” is theoretically immediately mixed and becomes homogeneous.
Computers & Operations Research
Abstract Open pit mine production scheduling (OPMPS) is a decision problem which seeks to maximiz... more Abstract Open pit mine production scheduling (OPMPS) is a decision problem which seeks to maximize net present value (NPV) by determining the extraction time of each block of ore and/or waste in a deposit and the destination to which this block is sent, e.g., a processing plant or waste dump. Spatial precedence constraints are imposed, as are resource capacities. Stockpiles can be used to maintain low-grade ore for future processing, to store extracted material until processing capacity is available, and/or to blend material based on single or multiple block characteristics (i.e., metal grade and/or contaminant). We adapt an existing integer-linear program to an operational polymetallic (gold and copper) open pit mine, in which the stockpile is used to blend materials based on multiple block characteristics, and call it ( P ^ l a ) . We observe that the linear programming relaxation of our objective function is unimodal for different grade combinations (metals and contaminants) in the stockpile, which allows us to search systematically for an optimal grade combination while exploiting the linear structure of our optimization model. We compare the schedule of ( P ^ l a ) with that produced by ( P n s ) which does not consider stockpiling, and with ( P ˜ l a ) , which controls only the metal content in the stockpile and ignores the contaminant level at the mill and in the stockpile. Our proposed solution technique provides schedules for large instances in a few seconds up to a few minutes with significantly different stockpiling and material flow strategies depending on the model. We show that our model improves the NPV of the project while satisfying operational constraints.