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By J. Githiria, D. Wachira

The conventional truck and shovel haulage system has become expensive to operate in most mines due to current strict environmental conditions, increase in depth and size of open-pit mines, increase in labour costs, and fuel costs. These factors have motivated the search for alternative material haulage options in open-pit mines. In-pit crushing and conveying (IPCC) system has been regarded as a plausible alternative in material haulage systems. However, usage of IPCC has been limited to a few mines due to limited knowledge of IPCC performance, and other technical factors of the system. This paper investigates, and evaluates the productivity performance of four types of IPCC systems (fixed, semi-fixed, semi-mobile, and fully mobile IPCCs) using mine productivity index (MPi). Using a model developed by MATLAB, the MPi for the four systems is computed using input variables such as availability, utilisation, performance and number of trucks and shovels in a limestone quarry. The mine productivity index for fixed, semi-fixed, semi-mobile, and fully mobile IPCC is obtained as 67.13%, 69.02%, 70.52%, and 71.52% respectively. In conclusion, the fully mobile in-pit crushing and conveying system is the most appropriate IPCC in the quarry, due to its better productivity performance compared to the other three IPCC systems and the truck and shovel system currently in use.

Sep 1, 2021

By K. B. Le Bron, T. van Aard

The empirical pillar strength formulae have been widely, and in most cases successfully, applied to design underground pillars for mines in the Bushveld Igneous Complex (BIC). This paper presents the case for combining the empirical method with numerical modelling when it comes to crush pillar stability analyses. The benefits include an understanding of potential failure mechanisms, which may then be accounted for in the designs. In addition, the impact of weak layers, such as shear zones, the impact of the dip of the orebody, differences in layouts, such as holing widths and the presence of advanced strike gulleys (ASGs) immediately adjacent to the crush pillars, and stress regime (k-ratio) may be studied using numerical modelling, as it is not accounted for in the empirical method.

Mar 5, 2025

By D. P. Roberts

This investigation aimed to simulate the experiments performed by Nic Gay (Gay, N.C.1976. Fracture growth around openings in large blocks of rock subjected to uniaxial and biaxial compression. International journal of Rock Mechanics and Minining Sciences and Geomechical Abstracts, vol. 13. pp. 231-243) on fracture growth around openings in blocks of rock subjected to uniaxial and biaxial compression, using the Elfen discrete element code. The results of the physical experiments indicated a number of trends that were successfully replicated in the numerical simulations, including crushing ahead of the face, the formation of a sub-vertical tensile fracture at centre-span, the formation of groups of fractures originating from the crushed face zone, the formation of large corner-to-corner fractures which precede sample failure, and linking of slot corner and sample corner fractures leading to sample failure. In addition, other features were apparent that were not reported by Gay. It is believed that these took the form of conjugate shear fractures (as reported by Gay in a previous paper) and other features that may have been altered or inhibited by the presence of pre-existing structure in the physical samples. It was found that the samples, though nominally made up of the same rock type, must have had significantly differing properties. The presence of pre-existing structures may have contributed to this discrepancy. Strain measurements from the physical experiments were reasonably well matched, except where the gauge lay directly in the path of advancing fractures.

Jan 1, 2012

By I. M. Macleod

An adaptive steady-state on-line optimizing regulator is proposed as an integrated approach to the control of autogenous run-of-mine milling circuits. This optimizing regulator continuously estimates an internal model of the controlled process, and, based on this, determines mill fresh solids feed rate, mill water flow rate and sump water addition flow rate such that a circuit performance objective is optimized. The dual -requirement of controlling both the mill pulp load and the load of particles of grinding media size is thus directly and simultaneously addressed. The concept and theory underlying the operation of the adaptive optimizing regulator are discussed.

Jan 1, 1987

Excessive dust generation from unpaved mine haul roads is a problem common to most surface mining operations. While optimal road wearing course material selection parameters reduce the inherent dust generation potential, they do not totally eliminate fugitive dust. Many different classes of suppression or palliative treatments are available for mine haul roads and this paper initially ascertains basic selection guidelines, using a set of ideal dust palliative product, application and performance parameters based on mine road-user requirements. An evaluation and modelling methodology for truck generated fugitive dust emissions is developed as a basis for the comparative assessment of dust control strategies. For water-based spraying, a watering model was developed to estimate individual mine road watering frequencies for characteristic site parameter combinations during summer and winter operating conditions, for a required level of control or maximum dust defect. This forms the base-case scenario with which to compare the performance of other types of dust palliatives under the same conditions. Finally, a basic palliative economic evaluation model is introduced with the aim of identifying and costing the establishment, application and maintenance rejuvenation activities associated with the use of chemical palliatives. While palliative cost and performance is generally site specific, it is shown that under certain combinations of conditions, the use of dust palliatives has the potential to deliver cost savings when compared to water-based spraying.

Jan 1, 2007

By C. Dorfling, M. Tadie, S. Grobbelaar

The physicochemical properties of the complex electrolytes used in direct copper electrowinning are an important consideration for the development of a high-fidelity model of the process. Direct electrowinning electrolytes typically contain a high background of metallic impurities. The effect of metallic ions on the properties and accompanying change in the limiting-current density for copper reduction have been the subject of several studies. Although various empirical correlations have been published for describing the physicochemical properties of electrowinning electrolytes, the correlations are only applicable to a limited range of conditions and cannot be extrapolated without further validation. Consequently, in this paper we validated existing physicochemical property correlations for the full range of operating conditions applicable to direct copper electrowinning and developed a new correlation for predicting the associated limitingcurrent density for copper deposition. Following, we evaluated the benefit of using the validated correlations as a component of a dynamic electrowinning model.

Jan 1, 2023

By L. Gunnewiek

An advanced real-time monitoring system called the tapblock diagnostic system (TDS) has been developed. The purpose of the TDS is to help furnace operators manage the safe operation and economical maintenance of furnace tapblocks. This system is an evolution of the current practice of using historical records and operator interpretation to assess the ?health? of a tapblock. The main parameters affecting tapblock health are heat removal capacity and refractory wear, and these are currently difficult to assess in situ except in a global way. By using monitored and operating data together with predictive numerical modelling and multivariate statistical methods, real-time tapblock performance is assessed relative to expected performance. A state indicator in the form of a green, yellow, and red light is used by furnace operators to monitor the tapblock performance and health status during operation. Access to historical operating data and the provision of diagnostic functions allow for probable health degradation events to be deeply investigated. A recent opportunity to evaluate the actual performance of a first generation TDS installed in the KIVCET furnace at Teck Cominco?s Trail Operations showed that a reasonable estimate of tapblock health was made. However, the evaluation also found that some areas of refractory wear were missed, and a new mechanism affecting refractory wear was discovered that was not previously known. This has reinforced the belief that there is a need to develop improved methods of monitoring so that data used to define the health of the tapblock is more comprehensive and accurate.

Jan 1, 2008

It is widely accepted that the type of grinding media has an impact on the grinding chemistry and subsequent flotation behaviour of the sulphide minerals being separated. There are countless laboratory investigations demonstrating that inert grinding media produces more oxidizing pulp potentials, reduced levels of grinding media corrosion products, and superior concentrate grades and valuable metal recoveries. However, taking these results to industrial scale has proved difficult. This paper provides details of the protocol developed and used during a high-chrome grinding media plant trial. It describes the test regime employed to measure changes in pulp chemistry as well as concentrate grades and recoveries to produce a statistically meaningful result. The work also highlighted the need for close cooperation between the metallurgists on site and the researchers conducting the trial. To demonstrate the protocol, data gathered during a plant trail in a PGM concentrate will be presented describing the changes in pulp chemistry and metallurgical response observed.

Jan 1, 2012

By C G. Robinson, B. K. Loveday, J. C. Paynter

"A method of optimizing the design of a processing plant has been developed which minimizes capital and operating costs for average stripping ratios and ore characteristics. Models were developed to describe the operating characteristics and costs involved in various operations such as up-grading, leaching and solid-liquid separation.The options available in up-grading policy and the relation between the cut-off grade and the costs incurred subsequently in the treatment of the ore formed the basis of the optimization. To arrive at an optimum plant configuration and a set of operating parameters, the interrelation between grinding size, leaching temperature, leaching time, and various plant recycle options was investigated."

Jan 1, 2014

By M. Pierce, E. Karampinos

"One of the main challenges in the numerical modelling of ground support in underground excavations is to reproduce the performance of the sequential installation of the reinforcement while capturing the rock mass behaviour of an advancing face in 3D. The 3D modelling approaches used to simulate the progressive advance of excavations are mostly continuum and often cannot reproduce the rock mass failure mechanisms. The 3D discrete element method (DEM) can better reproduce structurally controlled rock mass failure mechanisms and can explicitly represent the reinforcement elements. This paper builds on previous work that reproduced the structurally controlled squeezing conditions in an underground hard-rock mine using 3D DEM and the in situ behaviour of reinforcement under pull conditions. It addresses important issues on the way reinforcement is explicitly introduced in discrete element models. A pseudo-3D model is employed to overcome the computational restrictions and time limitations of a 3D modelling approach. The work focuses on the scaling of the material properties of the ground support elements when the thickness of the model is not equal to the out-of-plane spacing of reinforcement. It demonstrates the scaling methodology based on the type of the modelled reinforcement elements used and investigates the significance of this approach. The advantages and disadvantages of this approach with respect to 2D and 3D methods are discussed. The results are compared with field data and previous modelling work done at the mine. IntroductionNumerical models can provide significant insight into the anticipated behaviour of underground excavations. The modelling of ground support, however, is not a trivial exercise. An effective representation of ground support in underground excavations should capture the behaviour of both the rock mass and the support elements. When numerical models are used for design purposes, the complexity of the problem requires significant time and expertise (Sweby, Dight, and Potvin, 2016).At a laboratory scale, numerical models have successfully reproduced the results of laboratory tests on rockbolts by explicit modelling of the bolt, the borehole, and the grout. Chen and Li (2015) used a continuum FLAC3D (Itasca Consulting Group Inc., 2012) model to simulate the mechanical behaviour of D-bolts as observed experimentally. Grasselli (2005) used a 3D finite element code to model the behaviour of fully grouted rods and expandable bolts under shear."

Dec 1, 2018

By J. N. Van der Merwe

"The probability of survival of coal pillars is a more rational indicator of stability than the safety factor. Over time, pillars undergo reduction in size by progressive scaling of the sidewalls. The probability of survival is therefore not constant but reduces over time. The rate of scaling can be quantified, and the reduction of the probability of survival as a function of time can therefore also be quantified. The paper describes the link between the factor of safety, probability of survival, and reduction of the probability of survival. Using the safety factor, probability of survival, and the time at which the probability of survival will reduce to 50% is proposed as a more rational method of evaluating pillar stability than the safety factor alone.IntroductionCoal pillar strength has long been the subject of research in South Africa and several other coal-producing countries. However, it began receiving serious attention only after the Coalbrook disaster in 1960. The most important outcomes of the initial investigations were the groundbreaking research by Salamon and Munro (1967) that resulted in the well-known power formula for pillar strength, and the work by Bieniawski (1969) that resulted in a linear formula for strength. The former approach was based on empirical back-analysis of failed and stable pillar cases, and the latter on in situ strength tests on large specimens.The Salamon and Munro (1967) formula has been widely used in South Africa and even adapted for application to hard rock pillars by researchers such as Hedley and Grant (1972).At the time of the initial work by Salamon and Munro, there were only 27 failed pillar cases suitable for analysis. It was not possible at the time to determine site- or seam-specific strength, and the result was a general formula for use in all seams in all mining districts. Since that time pillars have continued to fail and the database continued to grow – as of 2013, there were 85 cases in the database. Using the additional data, there have been a number of re-evaluations of the strength formula and it has also become possible to differentiate between the different mining seams and areas."

Jan 1, 2016

By I. C. R. Gilchrist

A principal requirement in the design of a backfill transportation pipeline is the accurate prediction of the values of key slurry flow parameters. Input variables, such as particle size and solids concentration, are usually determined by the load-bearing requirements of the placed fill. It is therefore necessary to identify the optimum conditions of transport for a particular combination of input variables. This paper critically reviews the methods available to predict the values of flow parameters in slurry pipeline systems in the light of experimental data generated at a test facility. Particular reference is made to rod milled waste and deslimed tailings transport systems and, in the case of the former, it is shown that both pumping and load-bearing requirements can be optimized.

Jan 1, 1988

By Z. Bibak and S. Banisi

Granular systems, i.e. particles with realistic shapes, are commonly encountered in nature and industry. While the discrete element method (DEM) is a tool for the simulation of granular flow, in most of the DEM simulation particles are assumed to be spherical. It is questionable whether results drawn from a spherical particle could be easily transferred to a non-spherical particle. Thus, obtaining a fundamental understanding of the underlying physics of granular flows is not only of academic interest, but is also highly related to industrial applications. An in-house developed DEM software called KMPCDEM ©, which was coded to handle non-spherical particles, was used to simulate the particle behaviour. In this paper, the effect of particle shape on the dynamics of particles of non-spherical and spherical shape, including algorithms for the determination of the particle orientation, the moment of inertia, shape representation, and computation time was described. The assumption of a spherical shape has been justified by the complexity of simulation and significantly higher computation time if a realistic shape for particles was used. Dynamics differences showed that findings obtained from spherical particle systems could not be readily extrapolated to non-spherical particle systems. Consequently, particle shape is an important, if not even the most important parameter to be considered in DEM simulations, and therefore has to be captured accurately if DEM is to be used as a predictive tool. Keywords: Discrete element method (DEM), granular systems, non-spherical particles

Jan 1, 2020

By S. Swanepoel, A. V. Cherkaev, Q. G. Reynolds, M. Erwee

Ferrochrome (FeCr) is a vital ingredient in stainless steel production and is commonly produced by smelting chromite ores in submerged arc furnaces. Silicon (Si) is a componrnt of the FeCr alloy from the smelting process. Being both a contaminant and an indicator of the state of the process, its content needs to be kept within a narrow range. The complex chemistry of the smelting process and interactions between various factors make Si prediction by fundamental models infeasible. A data-driven approach offers an alternative by formulating the model based on historical data. This paper presents a systematic development of a data-driven model for predicting Si content. The model includes dimensionality reduction, regularized linear regression, and a boosting method to reduce the variability of the linear model residuals. It shows a good performance on testing data (R2 = 0.63). The most significant predictors, as determined by linear model analysis and permutation testing, are previous Si content, carbon and titanium in the alloy, calcium oxide in the slag, resistance between electrodes, and electrode slips. Further analysis using thermodynamic data and models, links these predictors to electrode control and slag chemistry. This analysis lays the foundation for implementing Si content control on a ferrochrome smelter.

Mar 14, 2024

By J. P. Germiquet

"Rock properties have a material impact on mining processes, including drilling performance. An investigation using point loaded index (PLI) data converted to uniaxial compressive strength (UCS) has revealed that a direct relationship between grain size and UCS exists at Mogalakwena Mine. This correlation is best seen in unaltered rock, with lower correlations for altered rock types. Measurements from the new RockMa system installed on drill rigs can be used to obtain rock strength data to validate the current rock strength domains and create additional data for the next benches below. An investigation of penetration rates in different lithologies shows that rock composition plays an important role in determining drill performance. Additionally, there is an inverse relationship between rock strength and drilling penetration rate – a measure of how efficiently a hole is drilled.The domaining of grain-size-adjusted UCS at Mogalakwena Mine will allow more accurate scheduling of drill rigs through increased knowledge of rock strength in various areas. Successful rock strength domaining has the potential to be incorporated into blast indexing and predicting crushing/milling performance.IntroductionThe optimization of mining and processing through geometallurgical characterization of ore are key drivers of value realization (Deutch, 2013). Rock strength is one such property and is affected by, among other variables, composition, texture, and grain size (Ozturk, Nasuf, and Kahraman, 2014). Mogalakwena Mine is exploiting the intrusive Platreef PGE (platinum group element)-bearing orebody which forms part of the northern limb of the Bushveld Complex. This complex orebody exhibits areas of metasomatic alteration, metamorphism, and sporadic mineralization of the footwall and hangingwall (Nex et al., 2006). Understanding this variability is paramount due to the implications for rock strength and hardness, which in turn affect crushing, milling, and liberation efficiency. These variables must be known prior to blasting in order to optimize mine and plant processes using in-situ variables. This necessitates predictive modelling (Deutch, 2013). Geological and geotechnical data was sourced from the Overysel (OY) exploration database for the study. Point load testing was done for each borehole and the results converted to uniaxial compressive strength (UCS) (Akram and Bakar, 2007). The relationship of lithology, texture, and grain size with UCS revealed an inverse relationship between grain size and UCS in unaltered rock. The relationship was not present in altered rock types. A comparison of mean strength and hardness results indicated that Bond work index and UCS may be related. Drilling performance is affected by UCS (Bourgoyne et al., 1986), and this was proven using recent measurements obtained during drilling. Lastly, grain-sizeadjusted UCS values were applied to a 3D model for the OY property."

Jan 1, 2016

By D. Borman

The location of underground positions in mines has usually fallen to their survey department's. Their usual tasks include: ? installation of a high-precision peg network like the National Survey grid as beacons ? offset measurements to the sidewalls, and sometimes hangingwall and footwalls, of development tunnels and excavations ? offsetting of stoping panels for the calculation of face ? advance and the square meterage of area removed. Other departments build their observations into the plans produced by the surveyors. If more precision is required, they ask the surveyors to `elevate' their points with a theodolite. Apart from the survey peg network and `elevations' these measurements are usually planer measurements suitable for producing plans, sections and projection sheets. When the only representation medium was a sheet of paper or transparency, this was perfectly suitable. However the development of CAD models of the workings has changed all this. Full 3D representation is not properly catered for in the tool sets in current use, and needless hours are spent converting analogue-type observations into digital form. The basic survey models need to be augmented by the observations of other disciplines that are also required to locate positions underground. These include: ? the need for geologists to plott their mapping and ? borehole logs into 3D space ? the need for samplers to position their sample points accurately because the geostatistical models are biased and inaccurate ? the need for stoping width recorders to position their thickness observations to prevent errant evaluation and bonuses ? the need for rock engineers to place their mappings into 3D to build true geotechnical models to manage geotechnical stresses ? the need for production officials to receive updated face ? positions during the month so that they can manage the ? production and utilize their resources properly. This paper covers a new method of positioning profiling points to a suitable degree of accuracy. I believe the method is sufficiently simple and cheap for all to use. Historical methods Platinum and gold orebodies, especially in South Africa, are generally narrow tabular deposits. This made them suitable for depicting on a 2D medium like paper. The determination of stoping or face widths was not a problem, as the ore is removed in a single stoping process. Such 2D representations could be easily positioned using tape offsetting between survey pegs or points tied in from survey pegs. Problems of dip were handled by using 'Stope Sheets' which chose a best fit projection for the whole area depicted or by using true dip section sheets for inclined tunnels. Rolling reef and potholes were the common areas of difficulty. Most mines now model their orebody and plan the extraction in computer graphics. This means that the representation of the current workings has to change to support this trend. It now becomes a truly 3D problem. Mining officials find it inconvenient to have their actual workings in single-line depictions while their orebody is depicted with top and bottom contacts and the planned tunnels in 3D shapes. Geological models which form the basis for the resource model and planning process are often out of date, as the updating process is slow. The geological mapping has to be plotted onto sections and plans. These are then digitized into graphics by a draughtsman and checked by the geologist. Only then does the interpretation and model update take place. Potential methods to create 3D 'Actuals' Global positioning systems (GPS) Surface mines have been blessed by the advent of GPS technology. These simple-to-operate pieces of equipment and compatible software make it possible for all types of mine employees to locate themselves, and therefore to locate their observations. GPS are often inexpensive and give an acceptable degree of accuracy. Only in deep pits or close to the highwalls are observations hindered. Such technology cannot however, work underground. Ground penetrating radar (GPR) GPR is reported to be very useful for estimating the positions of potholes and faults. However it is still considered as providing an estimate, not a definite measurement. GPR is good for seeing into solid rock, not into open spaces. Inertia reading devices Experiments with inertia reading devices have been conducted on the mines. They were the forerunners of GPS for military guidance systems, and were even used for city navigation in the early 70s. They do however work best with heavy or fast-spinning gyros. Anglogold Ashanti's attempt to use them were discontinued in the mid-90s when the developers asked for an additional few million rand for a device that would weigh more than 12 kg and have a limited operational life.

Jan 1, 2006

By M. R. Khalesi, S. Arfania

"Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs. The purpose of this paper is to introduce a new set of capital and operating cost models for major flotation machines based on the application of single (SRA) and multiple regression analysis (MRA). Thirty-seven major flotation machines were analysed for this purpose. Depending on the machinery type, different technical variables such as diameter, required air flow rate, required floor space, cell volume, required air pressure, and power were considered as predictor variables, individually (in SRA) or simultaneously (in MRA). Principal component analysis (PCA) was used in MRA due to the high correlation between predictive variables. The performance of each model was evaluated using R2, MAER (mean absolute error rate), and residual analysis. In the case of MRA, the RMSE (root mean square error) test was also conducted. Maximum obtained MAER of 13.5% and minimum R2 of 0.86 indicated that these models could be applied as credible tools in estimation of capital and operating costs of flotation machines for design and feasibility studies.IntroductionMineral processing is a vital part of mining projects and mainly involves comminution, sizing, concentration, extractive metallurgical processes, and dewatering. Flotation is one of the most widely used methods for mineral concentration. Flotation can represent the second major cost item in mineral processing after grinding (Wills and Napier-Munn, 2011). Accordingly, it is a main concern of mining project managers to select and optimize flotation circuits in order to decrease costs and increase productivity. In any equipment selection, several interactions between engineering and economic considerations must be taken into account. Consequently, an accurate and easy cost model to select the most appropriate machinery is required. Moreover, cost models could be used in flow sheet simulations applied in design and optimization. Models of unit operations built into the simulators could be improved by linking the equipment cost models (Khalesi et al., 2015)."

Jan 1, 2017

By J. L. Deutsch

Block model estimates are commonly calculated by the well-established technique of kriging. The mathematics are well established, but implementation details require site-specific considerations. Checking and measuring the performance of the estimates is important to ensure the block model is suitable for its intended purpose. There are different criteria for long-term planning and short-term planning. The implementation of kriging should be checked with cross-validation and assessed for conditional bias and departure from theoretical optimality with the calculation of kriging efficiency. A new expression of kriging efficiency, which compares the kriging variance with the theoretically optimal kriging variance, is developed to aid in this assessment. The assessment tools presented here can be applied in a number of situations; however, ordinary kriging with a reasonably large search performs well in most cases.

Jan 1, 2014

By B. D. H. Knights

In November 2009 Mintek installed the FloatStar? advanced flotation stabilization system on Vale's Cauê iron ore beneficiation plant in Brazil. In September 2010 the system was upgraded to include flotation optimization. The circuit consisted of two parallel cleaner circuits producing final concentrate. The tailings from the cleaner section passed through a scavenger circuit. Large, well-instrumented feed sumps played an important role in circuit stability, presenting a good opportunity for advanced control. Previously the plant was controlled using distributed control system (DCS) level control only. The flotation circuit processes roughly 30kt/day. The FloatStar system provided advanced control of the flotation circuit as well as of the sumps feeding the circuit. The system underwent a lengthy trial to assess the benefit that it provided. Two data sets were analysed, showing performance under advanced stabilization and optimization respectively. Several validation and consistency criteria were employed to ensure the quality of the analysis. Iron recovery and iron tailings grade were used to measure system performance. The analysis showed that the system increased recovery by up to 2.7%. In addition, the system decreased the iron tailings grade by between 1.2% (from 23.5% to 22.3%) and 4.3% (from 31.3% to 27.0%) during different test campaigns. The analysis also showed that the entire FloatStar stabilization system was active for 72.7% of the time from first activation to the end of the first data set (approximately 200 days). From the analysis it was concluded that under similar conditions for 'ON' and 'OFF' tests, the system provides a clear benefit. It was also found that over the longer term, the system continues to provide a benefit. This finding suggests that the results were not simply due to a short-term advantage. The size of the data set, as well as the magnitude of the recovery improvements, lends considerable confidence to these results. Therefore, it can be concluded that the FloatStar control system provides substantial benefit to operations at this site.

Jan 1, 2012

By Rajib K. Mohapatra, K. Vizaya Kumar

In any manufacturing organization internal logistics plays a vital role in improving and maintaining the productivity. In Ferro Alloys manufacturing organization where there is huge input of raw material in terms of ore, reductants and variety of fluxes amounting to about four times of the mass of alloy produced need to be handled from yard to furnaces , internal logistics requires utmost attention. Any deviation or mismatch between stock and requirement will affect furnace operation. Though the activities are being outsourced by most of the organization, these require close monitoring. This communication presents an optimization model which can work as a ready reference for the manager to decide upon the material quantity and the furnace to be fed with an objective of minimizing the cost of handling and zero production loss.

Jan 1, 2007