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Estimation of incremental haulage costs by mining historical data and their in�uence in the �nal pit limit de�nition typical input economic parameters. Examples of physical parameters Diverse economic and physiR. Benito and S.D. Dessureault, members SME, are graduare the ore grade distribution, geocal parameters are considered for ate research assistant and associate professor, respectively, technical constraints and metalluropenpit optimization. Mining costs, with the Department of Mining and Geological Engineering, gical recoveries. included in the block-valuing proUniversity of Arizona, Tucson, AZ. Paper number TP-07-030. Block models are widely used by cess, are defined by the main acOriginal manuscript submitted August 2007. Revised manuspecialized mining software to assist tivities involved: drilling, blasting, script accepted for publication June 2008. Discussion of this in the final pit outlining process, by loading, hauling and ancillary operpeer-reviewed and approved paper is invited and must be storing the economic and physical ations (pit roads and dumps). From submitted to SME Publications Dept. prior to Jan. 31, 2009 . parameters in each block. Block valthe main activities mentioned, haulue or profit per block is calculated ing is considered the most resource-consuming activity by subtracting the revenue generated from selling the in a typical openpit truck-shovel operation (Blackwell, recoverable contained metal minus the costs incurred to 1999). The The aim of this research was the determination of produce it. it . Variable costs (mining, processing, marketing marketi ng historical haulage costs and their variations by location. and restoration costs) and fixed costs (e.g., overheads) For this purpose, the fundamentals of the two-stage are usually considered for block valuing. After all blocks cost-tracing procedure (Cooper, 1987a) were applied conforming a three-dimensional model are valued, the to trace incurred haul costs by bench. This approach final step is the application of a numerical method for requires the definition of a measure of the quantity pit outlining. Lerchs-Grossmann algorithm is a popular of resources consumed during its second stage called method to determine the size and shape of the ultimate cost driver. Tracing costs by location from real data is a pit. This final shape maximizes the value of the mine challenging task due to the dynamic nature of haulage subject to slope constraints (Whittle, 1996). activity, which is usually controlled by truck dispatch Final pit limit definition continues, even during the systems. These systems assign trucks arbitrarily to loadoperation stage, in order to evaluate potential mine ing points. Their objective is the maximization of truck expansions. An updated version versi on of the life-of-mine life-of -mine plan utilization and reduction of waiting and delay times. (LOM), including the final pit limit definition, is usually In contrast, haulage costs are usually stored as general prepared once a year for budgeting purposes. Various transactions, not detailed by location, due mainly to the input parameters for openpit outlining may be updated structure of cost accounting systems. based on historical data. These input parameters may reflect the actual performance achieved in terms of proFinal pit limits duction and incurred costs. Variable haulage costs by Mine plans, in particular long range mine plans, are bench are economic inputs that can be updated using usually developed within a final pit outline. The process historical data. Detailed and extensive information rerequires the definition of various physical and economic lated to truck haulage performance and incurred costs is parameters. Commodity prices and anticipated costs mostly available in operating mines and stored in large (mining, processing, selling, rehabilitation costs) are operational database systems such as truck dispatch systems and financial transaction systems. This This vast Abstract amount of information can be integrated, processed and analyzed by using relatively new information technolThis paper describes the application of modern data-analogy, namely, data warehouse and data mining. ysis tools, such as data mining, to determine a representa-
Introduction
R. BENITO AND S.D. DESSUREAULT
tive cost driver for haulage activity. This cost driver was subsequently used to trace incurred haul costs by bench for openpit optimiza optimization. tion. For this purpose, large amount of previously unused cost and production data data from an open pit mine was extracted, extracted, loaded, transformed and integrated integrated into a data warehouse. Predictive modeling was performed using Microsoft Decision Trees Trees algorithm to compute ex pected unit haul costs by bench for future mine expansions expansions.. Finally,, a sensitivity analysis was carried out to determine Finally the effect of two cost drivers (if any) for incremental haul costs in the final pit outline process. 44
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Data warehouse and data mining Enterprises now maintain two databases, one containing operational data (to assist the day-to-day operation) and one called the data warehouse (DW), which contains decision support data (Date, 2004). Data warehouses are databases that are used to support management decisions. They are populated and updated on a periodic basis from operational databases called online transaction processing databases (OLTP). For a mining operation, a data warehouse may be populated
with historical production data and FIGURE 1 incurred operating costs. Figure 1 is Attributes stored in a production data table. a graphical representation of mine production data and their attributes stored in a transactional table for an openpit operation. This figure shows the detailed distribution of loading and dumping points, captured and stored using modern global positioning systems (GPS). The centroid of the bench is also shown, which is usually considered as a single loading point for the estimation of truck productivity during the preparation of the LOM plan. Data mining is a data-analysis which includes spot, load, haul, turn, dump, empty reprocess that identifies trends and patterns of a busiturn, wait and delay times (Hays, 1990). Usually, for ness process (Chao, 2006). Data mining, also known as mine planning purposes, the total cycle time is calcuknowledge discovery, is a rapidly developing trend in lated using truck simulation software. Projected haul data management. Data mining has become a popular profiles and truck rimpull/retarding curves are used tool for managers, analysts and experts in commercial to calculate expected total cycle times by bench and and government organizations. The development of destination. For simplification, it is assumed that the hardware and software technology allowed for the evohaul and return segments are the same. However, with lution of data analysis in large databases. Retrospective the use continuous use of dispatch systems, trucks are and static data delivery was only possible in the 1960s, often assigned dynamically to maximize their utilizawhile presently, data mining techniques allows obtaintion. This section describes the process to define a cost ing prospective and proactive information. driver that reflects adequately the resource consumpClassification, clustering, association, regression, tion (fuel, tires, parts, etc.) for haulage activity using forecasting, sequence and deviation analysis are typical historical data. Specifically, the cost driver should reflect examples of data mining tasks. Decision trees and neuvariances in haulage costs due to mining location. For ral networks are two popular data mining techniques this purpose, detailed information from a truck dispatch available in Microsoft SQL 2005. These techniques are system and a financial transaction system was provided mainly derived from statistics, machine learning and from an open pit mine and stored in a data warehouse. database (Tang, 2005). Data cleaning and data filtering were the initial tasks Data collection, data cleaning and transformation performed using Microsoft SQL 2005 Server Manageare required steps and must be achieved prior to the ment Studio. These tasks were accomplished by creating application of a particular data mining technique. Truck queries or views and integrating transactional tables. haulage performance trends (e.g., lower productivities Table 1 displays a summary of the main transactional due to increased haul distance) and the variables influtables. The data implied two years of production and encing such trends can be analyzed through data mining. cost transactions. Additionally, different truck performance measures may For integration purposes, the data were aggregated be defined and analyzed to determine the most repreon a monthly basis to balance the level of detail (granusentative for haulage activity. This measure may then larity) of production and cost tables. The steps menbe used as a cost driver to trace haulage costs by bench, tioned above are not detailed in this paper due to their applying the fundamentals of the two-stage cost tracing extensive nature. Considering the available data, the approach (Cooper, 1987b). The next section applies data following haulage performance indicators were considmining tools available in Microsoft SQL 2005 to define a ered as potential cost drivers (predictable attributes): representative cost driver for mine haulage activity.
Truck haulage performance analysis
• • • •
total cycle time (cycletime), haul time (haultime), haul time plus return empty (haulreturn) and haul distance (hauldist).
Truck performance is usually associated to the calculation of incremental haulage costs. Davey (1979) describes an approach to estimate variable haulage costs by combining truck hourly Table 1 costs and truck performance (in tons per operating hour), which is influenced by the Production and cost transactional tables. size, equipment type and the haulage pro- Table name Type Columns files (length and lift). Unit costs are then calculated by dividing the truck hourly lh_load_base Production 103 cost by the resulting truck productivity. lh_dump_base Production 41 Truck performance is typically expressed lh_location_base Production 10 in terms of hourly production rate (tons lh_equip_list_base Production 16 per hour), and it is calculated considering mdm_costs_base_updated Cost 64 truck payload and truck total cycle time,
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FIGURE 2
Dependency network for truck performance indicators.
For this analysis, total cycle time excludes wait and delay times in the truck cycle to determine the effective cycle time (spot, load, haul, turn, dump and empty return times). Microsoft Business Intelligence Development Studio was used for the data mining analysis. Considering the objective of defining a cost driver to trace haulage costs by location, the following variables were considered as input attributes: • • •
bench. destination. lift (Delta Z).
the level of correlation between input and predictable attributes. Each oval or node in the network represents an attribute (input or predictable), and the arrows represent the relationship between two nodes. The direction of the arrow points from the input and to the predictable attribute. According to the DN of Fig. 2, “haultime” has the strongest relationship (or most correlated) with the input attributes (bench, destination and lift). Mining accuracy charts are tools used to evaluate the quality and precision of a data mining model. Lift charts, used for continuous variables, are scatter plots that compare actual versus predicted values from a model. An ideal model should group the points on a 45° angle. Figure 3 shows a lift chart for “cycletime” attribute, and the corresponding score value achieved. Higher score values stand for better accuracy in a model. The overall score showed in lift charts for continuous attributes represent the geometric mean of the individual scores for the points conforming the scatter plot. The score of a particular point in a scatter plot is given by score [ a , b( m)]
P[b( m ) | (a, m )] =
(1)
P[ marginal _ mean | a ]
where a is the actual attribute value and b(m) is the predicted value using the model ( m).
Equation (1) assumes a normal distribution to comChen (2001) suggests dividing the data into three pute the probabilities for both predicted and actual subsets: training, testing and evaluation sets for predicvalues. Table 2 summarizes the different scores achieved tive modeling. For this analysis, two data sets were arfor the predictable attributes (potential cost drivers), for ranged: a training set to build the model (e.g., to define both training and testing data sets. Additionally, Table 2 equations between input/predictable attributes) and includes the square of the correlation coefficient (R2) a testing set to evaluate its accuracy. A data mining for the models. It can be noted clearly that “haultime” technique called Decision Trees was chosen for model achieved the highest score values compared to the other construction. For the case of continuous variables, the indicators in both data sets. Figure 4 shows the decision decision tree algorithm uses linear regression to decide tree for “haultime,” with a regression formula in each where a decision tree splits. A regression formula is crenode of the tree. For instance, a haul profile having the ated in each node of the tree. A split occurs at a point crusher (CR) as destination with a bench elevation less of nonlinearity in the regression formula. Generally, than 2,564 has the following expression: a regression formula contains one or more regressors (input attributes). If no regressor is present in the forHaul time = 8.808 + 0.024* (2) mula, the result tree contains a constant in each leaf (Delta Z - 122.071) – 0.024*(Bench – 2,541.929) node. Eight destinations were considered for model construction according to the material type asTable 2 signed. Twenty benches, with elevations between 2,510 and 2,770 m (8,230 to 9,090 ft) above sea Scores and R2 for training and testing data sets. level, were as well considered as origin points. Training set Testing set Figure 2 shows a dependency network, which is Attribute name Units Score R2 Score R2 used generally as an exploratory data analysis. This tool is included in the Microsoft Decision “haultime” minutes 5.50 0.94 4.98 0.96 Tree approach. The DN displays the relation- “haulreturn” minutes 4.16 0.92 2.94 0.82 ships among attributes (input and predictable) “cycletime” minutes 2.88 0.84 2.39 0.77 from the decision tree model’s content and their “hauldist” meters 3.24 0.87 2.43 0.83 associated weights. The weights are related with
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The diamond bars depicted in the FIGURE 3 nodes of the tree represent the value Lift chart for “cycletime” attribute. distribution of the given node. The width of the diamond indicates the level of accuracy of the node — the thinner the better in precision. Considering the results shown by the DN in Fig. 2 and the scores values in Table 2, haul time may be used as a representative cost driver for haulage activity. Data mining also allows predictive modeling to determine expected haulage costs for future benches. This calculation may then be used for block valuing purposes, the initial step of the pit outlining process. For this purpose, it was necessary to create a new data set, specifying only the input parameters (bench, destination and lift). The mining model prediction function available in Business Intelligence allows calculating expected haul time values according to the input values. This expected valincremental unit haulage cost curves for the two cost ue, combined with the haulage costs by month and the drivers having the crusher as the final destination. Simiaverage truck payload provide the means to calculate lar shapes were also obtained for the other destinavariable haulage costs by bench and destination. tions. The dotted lines represent expected unit costs for future benches. The expected values are the output Final pit limit analysis of the prediction function of the Microsoft Decision The objective of this analysis was to assess the effect Trees model. The haul time curve indicates that unit in the final pit limits outlining when using two differhaul costs are lower compared to the cycle time curve ent cost drivers to trace haulage costs by bench. Haul between 0 and -120 m (-400 ft) lift interval. Conversely, time, the most correlated attribute, and cycle time, the as the lift “increases,” unit haul costs are higher for the lowest scored attribute, were selected as cost drivers. haul time curve. Tracing incurred costs by bench requires the calculaBlock value was carried out using a regular threetion of burden rates (Cooper, 1987b). These rates are dimensional block model representing a low-grade computed dividing the total costs incurred (from a copper porphyry deposit, where heap leaching was the cost center) by the total of units consumed (e.g., haul current beneficiation method. For simplification, only hours). For the two cost drivers selected, the totals of two destinations were evaluated: crusher if leach ore units consumed (TUC) are expressed in time units. For and dump if waste. However, it is possible to include haul time, TUC is expressed as total truck haul hours; multiple destinations for diverse material types for a while for cycle time TUC is the total truck cycle hours complex pit optimization (e.g., beneficiation processes (effective hours). Full haulage costs include operating for various ore types, diverse types of waste). The foland maintenance expenses. These values were cumulowing economic parameters were considered for block lated over the range of the stored data. After dividing valuing: the total haulage costs by the TUC for each driver, Table 3 the following bur- Pit optimization results. den rates are obtained: $390 per Haul time cost Cycle time Cost hour hauled and difference, $173 per effective Summary of results Units Driver (1) Driver (2) (1)-(2) hour for haul time and cycle time, reNumber of total blocks mined – 7,456 7,171 285 spectively. An avNumber of ORE blocks mined – 2,758 2,674 84 erage payload of Number of WASTE blocks mined – 4,698 4,497 201 160 t (180 st) per Net revenue million US$ 163,324 159,954 3,370 truck was includ- ORE mined million st 98.7 95.7 3.0 ed in the calculaWASTE mined million st 161.1 154.2 6.9 tion to determine TOTAL material mined million st 259.8 249.9 9.9 unit haulage costs Stripping ratio – 1.63 1.61 0.02 ($/st). Figure 5 shows
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FIGURE 4
Decision tree for “haultime” attribute.
• Economic metal: copper • Commodity price: 0.9 $/lb • Mining costs: – Base: 0.50 $/st – Incremental: According to the cost driver • Processing costs: 2.3 $/st ore • Selling costs: 0.17 $/lb (includes rehabilitation costs). Pit optimization was performed after completing the block value step. Lerchs-Grossmann algorithm was used to determine the final pit limits, considering the actual topography and an overall slope of 38°. Two runs were performed for the block values using haul time FIGURE 5
Incremental haulage costs and predicted values.
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and cycle time as cost drivers. Table 3 shows the results of the pits generated. A significant difference of 9 Mt (10 million st) for the pits was achieved using two distinct cost drivers. The pit with haul time as cost driver is relatively bigger than the pit with cycle time as cost driver. Figure 6 displays a vertical cross section with the final contours, the actual topography and the economic ore blocks. A difference of 40 m (130 ft) between the final pits is displayed in the lateral expansion. However, both pits achieved the same pit bottom. The additional expansion for the pit using haul time is the effect of having lower unit haul costs for a lift range of 0 and -120 m (-400 ft), as mentioned above. The dissimilarity in pit size demonstrated that the deposit was sensible to incremental haulage costs, despite the mineralization is moderately shallow. Conclusions
Historical production data and incurred costs were integrated, processed and analyzed to establish a characteristic cost driver for haulage activity. The cost driver was then used to trace haulage costs by bench. A dependency network was used to find the most representative cost driver from different truck performance indicators. The dependency network showed that haul time attribute had the strongest relationship (most correlated) with the location-related input attributes: bench, destination and lift. The dynamic assignment of trucks by dispatch systems and the speed variation by grade segment are potential causes of the lack of accuracy for the other truck performance attributes evaluated. In real time, loaded haul and empty return segments are not always performed in the same route. Instead, the trucks can be reassigned to different locations. This event distorts typical truck performance indicators, such as total cycle time, that are widely used for mine planning purposes. Additionally, a sensitivity analysis was carried out to evaluate the effect
of using two different cost drivers for variable haulage costs in the final pit FIGURE 6 outlining process. For this purpose, Cross section for optimized pits. a predictive model was built to determine expected unit haul costs by bench. Microsoft Decision Trees was the algorithm used for model construction. The predicted output values (e.g., haul time) were then combined with their respective burden rates and average truck payload to calculate expected unit haul costs by bench for block valuing. Lerchs-Grossmann three-dimensional algorithm was then performed for pit optimization. The results showed a significant difference in shape and volume for the resulting pits. The pit with haul time as the cost driver was relatively bigger than the pit using cycle time as the cost driver, Cooper, R., 1987a, “The two-stage procedure in cost accounting: especially in the lateral expansion. This increase in size Part one,” Journal of Cost Management for the Manufacturing Indushad the effect of lower haulage costs for benches at the try, Vol. 1, No. 2, p. 43-51. proximity of the pit exit point when using haul time as Cooper, R., 1987b, The two-stage procedure in cost accounting: cost driver. The pit optimization analysis demonstrated Part two,” Journal of Cost Management for the Manufacturing Industhat, even with minimal cost increments, different retry, Vol. 1, No. 3, pp. 39-45. sults might be obtained. Finally, the updating of input Date, C.J., 2004, An Introduction to Database Systems, 8th Edition, parameters for final pit outlining with historical data is Pearson/Addison Wesley, Boston. highly recommended in order to reflect actual producDavey, R.K., 1979, “Mineral Block Evaluation Criteria,” AGARD tion and cost performances. ■ References Blackwell, G.H., 1999, “Estimation of large open pit haulage truck requirements,” CIM Bulletin, Vol. 92, No. 102, p. 143-149. Chao, L., 2006, Database Development and Management, Auerbach Publications , Boca Raton, FL. Chen, Z., 2001, Data Mining and Uncertain Reasoning: An Inte grated Approach, Wiley, New York and Chichester England.
Report: Open Pit Mine Planning and Design Workshop held at the annual meeting of AIME 1978, pp. 83-96. Hays, R., 199 0, “Mine operations: Trucks,” Surface Mining , pp. 672-691, Society of Mining Engineers of AIME, SME Littleton, CO. Tang, Z., and MacLennan, J., eds., 2005, Data Mining with SQL Server 2005, Wiley, Indianapolis, IN. Whittle, J., 1990, “Open pit optimization,” Surface Mining, pp. 470-475, SME, Littleton, CO.
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