NPV Scheduler Open Pit Planning: From Geological Model to Optimized Strategic Mine Plan
The mine design and production schedule are two elements of mine planning that are inextricably linked. Datamine recognizes this fact and hence NPV Scheduler is unique in the mining industry as the only strategic mine planning system that optimizes both of these elements in the search for maximum NPV. This paper explains the methodology behind the simultaneous optimization of design and schedule and how it results in a mine plan that is practical to extract while achieving the maximum possible NPV.
Dr Bolek Tolwinski Dr Malcolm Newton Andy Lapworth John Morrison The Datamine Group
This white fordocument informational purposes only, and does not constitute any form of performance commitment on behalf of Datamine Corporate Limited, norpaper doesisthis express or imply any warranties.
© Datamine Corporate Limited
EXECUTIVE SUMMARY
An optimal strategic plan for an open pit mine maximizes Net Present Value (NPV) while meeting a wide range of production, production, engineering and economic economic constraints. Since the “time value of money” is is the essence of evaluating NPV, strategic mine planners face an unsolvable “conundrum” : if the right time to mine a block of ore depends on its value, but its value depends on when it is mined – when is the right time to mine it? NPV Scheduler uses a combination of mathematical rigor and operational practicality to resolve this issue and produce a strategic plan where both the mine design and the production schedule are optimized for for maximum NPV. The secret is in the methodology. NPV Scheduler uses geological block models and mining costs, commodity prices and pit slope parameters to create Lerchs-Grossman (LG) nested phases and an Optimal Extraction Sequence that maximizes NPV. NPV. It then forms pushback shapes according to economic value, production targets and engineering constraints, but where traditional scheduling applications confine the pushbacks to the LG phase boundaries, NPV Scheduler takes the phase boundaries as a guide while respecting the need for practical mining shapes. The pushbacks are then scheduled into a period by period production plan by forming “activities” out of mineable groups of blocks and using a powerful optimizing engine to achieve maximum NPV while ensuring a steady flow of ore tonnes at mineable strip ratios. NPV Scheduler then refines the schedule by adding further engineering requirements:
Haulage Analyser / Optimizer specifies the right truck fleet. It tracks the tonnekilometres required to mine the resource and then adjusts the schedule over multiple years to minimize peak truck hours and limit the fluctuation in the truck fleet number.
Mine Flow Optimizer (MFO) increases (MFO) increases NPV by optimizing cut-off grade. It adjusts the schedule to create more value by mining higher grade ore earlier in the schedule if doing that compensates for the cost of wasting or stockpiling lower grade ore.
Material Allocation Optimizer (MAO) (MAO) re-allocates the processing of each block (leach pad, mill, stockpile, waste, etc) to optimize multiple blended products (e.g. iron ore) where production targets and product specifications can be blended from different inputs. inputs .
Multimine Scheduler solves Scheduler solves the problem of optimizing multiple mines simultaneously to meet shared production objectives. Its scalability makes it applicable to scenarios that range from a cluster of pits at the same site up to a regional mining complex.
Geo-Risk Assessment (GRA) manages the uncertainty inherent in interpolating grade distribution by considering conditionally simulated block models in the strategic planning process. GRA generates a range of risk-rated risk-rated pits which can be used as the basis for the
!
!
!
!
!
strategic plan – limiting the impact of grade uncertainty on planning outcomes. These features make NPV Scheduler the market leader in optimized strategic planning.
PREFACE Purpose of this document This paper is an introduction to the basic concepts of modern open pit planning techniques and the mechanisms used in Datamine’ s NPV Scheduler product to generate designs and schedules that provide the highest NPV while being practical to mine and safe to operate.
Prerequisites Readers will require a basic knowledge of the principles of Net Present Value as a mechanism for evaluating project viability, and a familiarity with the theories of Lerchs and Grossman ’ s 1 2 ultimate pit design and Ken Lane’ s cut off grade theory . An understanding of the conditional simulation of grade distribution in a geological model as a mechanism for analyzing uncertainty will also be helpful.
Definitions, Acronyms and Abbreviations Definitions of the terminology in this paper:
design - the physical layout and dimensions of a mine including macro issues such as design the size and shape of pushbacks through to the layout and gradient of ramps.
schedule schedule - the tonnes of material extracted and mineral produced in successive time periods from known locations
!
!
pla planni nning ng - the generic process of both designing and scheduling
!
!
optimal - observing all financial, engineering and production constraints while optimizing an objective; for example, maximizing Net Present Value (NPV)
The following acronyms are used throughout this document: Acronym
Description
NPV LG MAO
Net Present Value Lerchs Grossman Material Allocation Optimizer
MFO GRA OES LoM EFH
Mine FlowAssessment Optimizer Geo-Risk Optimal Extraction Sequence Life of Mine Equivalent Flat Haul
More information More information on NPV Scheduler can be found on www.datamine.co.uk www.datamine.co.uk.. If you have this product installed, you can also view the online Help and tutorials (select Help | Contents). Contents).
1
“Optimum Design of Open Pit Open Pit Mines” – Helmut Lerchs and Ingo F. Grossman. Montreal 1964 reprinted in the January 1965
Grossman, L, 1965. Optimum Design Design Bulletin of the Canadian Institute of Mining and Metallurgy. Full reference Lerchs, H and Grossman, of Open-Pit Mines, Trans. CIM, CIM, 2 “The The Economic Economic Definition of Ore ” by Ken Lane is currently published by Elsevier in its journal ‘Resources Policy’.
CONTENTS 1
Introduction and Background
2
2
The Basic Challenges
3
2.1 2.2
The Link between Mine Design and Production Schedule What to Mine, When to Mine
3 3
2.3 2.4
Determining Pushback Shapes Optimizing the Schedule
3 3
3
4
The NPV Scheduler Methodology
4
3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9
4 5 5 5 6 7 8 9 9
Summary Import the Data Define an Economic Model Create a Set of Nested Pits Create the Ultimate Pit Optimal Extraction Sequence Generate Pushbacks Schedule Optimize Mine Flow Optimize Material Allocation
Geo-Risk Assessment
4.1 4.2 4.3
Summary Economic Variance Derived from all Models Risk Rated k-Pits
11
11 12 12
5
Multimine Scheduler
13
6
Conclusion
14
Appendix A:
Haulage Analysis & Optimization
15
1 INTRODUCTION AND BACKGROUND Strategic Mine Planning is the process of determining the best mine design and production schedule to meet the long term goals for mineral production and financial returns of a mining project. The most common financial criterion used by management to evaluate any such proposed plan is to examine the Net Present Value of the mine over its projected life. There are usually multiple possible mine planning solutions that will provide a positive NPV assessment and so the real objective of strategic mine planning is to determine the optimal mine plan – one that maximizes NPV while meeting all known physical, mining and economic targets and constraints. Strategic mine planning is not an activity that is carried out just the once at the project feasibility stage with the expectation that the strategic plan will be followed rigorously over the life of the mine. In most mines the process process is carried o out ut at least yearly yearly during the budget cycle, and in many cases more often, for a multitude of reasons:
changing economic circumstances (commodity prices, mining costs, etc),
changing market conditions (demand, product mix, mi x, contracted specification, etc),
improved orebody knowledge (better understanding of structure and grade),
senior management enquiries as to the effects of accelerating / slowing production,
the need for corrective action because the previous plan was not followed, and
the next budget needs to include a life-of-mine (LoM) plan that takes all of these circumstances into consideration.
!
!
!
!
!
!
Determining the optimal strategic plan for an open pit operation is not trivial and requires the solution of complex mathematical problems which are bound by constraints such as:
the knowledge of the orebody (e.g. grade distribution, contaminants, structural geology etc) which is generally manifested as geological model,
the economic conditions for mining (e.g. mining and processing costs, start-up capital cost, mid-project capital, commodity value and discount rate),
!
!
!
the engineering requirements for pit slope, dilution, minimum mining width, mill recovery, etc.
The challenge for Datamine in developing NPV Scheduler has been to produce a commercial software package that solves all of these problems within reasonable processing times on an “everyday” laptop laptop computer. NPV Scheduler meets these challenges head on - making it the best strategic mine planning software tool in its class.
NPV Scheduler White Paper
2
August 2007
2 THE BASIC CHALLENGES 2.1
The Link between Mine Design and Production Schedule
Mine planners are often asked to change production targets or processing capacities during life of mine planning. If these changes changes are substantial it may not be possible to produce a practical schedule from the existing design and a completely new approach is required to maximize NPV. In short, “you can’ t schedule your way out of a bad design ” . The challenge is to provide the facility to go “right back to square one” and and start the mine design with a completely different set of parameters that can be used in a new family of planning scenarios.
2.2
What to Mine, When to Mine First Pushback
Last Pushback
Mining a block – first or last?
2.3
In addition to the design and schedule the requirement to maximize NPV burdens the mine planner with another, almost unsolvable, “conundrum” : the right time to mine any one discrete block of ore depends on its value – but its value depends on when it is mined. Take, for example, a waste block at the surface near the pit rim (see diagram) that might be mined early as part of the first pit or later during pre-stripping of the last pushback – perhaps a difference in scheduling of 20 years. The fact that both are possible makes it very difficult to determine the discount for that specific block and hence its value in the project. Early pit optimization methods did not take the “time value of money” into account because they were cash flow. The challenge for based on undiscounted cash modern financial analysis of a mining project, however, is to discount the block values before they are used to calculate the ultimate pit.
Determining Pushback Shapes
The foundations for determining pushback shapes are the set of nested Lerchs-Grossman pits, the optimal extraction sequence generated within the ultimate pit and the production targets for ore required from each pushback. The challenge is to find optimal pushback shapes within those constraints that are guided by the LG phases, but not rigidly rigidly bound by them at the expense a workable design.
2.4
Optimizing the Schedule
The blocks within the pushbacks shapes must be scheduled to meet production targets, specifications and engineering constraints. Each constraint penalizes the theoretical maximum NPV, but the result must still be a practical design that delivers maximum NPV. The number of possible outcomes is massive, so the challenge is to use a rigorous optimizing engine that produces maximum NPV while retaining a practical design approach.
NPV Scheduler White Paper
3
August 2007
3 THE NPV SCHEDULER METHODOLOGY 3.1
Summary
Import Data Data – geological block models, topography, geological surfaces, mining boundaries, slope regions, etc are imported or digitized through the user interface.
Economic Model Model applies product prices, product recoveries, mining costs and processing costs to the block model attributes for the life-of-mine scenario and stores the revenue and costs in the block model.
Ultimate Pit
!
!
!
A set of nested Lerchs-Grossman (LG) pit shells (phases) is created and these form a set of Ultimate Pits Pi ts for varying economic parameters.
The LG pit shells are used to determine the Ultimate Pit Optimal Extraction Sequence (OES) that results in the maximum theoretical NPV.
!
!
Generate Pushbacks Pushbacks uses the Ultimate Pit OES, the LG pits and pushback ore targets to optimize the practical pushback shapes and generate a Pushback OES that allows each block to be assigned its pushback number.
Scheduler uses the Pushback OES, production targets and mining constraints to generate an optimized schedule schedule of mining activities. activities. Each block in the block model is assigned a period number in the resulting Schedule OES. Scheduler can also schedule an externally generated pushback sequence.
Mine Flow Optimizer Optimizer optimizes the cut off grade by rescheduling the blocks to enhance NPV by mining higher grade ore earlier in the schedule if that outweighs the cost of wasting or stockpiling low grade ore for later processing.
Material Allocation Optimizer, especially useful for iron ore and industrial minerals, refines the allocation of ore classified by rock type and quality (grade) to processing methods and/or multiple blended products.
Geo-Risk Assessment manages the uncertainty inherent in interpolating grade distribution by considering conditionally simulated block models in the strategic planning process. GRA generates an ultimate pit for each conditionally-simulated block model and calculates its NPV and profit. From the full set of of ultimate pits GRA generates a range of risk-rated pits which enables mine planners to choose ultimate
!
!
!
!
!
pits their appetite appetite for risk. Pit, In addition, GRA provides MFO) tools to risk according associatedto with any OES (Ultimate Pushbacks, Schedule, in measure terms of standard statistical parameters. parameters.
NPV Scheduler White Paper
4
August 2007
3.2
Import the Data
The basic data for generating a strategic mine plan is a geological block model that contains the geology (lithology, grade, etc) that has been created using any one of the popular geological mining packages, including, of course, Datamine Studio. Other data can be imported or digitized using the NPV Scheduler Digitizer Window, including slope regions, pit limits and (later in the study) pushback adjustments. The system also includes facilities to visualize and plot the data that has been loaded or digitized.
3.3
Define an Economic Model
The economic model is defined by setting cost and price parameters for the life of the mine and then calculating an intrinsic value per processing method of each block as a function of its geo-metallurgical attributes. attributes. The value is usually usually calculated by NPV Scheduler but it can also be imported as an attribute of a block model if it has been calculated in another system. The parameters used to calculate the block value are:
the selling price of price of any commodity recovered from processing where the recovery is defined as a mathematical expression of values in the block,
a unit cost of mining mining (ore and waste) and a unit cost of processing processing (ore) and any adjustment factors which apply,
dilution and dilution and recovery factors factors for the ore,
a unit cost of rehabilitation rehabilitation for for waste, and
an additional cost for proc for process essing ing each each unit of a commodity.
!
!
!
!
!
3.4
Create a Set of Nested Pits
The Lerchs-Grossman (LG) method is used to determine the ultimate pit for given commodity prices and mining cost parameters as well as the engineering constraints of the pit wall slope. By varying the economic parameters in percentage increments, a set of nested LG pits can be generated where each pit represents the ultimate pit of maximum value corresponding to the particular price/cost conditions. In the smallest pit isasthe that per even ton that is possible in thegeneral early stages of mining it one is the pitrepresents that wouldthe stillbest be value valuable under the worst economic conditions. Similarly the largest largest pit represents the pit with the longest life under
NPV Scheduler White Paper
5
August 2007
the best economic conditions. As a consequence, the nested p pits its are therefore in the order order of highest to lowest value per tonne mined. The difference between each pit shell and the next is considered to be a “phase” as as shown in the preceding stylized diagram. Considering that realizing the best value first is a basic principle of maximizing NPV, the order of the phases represents the first high level categorization of the value and the first stage of determining the Optimal Extraction Sequence. Sequence. The LG algorithm requires that each an intrinsic valueand that can bedeposits calculated the values in the economic model. Forblock somehas industrial minerals iron ore theusing final value that can be derived from a block depends on how it is blended with other material, either from within the same pit, another pit, or from an external source. NPV Scheduler has unique functionality that allows the generation of the nested pits to take this into account. The first example of this functionality is that the ultimate pit generation can be modified to include all the material that has been defined as ore in the economic model. Using this option NPV is still optimized, but because the ultimate pit is forced to contain all the ore it will usually be larger than the pit that maximizes cash flow. This option can be used to maximize the resource and is particularly useful when blending material from an external source. NPV Scheduler can also generate the nested pits using an algorithm that is driven by blending requirements as well as block value. Targets can be set to specify the amount of material, or ratios of material to be mined in each period. These targets can vary over time. This means that the physical design of the mine is being appropriately influenced even at this early stage of optimization. Although the advantage of being able to generate these blended pits is clear for deposits such as iron ore, in fact this functionality can also be useful for analysis in precious metals where the ratio of ore to be processed by different methods needs to be maintained.
3.5
Create the Ultimate Pit Optimal Extraction Sequence
Each phase can be thought of as consisting of horizontally “sliced” benches benches where each bench is made up of layers layers of blocks in the geological block model. The Optimal Extraction Extraction Sequence of the model blocks which represents the highest possible NPV is determined by considering each phase in turn and then within each phase considering each bench (a “phase-bench” ) in turn from from the shallowest to the deepest. This is based on the reality that in an open pit mine extraction has to proceed generally from the surface down! To determine the block sequence within a phase-bench the blocks in the phase-bench are sorted in order of value from the highest to the lowest - once again seeking to maximize the NPV by selecting the highest value first. However, the value that is used in th this is sorting process to determine a block’ s relative position in the extraction sequence in the phase-bench is not simply the intrinsic block block value as calculated in the economic model. Using this approach would be simplistic and lead to extraction sequences that, while not random, might be neither practical nor desirable from the mining point of view. Therefore, blocks are assigned a more sophisticated value for sorting known as their “proximity value” and and it is this value that is used for determining a block’ s position in the extraction sequence. In brief, for for each phase-bench phase-bench the block with the highest intrinsic value is first selected for consideration. The remaining blocks are then sorted according to a metric that is a combination of each block’ s intrinsic value and its proximity to the current block. This metric value is referred to as a proximity value. value. As each block is assigned a position in the sequence it i t becomes the current block for consideration. Using this proximity value to determine when a block is extracted can change the order of extraction considerably. A block of relatively low intrinsic value may be pushed up the
NPV Scheduler White Paper
6
August 2007
extraction sequence order because it is physically closer to blocks with a higher intrinsic value. This is intuitively intuitively what mine production personnel personnel do when extracting o ore re while still adhering to the overall strategic strategic plan. One of the positive consequences consequences of this approach is that it tends to create large groups of contiguous blocks for extraction which in turn leads to practical and efficient mining.
NPV Scheduler’ s appreciation of these practical mining factors (while always honouring pit wall slope constraints) creates an extraction sequence which is more realistic than the simple sorting of the blocks into a sequence based on the calculated or intrinsic block value. This process is repeated for each bench in each phase until the ultimate pit is exhausted. The extraction sequence that is created using this method is called the Ultimate Pit OES as it provides the highest theoretical possible NPV for the ultimate pit.
3.6
Generate Pushbacks
Once the Ultimate Pit OES has been established the pushback generation can commence. The basic objective is to create a pushback shape which meets some primary targets, namely the ore tonnage to be won from each pushback as well as its minimum mining width. The other parameters which can be set include mining constraints on the maximum number of pushbacks generated as well as some more general parameters for making the pushbacks practical. These include (i) defining the feas feasible ible size of the “remnants” between between a pushback and the ultimate pit that must be included so that later mining need not return to capture this ore as well as (ii) defining the “smoothness” of of the pit walls to make the shape practical to blast and mine.
NPV Scheduler White Paper
7
August 2007
The diagram above shows the steps by which the pushback generator selects blocks for the pushback, joins them together to form contiguous shapes, takes the remnant blocks into the pushback shape and then joins the two pushbacks so that they form practical mining strategies. For example, PB2i PB2i represents represents a grouped sequence of blocks established by the Optimal Extraction Extraction Sequence. These groupings are expanded to create PB2ii PB2ii by including later sequenced blocks so that a specific ore tonnage condition for the second pushback is achieved. The further addition of blocks to create PB2iii PB2iii successfully successfully joins pushback 2 to the previous pushback and creates smooth edges. NPV Scheduler then creates the pushback shapes by re-sorting the Ultimate Pit OES to get contiguous that pushback. create ak.practical mining shape is then way adjusted to meet the physicalblocks criterof criteria ia ore of the pushbac This approach is a which far superior of designing pushback shapes than traditional methodologies that restrict the pushback to the artificial economic boundary of the LG phase. The sheer practicality of mining may require require boundaries which do not reach or may indeed even cross an LG phase boundary. NPV Scheduler employs a “trial and error” technique technique to find pushbacks that follow the user’ s specifications as as closely as possible. This process has already been “pre-conditioned” for maximum NPV and practical mining by the way in which the Ultimate Pit OES was created using proximity values. The generation of different pushback strategies is therefore quite fast while the remnants and smoothing ensure that the result will produce a pit that has access, size and a practical shape while at the same time meeting the ore tonnage criterion. It should be noted that any one pushback shape that is generated in this process will seldom, if ever, be mined as one unit, where mining only starts in that pushback after the previous pushback has been fully depleted and the entire pushback shape is extracted before another pushback is started. In short, while a pushback is very definitely a physical shape, it is never a shape that occurs at a single point in time during the mine’ s life, because as the ore mined by each pushback lies deeper it must be pre-stripped while previous pushbacks are being mined. The importance of the pushback shapes therefore is that rather than being the physical stages in a mine design they form economic boundaries about which management decisions must be made regarding the mine life. Because of the requirement for pre-stripping pre-stripping in advance of mining it is often necessary to make a decision about whether a pushback should be extracted years in advance of ore being won from it.
3.7
Schedule
The objective of the Scheduler is to find a practical practical schedule for mining the the pushbacks. For the highest NPV it would theoretically be best to mine the pushbacks in sequence, one at a time. Unfortunately, this strategy strategy is rarely practical because because it does not satisfy tar targets gets such as ensuring a steady output of ore at manageable strip ratios, nor does it satisfy other possible requirements like ore blending or contamination control. The scheduler provides much more practical mining strategies by allowing for mining two or more pushbacks at the same time while targeting these other objectives. The scheduler uses the concept of activities activities for for creating a life of mine (LoM) schedule from the Pushback OES. An activity is comprised comprised of a set of contiguous blocks on a bench (or benches) within a pushback. An appropriate optimizing engine is used to order order the activities and hence derive the LoM schedule that maximizes NPV while honouring production targets. This approach builds multiple solutions meeting the targets such as ore tonnes and truck hours, eventually selecting the solution with best NPV and/or most closely tracking the ideal value of a chosen target. See Appendix 1 for more detailed information on using tthe he Haulage Optimizer.
NPV Scheduler White Paper
8
August 2007
The system can target any variables or combinations of variables that are defined by mathematical expressions of attributes of the economic block model. Therefore, the schedule can be set to target target mining rates, truck hours, mill throughput, stripping ratios etc. For each of these variables the user defines an upper and lower limit as well as an ideal target and the system will search for a solution that meets all of the targets if possible, relaxing these constraints if no solution can be found. The result is a long term mine schedule which is strategic with respect to NPV, practical with respect to mining shape and pit slope requirements and achievable with respect to the mining equipment fleet and the ore processing capability – in short an optimal combination of maximum NPV within a practical, workable schedule. The Scheduler also produces a modified Optimal Extraction Sequence so that in addition to each block having a unique sequence position, pushback number and processing destination, each also contains the period number in which it will be mined. It is this Scheduler OES that is used in the Mine Flow and Material Allocation Optimizers.
3.8
Optimize Mine Flow
Mine Flow Optimizer (MFO) is used to determine whether the NPV of the mine plan can be further increased by accelerating the rate of mining in order to extract and process higher grade ore sooner even without upgraded processing capacities. The NPV will increase increase if this higher grade ore is processed processed instead of ore scheduled for processing by the Scheduler. MFO includes in its optimization the consideration of whether the ore being replaced by mining faster should be output stockpiled or treated as waste, and if it is to be updated stockpiled, when itperiods should for be processed. The of MFO is a Mine Flow OES containing schedule extraction. It should be noted that increasing the rate of mining to release higher grade ore sooner effectively increases the ore cut off grade during the periods for which the mining rate is increased. NPV Scheduler’ s method for optimizing the mining rate, or cut off grade has the following advantages over traditional methods of cut off grade optimization:
Because the input into MFO is an OES there is no averaging of grades over a year and there is much greater certainty that the increase in NPV can actually be achieved.
It is common for cut off grade optimization to be calculated using grade tonnage curves or grade classes for sections of the mine as inputs.
!
!
For example a set of grade classes that defines the tonnages of ore within a set of grade ranges may be calculated for each pushback. Cut off grade calculations then determine the amount of material material to be taken from each each pushback each year to maximize maximize value. The problem with this approach is that the physicality of where the material lies within each pushback is lost and value calculations can vary considerably depending on whether ore can actually be mined at the beginning or end of a year. In the worst case the theoretical NPV produced using grade classes cannot be reproduced in a physical mine plan. Both the Scheduler and Mine Flow Optimizer within NPV Scheduler produce precise physical plans and do not suffer from these disadvantages.
3.9
Optimize Material Allocation
For industrial minerals-type deposits such as limestone, clays and also iron ore deposits there is often a requirement to deliver multiple products where a product is produced by blending several rock types in order to meet a set of specific quality targets for a number of different
NPV Scheduler White Paper
9
August 2007
elements. It is also common to use multiple processing methods with which to produce the required products. NPV Scheduler’ s Material Allocation Optimizer (MAO) uses a linear programming implementation to offer a complete solution for this type of optimal allocation problem, allowing the engineer to determine how to best transport, stockpile and treat material to generate all required products. The main features of MAO are:
Inputs to MAO can be mine production, stockpiles, or externally sourced material for blending.
Destinations determined by MAO can be processing methods and / or stockpiles which also serve as inputs for the next period.
Destinations can have any number of quality targets expressed as rates or ratios of elements.
Capacities of destinations can be unlimited (leach pads or waste dumps), limited (stockpiles) or specifically targeted (processing plants).
Global constraints can be set over several rock types, for example to ensure a processing plant has a fixed ratio of rock types as its input.
Destinations can have positive or negative costs. A negative cost is equivalent to a selling price thus allowing any number of complex products that vary over time to be specified.
!
!
!
!
!
!
MAO does not change the sequence of mining - it changes the processing destination of where material is sent and determines a stockpiling strategy to meet different product delivery requirements. The outcome from MAO is an amended optimal destination for each block along with all the other information inherited from the Scheduler’ s OES. MAO is a powerful tool for evaluating whether the mine plan can deliver variable products and can also be used to test the mine plan’ s resilience to changing sales contracts over the life of the mine.
NPV Scheduler White Paper
10
August 2007
ISK ASSESSMENT 4 GEO-R ISK
4.1
Summary
All mine plans are ultimately derived from a mathematical model that describes the geology and in particular the grade - of the deposit to be mined. Geological models should represent the best possible understanding of the real world, but it should also be recognized that they are subject to (often significant) statistical error and, in many cases, this may be a limitation on the ability to plan strategically. For example, gaining an improvement in the NPV of a mine plan of one or two percent is not particularly useful if the confidence in the grade estimates of the resource model is very low. Starting with Version 4, NPV Scheduler has a set of integrated tools for using conditionally simulated models to assess the level of risk of a project that is derived from the inherent uncertainty of the geological model. In order to explain how NPV Scheduler allows this risk to be assessed a few definitions are useful: Conditional Simulation: Simulation: a geostatistical method of modeling mineral deposits that is designed to reproduce the statistical properties and spatial variability of the sample grades. Instead of producing a single average case model, conditional simulation generates a set of equally likely models, each different from the others, but each consistent with the sample data. Simulated grades: grades: grades in any one of the models generated by conditional simulation. Reference grades: grades: block grade estimates used for building standard economic models, pit optimization and scheduling. Usually, reference grades are obtained by other geostatistical methods like kriging, although the average of multiple simulations can also be used. Geological risk : the potential effects of statistical errors in reference grades estimation on the life of mine plans based on the reference grades. The two main concerns are:
The life of mine plan may significantly overestimate the profits and NPV; therefore, the true return on investment may turn out lower than expected.
The mining strategies described by the plan may not be optimal.
!
!
Value models: models: block models with a single field representing block net value for a particular conditional simulation model and given economic settings. To assess the geological risks of a life of mine plan the conditionally simulated models need to be related to economic and technological parameters. parameters. The corresponding value models of the deposit are built and used to infer the probability distributions of vital planning statistics like profits and NPV. NPV. GRA allows this to be done and also offers a risk based based method of selecting the ultimate pit limits.
NPV Scheduler White Paper
11
August 2007
4.2
Economic Variance Derived from all Models
In NPV Scheduler all the various stages of mine planning are represented by optimal extraction sequences. sequences. The sequences are optimal with with respect to the reference grades; however the value models can be used to evaluate profits and NPV for the simulated grades. Suppose there are 50 value models built from 50 equally likely conditionally simulated models. Using the mine plan based on the reference grades, GRA can calculate 50 equally likely profit and NPV values representing their respective probability distributions and the associated parameters like median, mean, standard deviation, range, etc. ” model In short, the basis optimal extractionallsequence derived frommodels, the “best estimate be used as the to schedule simulated geological each resulting in a can unique profitability and NPV. The variance in the NPV over all simulations can can be used as an indication of the risk to the project that is inherent in the grade distribution model. The risk can also be expressed as confidence limits around the mean NPV value.
The probability distribution parameters, and in particular the variance, give a measure of risk. Large deviations relative to the mean indicate that the true profit (NPV) is likely to differ significantly from the predicted (mean) profit (NPV) and therefore signal that the project may be risky.
4.3
Risk Rated k-Pits
NPV Scheduler generates “risk rated pits” by by creating a unique ultimate pit for each of the simulated geological models. Suppose there are N value mo models dels built from N conditionally simulated models. For each value model an LG ultimate pit can be generated giving N pit shells each of which is equally likely to be the “true” profit profit maximizing the optimal final pit shell. There may be blocks blocks in the model that are included in all N shells; others may be included in N-1 shells, N-2 shells, and so on, finally some blocks will not be included in any shell at all. Consider the pit shell (k-Pit) that consists of all blocks included in at least k LG ultimate pits, where k is an integer between 1 and N. Considering that any k-Pit a adheres dheres to the same same slope rules as the LG ultimate pits it can be used as the mine ’ s final pit shell. Like LG pits parameterized by product prices, k-Pits are nested, that is, the k-Pit is wholly contained in the (k-1)-Pit. The difference is that the k-Pits are ranked by geological risk whereas LG phases are ranked by economic economi c risk stemming from price or costs un uncertainties. certainties. The risk rating of a k-Pit can be quantified as s = (100*k/N); the N-pit is rated as 100% safe, carries no risks, and the rating diminishes (the risk grows) grows) for smaller values of k. A risk rated pit with a “k” number number of 90 is the pit outline defined by the blocks which occur in at least 90% of all ultimate pits. Therefore the 85-pit is the pit defined by those blocks which occur in at least 85% of all ultimate pits and so on. Like any other pit, a k-Pit can be evaluated for costs, revenues, NPV, tonnages and grades. A particular k-pit can therefore be used as the ultimate pit from which the nested phases are created that form the basis of the design and schedule of the mine - in essence allowing the mining engineer to generate a mine mine plan aligned to the appetite for risk. Geological risk ratings in conjunction with these standard statistics help to choose the final pit shell that strikes the right balance between risks and opportunities associated with any mining venture. In summary, Geo-Risk Assessment (GRA) manages the uncertainty inherent in grade estimates by considering conditionally simulated block models in the strategic planning process. GRA generates an an ultimate pit for each conditionally-simulated block model and calculates its NPV and profit. These ultimate pits are are used to generate a range of risk-rated risk-rated pits which become the basis for the strategic plan – limiting and measuring the impact of grade uncertainty on planning outcomes.
NPV Scheduler White Paper
12
August 2007
5 MULTIMINE SCHEDULER
Multimine Scheduler Scheduler solves the problem of optimizing multiple mines simultaneously to meet common production objectives or constraints. Examples of common objectives include meeting metal output quotas and blending material from multiple pits to obtain one or more products with particular quality specifications. Common constraints include having a single truck fleet within a cluster of pits and using the same plant to process material from several mines. In the absence of common objectives and targets the best results are obtained by optimizing each mine separately with NPV Scheduler. The approach taken by Multimine Scheduler to manage the problem of multiple mines is to allow for the input of multiple geological block models that define the different mines. They are all then processed in parallel in exactly the same way as in the single mine methodology, without favouring (or disadvantaging) any one pit in the process (unless instructed). One of the major strengths of NPV Scheduler Version 4 is that its optimization process considers the design and schedule of the mine from the outset. This principle is, uniquely, also true when using Multimine Scheduler. Commercial schedulers used for multiple mine planning generally take as an input the pushbacks or pushback benches from each pit. NPV Scheduler however, because its input is the geological models, considers the multiple deposits at the ultimate pit generation phase (as well as all subsequent phases). When creating blended pits each of these input models is considered and since the nested pits are used to determine the pushbacks, the pushbacks themselves are designed to have an appropriate blend for scheduling. At a practical level the system can import geological block models with completely different configurations (cell sizes, bench heights, rock types, etc) as it is often the case that the geology of certain deposits lends it to being modeled differently from other deposits even though both may serve as inputs to a single mine plan and schedule. This enables mine studies for multiple mines to be performed without the potential loss of accuracy and lead times required to regenerate geological models in the same format. The input models can either be closely geographically located or many kilometres apart. Multimine Scheduler’ s scalability allows it to be used in a range of situations from a simple cluster of pits at the same mine site up to a large mine complex that extends over an entire geographical area.
NPV Scheduler White Paper
13
August 2007
6 CONCLUSION NPV Scheduler has been developed over ten years to become the most versatile tool for strategic open pit mine planning on the market. It represents represents ground-breaking thought leadership in the theory of mine planning and geological assessment, it is a careful balance between mathematical optimization and practical mining necessity and it has also been refined as a piece of software to be accessible and usable with the minimum of training. The current release, has many improvements that have been suggested after use in thousands of mine Version planning4,exercises. NPV Scheduler:
Mine design and production schedule considered as two aspects of the same planning problem.
Elegant methodology employed that balances mathematical rigor with mining pragmatism.
Pushback generation that respects the twin goals of mining shape and optimal design.
Practical and appropriate optimization engine used at each stage of the planning.
Haulage fleets analyzed, specified and optimized at a detailed level for all truck types.
Significant blending requirements solved with stockpiling and blending tools.
Cut-off Grade Optimization of multiple rock types with different cut-off grades throughout the mine’ s life.
Multiple mine design and schedule capability with separate geological models and pit designs to meet common production targets or blended product specification targets.
Conditional simulation models used to assess risk due to the uncertainty of grade estimates.
Improved user interface with sophisticated case management tools (copy, modify, etc) to allow multiple cases to be assessed simultaneously.
!
!
!
!
!
!
!
!
!
!
!
Batch processing tools for easier use.
NPV Scheduler is a robust mine optimization system that uses sophisticated mathematics and elegant programming to solve substantial mining problems. It provides a stepwise work progression that can be controlled, reviewed and adjusted by the user to logically build multiple mine strategy scenarios for comparison and evaluation for their financial merit and engineering robustness. As a consequence it is no surprise that NPV Scheduler is now the market leader in open pit mine strategy solutions.
NPV Scheduler White Paper
14
August 2007
Appendix A:
H AULAGE ANALYSIS & OPTIMIZATION
The total required truck hours is an important consideration for any level of mine planning, including for strategic plans. A good strategic plan will minimize the peak requirement for truck hours, which can represent significant capital expenditure; it will delay the peak requirement in order to delay capital expenditure and hence increase NPV; and it will avoid large fluctuations to ensure a consistent truck fleet size is required for periods of several years. Finally the schedule should require that the fleet size is fully utilized in order to meet all required targets. It is sometimes the case that the total truck hours required at the start of mining is higher in order to carry out waste pre-stripping, but this can often be done using contract fleets. The traditional approach to achieving acceptable required truck hours is to create a strategic plan that meets production targets and then as a result of that schedule carry out haulage analysis to assess the total truck hours required for each year. In order to resolve fluctuations in truck requirements or delay early capital expenditure the schedule is rerun with refined targets. This process tends to require several iterations and potentially produces sub optimal plans. At worst plans are produced that are in fact not practical because the fleet size required to mine them is too variable. For an operation that can potentially process material at a multiple number of destinations the process of obtaining a schedule with feasible and acceptable total annual truck hours that also maximizes value is complex. NPV Scheduler is unique in being able to employ a one-step optimization of the mine schedule and haulage plan, combining the "scheduling" and "haulage analysis" functions without the need for iterations. The following section describes the basic methodology NPV Scheduler uses to simultaneously produce a schedule that meets annual targets for truck hours in addition to meeting all other scheduling targets, whilst maximizing NPV. Haulage Optimization Methodology The haulage route from block to destination is broken down into four components as shown in the diagram below:
Where:
p is the distance from load point (shovel) to bench exit point (entry to ramp).
P is the EFH distance from bench exit point, up the ramp to the pit exit point.
F is the EFH distance from the pit exit point to the destination entry point.
D(x) is EFH distance from the destination entry point to the dump point where D is a D(x) is linear function of the total tonnes delivered to the destination (x).
!
!
!
!
NPV Scheduler White Paper
15
August 2007
The bench haul (p) will (p) will vary for every block mined and is dependent upon the position of the mining face and the position at which the ramp intersects the bench. For strategic planning a reasonable approximation, which takes due account of the different pushback geometries, is to at least specify the average equivalent flat haul (EFH) distance for each pushback. NPV Scheduler allows an exit point to be specified for each phase-bench, with a minimum of one exit point per pushback being required. The ramp haul (P) (P) is calculated simply by measuring the elevation difference from the bench to the pit exit point. If we have 10m benches and the truck has to climb 12 benches to exit the pit on a ramp with a gradient of 1:7, then the inclined distance (whatever route is 2
2
taken) is for readily calculated (= ! (120 +an (120 (120*7) ) = way 848)inclined and then converted to have an EFH distance, example at a 1:7 gradient 848m one distance might an EFH of 1520m. So we can calculate ramp haul EFH by simply multiplying the number of benches by a factor. In our example, the Gradient Factor Factor is equal to 127 (EFH = 127*B where B is the number of benches the truck travels up from the shovel to the pit rim). Or expressed another way, the inter-bench EFH distance is 127m. This is a universal constant applied to the entire pit. The surface haul (F), (F), EFH from the pit rim to each destination entry point is constant and supplied by the user. The dump haul (D) may (D) may be zero, as in the case of a fixed crusher, or may be a function of the tonnes already delivered to that destination. A simple linear relation is assumed between distance and tonnes at dump. The user specifies a Dump Haul Factor for Factor for each destination such that the dump haul is calculated by EFH =( Dump Haul Factor)*(ktonnes at dump). For example, a dump with a DHF of 0.08 means that when 10m tonnes has been dumped, the EFH = 0.08*10000000/1000 = 800m. Multiple destinations are defined. Destinations can be restricted to accept specific rock types and processes e.g. a mill crusher may only accept one type of ore and leach pads only accept other types. Where multiple destinations are defined for the same rock-process types, the program will preferentially send the material to the closest destination, and when that has been filled, will divert the material to the next closest destination. Note that the same physical destination can be defined by multiple sequential destinations allowing for changes in the haulage distances over the life of the mine.
NPV Scheduler White Paper
16
August 2007
www.datamine.co.uk
[email protected] [email protected]
NPV Scheduler White Paper
17
August 2007
