Short-Term Shovel Sequence Optimisation

Short-Term Shovel Sequence Optimisation — Problem Definition and Initial Solution 1

P F Knights and S Li

2

ABSTRACT Variance in shovel availability, effective utilisation, productivity and short-term extraction sequences affect crusher feed rates and feed quality in metalliferous open pit operations. Shovel availability is a function of planned and unplanned maintenances, repairs and inspections. Effective utilisation is affected by shovel repositioning, face preparation and development work, and shovel productivity exhibits a spatial variance due to bench geometry restrictions and muckpile characteristics. Shovel sequencing influences the ability of a mine to maintain mill feed within consistent hardness and grade targets. At present, the short-term planning engineer is tasked with elaborating the weekly extraction plan. This is a time consuming task, as it involves liaison with multiple stakeholders. The manual way in which such plans are elaborated is no guarantee for optimising mill feed, quality requirements and resource utilisation. In addition, the lead time necessary to prepare the weekly plan invalidates the possibility of rapidly rescheduling when unforseen events occur. This paper outlines research being conducted by CRCMining to address these problems. The problem (or opportunity) is outlined and the results are presented for an initial algorithm to improve shovel extraction sequences.

INTRODUCTION The objective of quarterly short-term plans is to balance developed ore reserves with mill demand in order to satisfy short-term cash flow objectives. Short-term supply of ore is dictated by those reserves that are available and planned for development within the planning period, plus the available equipment, labour and infrastructure resources to mine these reserves. The objectives of the short-term plan are a compatible subset of the medium-term and long-term mine plans. In order to execute the short-term plan, most mines develop weekly plans. These plans deal with the scheduled availability of equipment, planned equipment moves within the mine, development activities, and provide detailed estimates for the grade and tonnage variation of ore and waste streams. In surface mining operations, weekly plans often revolve around shovel movements and availabilities. Production benches are subdivided into selective mining units (SMUs) comprised of mining blocks, or polygons that can be practically mined. The size and geometry of these units are determined by criteria such as material classification (sulfide/oxide ore/waste), and ore quality (product/subproduct and contaminant grades, hardness and metallurgical recovery). These mining units permit selective mining in order to optimise the mine’s economic outcome. Once a production bench has been subdivided into selective mining units, loading equipment are sequenced in such a way as to maintain full capacity utilisation of the primary crusher and supply consistent quality of feed (grade and hardness) to the mill. Shovel and loader sequencing is constrained by: 1.

The University of Queensland and Program Leader – Smart Mining Systems, CRCMining, 2436 Moggill Road, Pinjarra Hills Qld 4069. Email: [email protected]

2.

The University of Queensland and CRCMining, 2436 Moggill Road, Pinjarra Hills Qld 4069. Email: [email protected]

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FIG 1 - Typical production bench showing blast blocks and selective mining units.

• The logical extraction sequence of blocks: exterior SMUs must be removed before interior SMUs can be mined. This is also affected by the position of the entry ramp with respect to the bench perimeter; ramps located at the bench extremes limit extraction sequences to one direction; centrally located ramps permit simultaneous extraction in opposite directions by two or more shovels.

• Development considerations: access to ore reserves depends on the development plan. Safe access and transport routes to and from the bench must be ensured, and transformer stations and cable bridges must be in relocated at times to ensure power supply to shovels.

• Ore feed considerations: the planner attempts to ensure full utilisation of installed crusher capacity. • Ore quality considerations: the planner attempts to supply material of consistent grade and hardness to the mill; harder ore increases mill retention times and reduces mill throughput. Shipping schedules dictate short-term product specifications and ore requirements.

• Availability considerations: shovels and loading equipment will be unavailable for periods of time due to scheduled and breakdown maintenance activities.

• Loader productivity considerations: shovel productivity varies according to muckpile characteristics (fragmentation, shape, swell and looseness), operator proficiency and restrictions due to bench geometry. At present, the short-term planning engineer is tasked with elaborating the weekly extraction plan. This is time consuming, as it involves liaison with multiple stakeholders. The manual way in which such plans are elaborated is no guarantee for optimising mill feed, quality requirements and resource utilisation. In addition, the lead time necessary to prepare the weekly plan invalidates the possibility of rapidly re-scheduling when unforseen events occur such as loader breakdowns or development delays. This problem is recognised by Datamine, a major mine planning software producer, who stated that:

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SHORT-TERM SHOVEL SEQUENCE OPTIMISATION

most existing technology relies on a high level of manual input and does not use optimisation techniques to generate short-term schedules automatically (Chadwick, 2005). As a result of the perceived inadequacies of the manual approach, CRCMining is actively developing algorithms to assist planning engineers to rapidly generate optimal sequences for cable shovels in surface mines.

OBJECTIVE The objective of this work is to develop an algorithm that will determine the optimal weekly schedule for shovels. The algorithm will ensure: 1. consistent ore feed rates to the primary crusher so as to fully utilise installed crusher capacity; and 2. consistent mill feed quality grade: ensuring that ore, by-product and contaminant grades, mineral hardness and metallurgical recovery factors are within acceptable limits.

PREVIOUS RESEARCH Bostwick et al (1993) describe the integration of long- and short-term planning objectives at Barrick Goldstrike mine. The mine planning software, Q-Pit, is used to generate bench plans and to divide the production bench into strips: typically crest, production and trim cuts. These strips are then sized into daily mineable units by considering average shovel productivities. The user then defines a feasible shovel sequence and an interactive spreadsheet enables the grade and tonnage variations of ore flow to be evaluated. No algorithm is included to optimise the sequence; this is left for the planner to perform on a trial and error basis. Lestage et al (1993) describe the development of a short range planning optimiser for the Mont Wright Iron Ore mine in Canada. Their algorithm uses a dynamic programming approach to establish quarterly blasting sequences, shovel displacements and priorities. The algorithm aims to fulfil the quarterly production plan whilst minimising shovel relocations, the cumulative deviation from the required stripping ratio, ensuring minimum production requirements, provided access to new working faces and facilitating grade control. Because the program was developed for a 90 day planning horizon, insufficient resolution is provided for use in weekly planning where parameters such as spatial variance of shovel productivity across a bench must be taken into account. Cai (2005) presented an approach to developing quarterly schedules for an open pit iron ore mine with blending constraints which include: meeting two types of ore targets; smoothing stripping ratios; and satisfying two quality requirements jointly for two types of ore. The scheduling approach was based on an enumeration method mixed with linear programming as coded into the MineSight™ Strategic Planner module. Other commercially available products include MineMax’s iGantt 3.0 software for production scheduling. iGantt is unique in linking Gantt chart activities to 3D mining objects such as blast blocks and development workings. This linkage allows users to visually schedule operations. An auto-scheduling module is included to smooth resource utilisation. However, the software does not consider blending constraints.

PROBLEM DEFINITION Based on the subdivided mining blocks (or polygons), an algorithm for determining weekly shovel production schedules has been formulated. The sequencing algorithm uses a goal programming (GP) technique to model the short-term mine production process with the aims to follow the long-term and

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medium-term production schedule and achieve mill feed with consistent parameters. Consistent ROM quality is important as it permits mill control settings to be optimised to maximise metallurgical recoveries. The goals for shovel sequencing in the short-term mine production schedule are: 1. to minimise the deviation of ore production tonnage from the target defined by mills, and 2. to minimise the deviation of ore grade from the target. However, there are various constraints to keep the shovel sequencing in the production schedule on check including the mining cost, processing cost, shovel productive capacity and block accessibility. The formulation has been tested and validated using a hypothetical ore deposit data. The formulation is run seven times with each run for a single period, ie one day period. After each run the reserves model is updated, and the shovel performance data will also be updated and incorporated into subsequent runs. The final results for each day will be aggregated and show the multi-period production schedule. This enables a ‘rolling horizon’ approach to be implemented for shovel sequencing in the short-term mine production schedule in order to rapidly respond to the uncertainty associated with ore deposit and mining equipments. The test shows that the formulation can fulfil the goals to generate an optimal shovel sequencing for short-term mine production. The formulation of the shovel sequencing for short-term mine production schedule is as follows: 1. Objective function: nq

nq

j =1

j =1

Min DC = p1 ot + + p 2 ot _ + ∑ p 3 j q +j + ∑ p 4 j q _j Subject to: 2. Goals: nb

∑ ot x i

d i

+ ot − − ot + = OT

(d = 1, … , nd)

i =1

nq

nb

∑ ∑ ot x i

d i

( q ij − qg j ) + q −j − q +j = 0

(d = 1, … , nd)

j =1 i =1

3.

Cost constraints: nb

∑ cm x i

d i

≤ MC max

(d = 1, … , nd)

d i

≥ MC min

(d = 1, … , nd)

d i

≤ PC max

(d = 1, … , nd)

d i

≥ PC min

(d = 1, … , nd)

i =1 nb

∑ cm x i

i =1

nb

∑ cp x i

i =1 nb

∑ cp x i

i −1

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4.

Ore tonnage constraints: nb

∑ ot x i

d i

≤ OTmax

(d = 1, … , nd)

d i

≥ OTmin

(d = 1, … , nd)

i =1 nb

∑ ot x i

i =1

5.

Quality (grade) constraints: nq

nb

∑ ∑ ot x

d i

( g ij − gu j ) ≤ 0

(d = 1, … , nd)

d i

( g ij − gl j ) ≥ 0

(d = 1, … , nd)

i

+ wt i ) x id ≤ EC max

(d = 1, … , nd)

i

+ wt i ) x id ≥ EC min

(d = 1, … , nd)

i

j =1 i =1 nq

nb

∑ ∑ ot x i

j =1 i =1

6.

Shovel capacity constraints: nb

∑ ( ot i =1 nb

∑ ( ot i =1

7.

Reserve constraints: nd

∑x

d i

=1

d =1

8.

Other constraints: x id = { 0,1} ot i , wt i , ot + , ot _ , q +j , q _j ≥ 0 ot + × ot _ = 0 q +j × q _j = 0 Where the variables are defined as follows:

+ i − i + i _ i + j _ j

cm cm cp cp q q

Positive deviation of mining cost from the target Negative deviation of mining cost from the target Positive deviation of processing cost from the target Negative deviation of processing cost from the target Positive deviation of quality parameter j from the target Negative deviation of quality parameter j from the target

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ot + ot − ec + ec − P1 P2 P3 P4 x id ot i wt i cm i cp i q ij qg j OT nb nq MC max MC min PC max PC min OTmax OTmin qu j ql j EC max EC min

Positive deviation of ore tonnage from ore tonnage target Negative deviation of ore tonnage from ore tonnage target Positive deviation of shovel tonnage capability from target Negative deviation of shovel tonnage capability from target Penalty of variation from the target Penalty of variation from the target Penalty of variation from the target Penalty of variation from the target A 0/1 binary decision variable, it take value 1 if it is mined from mining block i or polygon i in day d, otherwise it take value 0 Ore tonnage contained in the mining block i Waste tonnage contained in the mining block i Cost for mining block i Cost for processing ore in block i Ore quality content j in block i Target of ore quality content j Target of ore tonnage Number of mining blocks Number of quality parameters Constraint of maximum mining cost Constraint of minimum mining cost Constraint of maximum processing cost Constraint of minimum processing cost Constraint of maximum ore tonnage Constraint of minimum ore tonnage Upper limit constraint of quality j Lower limit constraint of quality j Constraint of maximum shovel tonnage capacity Constraint of minimum shovel tonnage capacity

INITIAL SOLUTION A case study has been conducted using the formulation developed based on a hypothetical ore model. The shovel sequencing in the short-term mine production schedule is a weekly schedule. The results show that the formulation is valid and meets the targets and all the constraints. Those targets include daily ore tonnage target and ore grade target for each day. Those constraints include the mining cost, processing cost, shovel capacity constraints and the shovel accessibility constraints. The above approach is to schedule the shovel sequencing once per period (in our case, one day) and later to aggregate them into a multi-period shovel sequencing schedule. In this way, it will enable to incorporate the updated information into shovel sequencing. In addition, the program runs very fast and saves computational resources.

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Figure 2 shows the weekly shovel sequencing schedule for mining the ore deposit in terms of the mining blocks. The mining blocks mined within one day can be grouped into a polygon and to draw the dig boundary for that day. Note that the mining blocks for one day period are sometimes not connected. This is due to that the formulation has not accounted for the minimisation of equipment movement and relocations. This is an important issue which will be considered in the further development.

FIG 2 - Weekly shovel sequencing for short-term mine production schedule; shovel operation starts from south-west corner.

The ore should be sent to the mill and the mill capacity to treat ore is limited. To keep a constant ore feed is vital to the efficient operation of the mill. Therefore, minimising the deviation of ore tonnage in the production is one of ultimate goals for the short-term mine production scheduling. Figure 3 shows that the formulation can generate a weekly schedule with ore tonnage deviation minimised from its production target of 3900 tonne per day.

FIG 3 - Ore production schedule and its production target.

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In addition, the variation of ore grade may have adverse impact to the mill operation. In the mine production scheduling, the ore grade in production should also be maintained in constant. Hence, the formulation developed considers ore grade as a goal component to minimise the deviation of ore grade from its target. Figure 4 shows that the deviations of ore grade are minimised and close to its target of 4.3.

FIG 4 - Ore grade schedule and its target.

To effectively operate a mine, the ore production and ore grade should be maintained in constant. At the same time, the mining and processing cost should also be maintained within certain limits. Figures 5 and 6 show the variation of the mining and processing costs. They vary within the limits set by mine operators.

FIG 5 - Variation of mining cost.

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FIG 6 - Variation of processing cost.

Also, the shovel productive capacity may affect the economics of a mining operation. The production must efficiently utilise the shovel capacity. The formulation accounts for variations in shovel productivity. This also provides opportunities to incorporate the shovel availability in the short-term production scheduling. Figure 7 shows the variation of shovel capacity used in the weekly schedule.

FIG 7 - The variation of shovel capacity used.

The case study shows that the formulation can fulfil the goals to generate an optimal shovel sequencing for short-term mine production to achieve a constant of ore grade and tonnage. At the same time, the shovel sequencing can keep the mining cost and processing cost within the range of plan, and the shovel capacity within its limit.

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FUTURE RESEARCH In the next stage, the following work will be conducted to enhance the formulation for short-term mine production scheduling:

• incorporate the spatial variance of shovel productivity across production benches into the formulation of production schedule;

• • • •

incorporate variance in shovel availability and utilisation into the formulation of production schedule; eliminate the mining cost constraint due to minor variance observed in this parameter; expand the sequencing model developed to a multiple shovel scenario; and develop a computer toolkit to facilitate the application of technology developed.

CONCLUSIONS A goal programming algorithm for rapidly establishing weekly shovel extraction schedules has been developed and conceptually proven using hypothetical data. Scheduling software based on these principles will to add value to metalliferous surface mining operations by ensuring:

• full capacity utilisation of primary crushers, and • consistent mill feed quality: minimising grade and hardness target deviation. The next phase in development of short-term shovel sequencing algorithm involves demonstration on real data, which requires collaboration with a member company of CRCMining.

ACKNOWLEDGEMENTS The authors would like to acknowledge the supported of CRCMining through the use of core discretionary funds during the 2005/06 business year.

REFERENCES Bostwick, C J and Buchanan, T L, 1993. Computer-aided achievement of mine planning and production goals at Barrick Goldstrike Mines Inc, in Innovative Mine Design for the 21st Century (eds: Bawden and Archibald) pp 303-311 (Balkema: Rotterdam). Cai, W L, 2005. Quarterly schedule development for an open-pit iron ore mine with blending constraints, in Proceedings Application of Computers and Operations Research in the Mineral Industry, Tucson, Arizona, pp 291-296. Chadwick, J, 2005. Softly, smartly, Mining Magazine, Feb, pp 31-34. Lestage, P, Mottola, I, Scherrer, R and Soumis, F, 1993. Integrated short range production planning at the Mont Wright operation, in Innovative Mine Design for the 21st Century (eds: Bawden and Archibald) pp 323- 330 (Balkema: Rotterdam).

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