Short-term planning of openpit mines with semimobile in-pit crusher

Openpit mines are getting deeper with time, and transportation expenses are rising because of the increasing haulage distance. In-pit crushing and conveying (IPCC) is getting popular in deeper openpit mines as a suitable alternative to truck haulage because it offers a lower operating cost due to shorter haulage distances and less truck requirement. A semimobile in-pit crusher, currently the most popular IPCC system, is relocated every two-tofive years and the short-term plan needs to be updated accordingly. Short-term planning with IPCC is an area of research that has not been explored extensively yet, and hardly any model can generate a short-term extraction sequence considering an IPCC in place. This research work proposes a mixedinteger programming model to generate shortterm production plans within a time horizon of 12 months. The objective of the model is to optimally allocate shovels to minimize cost of material handling and maximize revenue subject to meeting plant requirements, and maximum allowable tonnage variation and IPCC location constraints to achieve production and net present value (NPV) targets set by a strategic plan. The proposed model has been implemented in a hypothetical case study for verification. The comparison of results between scenarios with and without IPCC is expected to justify the use of IPCC in large openpit mines from a short- to medium-term perspective. A semimobile IPCC system with one relocation is considered in the case study. Introduction Mining is a highly capital-intensive operation, and proper production planning is required to keep the overall setup including all the equipment from performing suboptimally. The primary objective of any mining project is to maximize the profit by keeping the cost at a minimum. Optimal use of the equipment used in mining is of vital importance because the truck-shovel operation may account for more than 50 percent of the total operating cost (Moradi Afrapoli and Askari-Nasab, 2017). This optimality can only be realized with efficient utilization of all the assets involved, to achieve the production targets set by the long-term production plans. Therefore, shortterm scheduling by optimal allocation of resources, such as trucks and shovels, is of utmost importance. Mixed-integer programming (MIP) models have been used extensively to generate shortterm schedules of openpit mines. Most of the modern short-term planning models are MIPbased with explicit precedence constraints applied. Smith (1998) was the first to use the precedence constraints in mine planning and scheduling. The model uses an MIP for constructing short-term schedules with explicit accessibility constraints, requiring the nine blocks above a block to be mined before that block can be accessed. Gholamnejad (2008) proposed a binary integer programming model to solve the short-term mine scheduling problem to decide which blocks of ore and waste must be mined in which period (shift, days, weeks or months) by satisfying several operational and geometrical constraints simultaneously. Eivazy and Askari- Nasab (2012) solved a short-term planning MIP model under several different scenarios, in which the direction of mining varies with different mining precedence constraints. The objective is to minimize the overall cost of mining operations including mining, processing, haulage, rehandling and rehabilitation costs. L’Heureux et al. (2013) proposed a detailed mathematical optimization model for shortterm planning, with operational details for a period of up to three months. The objective was to minimize operational costs of trucks’ and shovels’ activity, drilling and blasting. They solved the problem for up to five shovels, 90 periods and 132 faces. Kozan et al. (2013) modeled drilling, blasting and mining of blocks, and allocation of equipment to these activities with an objective of minimizing the make-span (elapsed time between the start and end of a schedule). Later, Kozan and Liu (2016) formulated another shortterm planning model to maximize the throughput and minimize the total idle times of equipment at each stage of drilling, blasting and excavation subject to equipment capacity, speed, read times and activity precedence constraints. The latest contribution of Liu and Kozan (2017) is an innovative mine management system. The proposed methodology integrates a series of mathematical models for ultimate pit limit determination in long-term, medium-term block sequencing over quarterly, half-yearly or yearly time periods, and operational level planning of equipment with a job-shop scheduling model to achieve an overall mining efficiency improvement. Figure 1 Flow of material from pit to crusher and waste dump. Blom et al. (2017) presented a rolling planning horizon-based MIP model to generate multiple short-term production schedules to optimize equipment use and shovel movement constrained by precedence relationships, blending requirements, equipment availabilities and trucking hours considering multiple processing paths. Integration of simulation with MIP is a tool that has been used by some researchers to account for the uncertainty that exists in mining operations such as equipment failure and haulage. Upadhyay and Askari-Nasab (2016) and Upadhyay and Askari-Nasab (2017) integrated simulation with an MIP-based short-term planning model to illustrate how proactive decisions can be made in the dynamic environment of mining, and how operational plans can be synced with long-term planning to reduce opportunity cost and maximize production and equipment utilization. The authors solved the MIP model to optimally allocate shovels to meet production and grade requirement and minimize shovel movement time. Manríquez et al. (2020) proposed a similar simulation optimization framework to increase the adherence of short-term mining schedules to execution for an underground mining operation. The model generates an initial schedule based on a mixed-integer linear programming (MILP) model embedded in UDESS and then simulated in any data encryption standard (DES) software to replicate the schedule and estimate equipment utilization. The short-term planning models discussed so far are all designed to generate schedules assuming a truck-shovel haulage system. While there are studies such as those of Paricheh and Osanloo (2019), Samavati et al. (2020), Shamsi et al. (2022) and Liu and Pourrahimian (2021) that justify the use of in-pit crushing in the long term, to the best of our knowledge there is hardly any research work that does the same at an operational level. Haulage is one of the largest sources of expense in any openpit mine. IPCC has the potential to reduce this cost and in turn maximize profit. Hence, it is crucial to explore the effects of IPCC on short-term planning of openpit mines. Several key decisions regarding IPCC, such as optimum location, relocation time, and conveyor design and length, are made at the strategic level of mine planning. Therefore, shortterm planning needs to investigate the changes in schedules that occur because of housing and moving a crusher inside the pit over time. It is also important to verify if the operational plans can sync with the long-term plan to deliver the desired NPV of mine in presence of IPCC. This research formulates a short-term planning methodology to generate monthly production schedules by optimum shovel allocation. This is a general shovel allocation model that can generate short-term schedules for both truck-shovel haulage and IPCC systems. The model has been used to compare scenarios with IPCC and a traditional truck-shovel haulage system to determine which one provides more cost saving and generates higher revenue from a short-term perspective within one year. Problem definition The goal of this research study is to demonstrate the effects of IPCC installation on short-term planning by generating near-optimal schedules. The proposed model is intended as a tool to compare IPCC and a truck haulage system from the operational perspective of mine planning. The model will generate monthly schedules for a 12-month plan. The idea is to present two scenarios, one with IPCC and the other with traditional truck haulage, and compare the results to find out the overall revenue generated and haulage cost incurred in each of the scenarios. Figure 1 shows the flow of material from pit to destinations for scenarios with or without IPCC. The difference in scheduling or extraction sequence based on shovel allocation will also be highlighted to demonstrate how IPCC installation affects mine plan from an operational viewpoint. The comparison of results should enable mine planners to decide on the better haulage option for a specific year of mine life. Model formulation The proposed MILP model has three operational objectives: Maximize revenue earned by ore material per period.Meet production requirement to feed the mill to its capacity.Minimize haulage cost. Obj function, f = cost of transporting material to crusher or waste dump from mine by trucks + cost of conveying ore material from crusher to processing plant – revenue per period. The distance of each face from the crusher and waste dump will be fed to the model as a road network graph. The objective function will be optimized subject to shovel allocation, grade blending, minimum plant requirement, maximum allowable grade variation and IPCC location constraints to achieve the required production and grade targets set by the strategic plan through accommodating crusher within ultimate pit limit. Optimum allocation of shovels to mining faces will extract required tonnage of material to feed the plant. The case study will be run for two cases: one with an IPCC system with a reduced number of trucks, and the other with a traditional truck-shovel haulage system without IPCC. The comparison of these two scenarios will verify whether the SMIPCC offers cost benefits by meeting long-term production targets within a short-term planning horizon of one to three years. Scope and assumptions of the model. The proposed model provides a tool to generate and compare short-term schedules for openpit mines. The MILP is a general shovel allocation model. It can generate schedules for both truck-shovel haulage and IPCC systems.The model allocates shovels considering both cost minimization and revenue maximization per period unlike the previous models of Upadhyay and Askari-Nasab (2016), Upadhyay and Askari-Nasab (2017) and Manríquez et al. (2020), where a revenue component was not considered.The model can be integrated with haulage simulation models to account for operational uncertainty.The model can be extended to find the optimal number of trucks required in a specific period of mine life. Figure 2 Pit layout with roads and ramps in year 11. Figure 3 Shovel assignment to faces on bench 1610 for scenario 1. Figure 4 Mining period of faces on bench 1610 for scenario 1. The model is based on the following assumptions: The IPCC system is semimobile. The optimum locations and relocation time of the crusher are known throughout the life of mine from strategic planning. The ore and waste faces are known from a long-term plan. Hence, ore material will go to mill or crusher, and waste material will go to a waste dump. Ore shovels are locked to ore faces and waste shovels are locked to waste faces. There is no stockpiling. The model does not consider ore blending in its current state. The model does not consider multiple processing destinations. Production loss due to shovel movement time is not considered. Production loss due to equipment failure and maintenance is not considered. The model is strictly deterministic. The mill requirement is constant throughout the planning horizon. Case study The case study presents two scenarios in an iron mine with IPCC and traditional truck-shovel mining method to verify the model. The shortterm schedule will be generated for the 11th year of mine life. Two benches at elevations 1,595 m and 1,610 m (5,232 ft and 5,282 ft) are available to be mined with a total 16 Mt (16.6 million st) of ore and 16.5 Mt (18.2 million st) of waste. There is only one mill to process material. The in-pit or plant crusher requirement is 2.5 kt/h (2,700 stph). Assuming 16 hours of operation in a day with two eight-hour shifts, the monthly crusher requirement is 1.33 Mt (1.46 million st). The mine layout is shown in Fig. 2 for year 11. The distances from each face to the waste dump, crusher and plant are calculated using the nodes in the road network. The grade of the designed ramps is 8 percent. The length of the conveyor belt for the IPCC scenario is 2,550 m (8,366 ft), which comes from the strategic plan. The element of interest in the mine is magnetic weight recovery of iron (MWT). A hierarchical clustering algorithm has been used (Tabesh and Askari Nasab, 2013) to aggregate similar blocks together to generate 78 mining faces (polygons) out of 1,900 blocks to be mined in year 11 within two benches. The mine employs a total of four shovels including two Hit 2500 shovels (shovel index 3 and 4) specifically for ore and two Hit 5500Ex shovels (shovel index 1 and 2) for waste mining. The Hit 2500 shovels have a bucket capacity of approximately 10.8 t (12 st) and a bucket cycle time of about 22 seconds; whereas the Hit 5500Ex shovels have a bucket capacity of approximately 20 t (22 st) and a bucket cycle time of about 23 seconds. To haul the material from the faces, the mine employs Cat 785C and Cat 793C trucks with nominal capacities of 127 t (140 st) and 217 t (240 st), respectively. Cat 785C trucks are locked to ore shovels and thus they may be loaded only by Hit 2500 shovels, and Cat 793C trucks can only be loaded by Hit 5500Ex shovels. The truck requirements for both scenarios are calculated and compared based on the truck cycle time, shovel capacity and production requirement. Figure 5 Shovel assignment to faces on bench 1595 for scenario 1. Figure 6 Mining period of faces on bench 1595 for scenario 1. Figure 7 Monthly ore and waste production for scenario 1. Results The MIP model is solved for two scenarios: one with semimobile IPCC and one with truckshovel only. The model runs for 12 months in four steps where it allocates shovels to faces for three months, saves the results and then looks for available faces for the coming three months. The problem has 3,696 variables to be solved for. The model is formulated and solved in MATLAB 2021(B). The solution time for both scenarios is less than 200 seconds with an optimality gap of less than 0.5 percent. Scenario 1 (No IPCC). This scenario represents a traditional truck-shovel (TS) mining operation where the mined material is hauled to the plant crusher and waste dump by trucks. Pragmatic and near-optimal shovel assignment to the faces is the primary goal of the model. Shovel positions and the working periods are summarized to analyze the allocation decisions made by the model. The model does not take shovel movement time into account. A shovel availability of 80 percent is assumed to account for the lost time for movement among faces and maintenance. The optimal objective function value for this scenario is $2,138 million. Figures 3 and 4 show the shovel assignments and corresponding mining periods for bench 1610 and Figs. 5 and 6 display the same for bench 1595. The model assigns shovels to bench 1610 from period 1 and mining starts at bench 1595 from period 2 because of the vertical precedences that exist between the two benches. Generally, the waste faces are mined in the earlier periods than ore faces for both benches because the waste faces precede the ore faces in many of the cases. The shovels do not look for the nearest faces for next assignment after a face is mined out because the model does not consider shovel movement costs. The allocations demonstrate that the model is capable of assigning shovels to faces respecting the precedence relationships and the production requirements. All the faces are mined within the 12-month optimization time frame, making sure that the production requirement of the strategic plan is satisfied. Figure 7 shows that the production of ore is steady and enough to feed the mill to its capacity. The waste production is also uniform with some minor variations in the last three periods. Figure 8 Shovel allocation on bench 1610 for scenario 2. Figure 9 Mining period of faces on bench 1610 for scenario 2. Figure 10 Shovel assignment to faces on bench 1595 for scenario 2. Figure 11 Mining period of faces on bench 1595 for scenario 2. Figure 12 Monthly ore and waste production for scenario 2. Scenario 2 (IPCC). This scenario assumes an in-pit crusher for ore crushing. The trucks haul the mined material to the crusher. The crushed material is conveyed to the processing plant by a 2.5 km- (1.5 mile)-long conveyor belt. The location of the crusher is face 3 for the first six months and face 18 for the rest of the periods. The constraint for IPCC prevents mining of the face that houses the crusher. The optimal objective value is $2,152 million. Figures 8 and 9 and Figs. 10 and 11 display the shovel assignment and corresponding mining periods for benches 1610 and 1595, respectively. The faces of bench 1595 starts from period 2 while mining in bench 1610 starts from the first period. The waste faces are generally mined in earlier months compared to ore faces. This proves that the shovel assignments are made respecting the precedence relations. The crusher was located on face 3 of bench 1595 from period 1 to period 6, and it has been mined on period 12. Face 18 has been left unmined as the crusher has been located here from period 6 onward. This face has to be mined when the crusher is relocated in a next period. The assignment of shovels to the faces where the IPCC is located shows that the model can generate optimal short-term schedules with IPCC. Figure 12 shows the production of ore and waste for this scenario. The ore production is low in the last period because of unavailability of ore faces. The production of ore and waste otherwise is steady and meets the crusher requirements for the rest of the periods. Figure 13 Ore truck requirement for scenarios without IPCC and with IPCC. Figure 14 Comparison of ore haulage cost per period between scenarios. Figure 15 Truck operating cost versus haulage cost. Table 1 Ore haulage cost summary between scenarios. Discussion The following are the outcomes of the model by comparing the two scenarios with and without IPCC. Number of required trucks is 35 percent lower in scenario 2 than in scenario 1. The total ore haulage cost is 43 percent lower in the scenario with IPCC (scenario 2) than the scenario with truck haulage (scenario 1). The average ore haulage cost per period is $7 million and $3.8 million for scenarios 1 and 2, respectively. The impact of increasing truck operating cost is lower on the ore haulage cost in scenario 2 than in scenario 1. The objective function value is $14 million higher for scenario 2 with IPCC than scenario 1. Conclusion and future work The proposed shovel allocation model shows an approach to selecting a better haulage option for mines and a unique approach toward shortterm planning with IPCC. The results show that the scenario with IPCC, scenario 2, generates Figure 13 Ore truck requirement for scenarios without IPCC and with IPCC. 0.66 percent higher objective function value, which is the difference between revenue and haulage cost, compared to the scenario with no IPCC, scenario 1. The truck requirement and ore haulage cost in scenario 2 is also 35 percent and 43 percent lower, respectively, than scenario 1. Since both scenarios have been able to meet the long-term production target for year 11, introduction of IPCC in year 11 is justified in the mine in terms of haulage cost saving and revenue generation. While the model performs well in the case study shown, the model has the following discrepancies: The model allocates shovels without considering ore blending requirements.The model does not consider shovel movement cost and constraint shovel movements between benches. This is the reason why in several periods, shovels move to a new face in a different bench after mining a face. This is acceptable in this scenario with two consecutive benches, but for cases with more than two nonconsecutive benches, this issue needs to be addressed.The model does not consider the capital investment required for IPCC installation.The model cannot consider any operational uncertainty in its current state. Constraining the model by blending requirements and shovel movement between benches to minimize shovel movement costs will generate more realistic shovel allocations. Combining the model with a haulage simulation model will enable it to capture uncertainties associated with haulage operations. These modifications in the future will make the model more pragmatic, and provide a more comprehensive tool for short-term production planning and analysis purposes. Figure 16 Comparison of (revenue – cost) between scenarios. References Blom, Michelle, Adrian R. Pearce, and Peter J. Stuckey, 2017, Short-term scheduling of an open-pit mine with multiple objectives. Engineering Optimization 49(5):777-795. Eivazy, H., and H. Askari-Nasab, 2012, A mixed integer linear programming model for short-term open pit mine production scheduling. Transactions of the Institutions of Mining and Metallurgy, Section A: Mining Technology 121(2):97-108. Gholamnejad, Javad, 2008, A zero-one integer programming model for open pit mining sequences. Journal-South African Institute of Mining and Metallurgy 108:759-762. Kozan, E., and S. Q. Liu, 2016, A new open-pit multistage mine production timetabling model for drilling, blasting and excavating operations. Mining Technology 125(1):47-53. Kozan, E., S. Liu, and R. Wolff, 2013, A short-term production scheduling methodology for open-pit mines, 2013. L’Heureux, G., M. Gamache, and F. Soumis, 2013, Mixed integer programming model for short term planning in open-pit mines. Transactions of the Institutions of Mining and Metallurgy, Section A: Mining Technology 122(2):101-109. Liu, Dingbang, and Yashar Pourrahimian, 2021, A Framework for Open-Pit Mine Production Scheduling under Semi-Mobile In-Pit Crushing and Conveying Systems with the High-Angle Conveyor. Mining 1(1):59-79. Liu, Shi-Qiang, and Erhan Kozan, 2017, Integration of mathematical models for ore mining industry. International Journal of Systems Science: Operations & Logistics 6:1-14. Manríquez, Fabián, Javier Pérez, and Nelson Morales, 2020, A simulation–optimization framework for short-term underground mine production scheduling. Optimization and Engineering 21(3):939-971. Moradi Afrapoli, A., and H. Askari-Nasab, 2017, Mining fleet management systems: a review of models and algorithms. International Journal of Mining, Reclamation and Environment:1- 19. Paricheh, Morteza, and Morteza Osanloo, 2019, Concurrent open-pit mine production and in-pit crushing–conveying system planning. Engineering Optimization:1-16. Samavati, Mehran, et al., 2020, Production planning and scheduling in mining scenarios under IPCC mining systems. Computers & Operations Research 115:104714. Shamsi, Mohammad, Yashar Pourrahimian, and Mehdi Rahmanpour, 2022, Optimisation of open-pit mine production scheduling considering optimum transportation system between truck haulage and semi-mobile in-pit crushing and conveying. International Journal of Mining, Reclamation and Environment 36(2):142-158. Smith, M. L., 1998, Optimizing short-term production schedules in surface mining: Integrating mine modeling software with AMPL/CPLEX. International Journal of Surface Mining, Reclamation and Environment 12(4):149-155. Tabesh, Mohammad, and Hooman Askari Nasab, 2013, Automatic Creation of Ore-Selection and Blast Polygons using Clustering Algorithms. Upadhyay, S. P., and H. Askari-Nasab, 2016, Truck-shovel allocation optimisation: A goal programming approach. Transactions of the Institutions of Mining and Metallurgy, Section A: Mining Technology 125(2):82-92. Upadhyay, S. P., and H. Askari-Nasab, 2017, Dynamic shovel allocation approach to short-term production planning in open-pit mines. International Journal of Mining, Reclamation and Environment:1-20.

Short-term planning of openpit mines with semimobile in-pit crusher

Authored by:
H. Askari-Nasab, E. Ben-Awuah, N. Al Habib

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