Integrated Parametric Graph Closure and Branch-and-Cut Algorithm for Open Pit Mine Scheduling under Uncertainty

Open pit mine production scheduling is a computationally expensive large-scale mixed-integer linear programming problem. This research develops a computationally efficient algorithm to solve open pit production scheduling problems under uncertain geological parameters. The proposed solution approach for production scheduling is a two-stage process. The stochastic production scheduling problem is iteratively solved in the first stage after relaxing resource constraints using a parametric graph closure algorithm. Finally, the branch-and-cut algorithm is applied to respect the resource constraints, which might be violated during the first stage of the algorithm. Six small-scale production scheduling problems from iron and copper mines were used to validate the proposed stochastic production scheduling model. The results demonstrated that the proposed method could significantly improve the computational time with a reasonable optimality gap (the maximum gap is 4%). In addition, the proposed stochastic method is tested using industrial-scale copper data and compared with its deterministic model. The results show that the net present value for the stochastic model improved by 6% compared to the deterministic model

Production scheduling and mine fleet assignment using integer programming

Production Scheduling, extraction sequence of mining blocks in different production periods to maximize profit over the life of the mine and subjected to different constraints, is an important aspect of any mining activity. Mine production scheduling problem can be solved using various approaches, but the best approach is one which can give an optimal result. Production scheduling solely cannot result in a proper planning thus, fleet assignment problem needs to be incorporated into production scheduling problem to have a realistic mine plan. Proper fleet assignment ensures that the fleet is not under or over utilized. Fleet assignment problem is integer type programming since, size of fleet cannot be a floating number. In this thesis, production scheduling and fleet assignment problem are solved using branch and cut algorithm. Production schedule for 4736 blocks from a case study of coal mine is done with a production period of 5 years. Solution time for solving the production scheduling problem was 48.14 hours with an NPV value of Rs 4.45938x1011. Short terms production scheduling is done for one year and the NPV value obtained was Rs 7.59796x1010 with a solution time of 57.539 minutes. Fleet assignment is done for first year and is observed that the size of dumper fleet can be reduced to 30 thus saving huge amount of initial capital investment

Optimization of production planning in underground mining

Use of Integer programming (IP) or mixed integer programming (MIP) for formulation of mine optimization problem is best suited modelling approach for underground mining. Optimization algorithm for underground stope design problems cannot be generalised as geotechnical constraints for each method is different. This project concentrates on optimization model for open stoping mining method. The stope design model maximizes Net cash flow of the stope while adhering to the stope constraints. The methodology considers open stoping sequence, in which every block is moved towards the cross-cuts at the lower level. In this thesis, stopes are designed to maximize the undiscounted cash flow from the stope after satisfying stope height and extraction angle constraints. An integer programming formulation is developed and solved using CPLEX solver for single stope. The proposed algorithm is solved for first stope and then blocks for the crown pillar for first stope is identified. After eliminating the first stope and respective crown pillar data from the data set, algorithm is solved again for the second stope from the remaining data set. After stope design, production scheduling is done by applying heuristic approaches. Blocks from the stopes are extracted heuristically satisfying extracting angle, mining and processing constraints. Initially blocks from the first stope are selected and then to fulfil the constraints, some of the blocks from the second stope are selected. A study is carried out on the part of the Zinc mine data of India which contains 4992 number of blocks. Total 3 numbers of stopes are designed. The NPV of the considered data is found to be 7313.346 million rupees in 3 periods with total tonnage of 1.103 million tonnes. Metal content in 3 periods is found to be 86.485 thousand Tonnes. The overall dilution is found to be 3.82% with average dilution of 2.692

Stratified Deposit Production Schedule Optimisation Considering In-Pit Dumping and Haul Road Selection

In mining operations, selecting a schedule for waste mining and hauling to dump locations including in-pit dumps and ore to plants and stockpiles, through a network of roads, poses a huge combinatorial problem. A mathematical model has been proposed to simultaneously optimise pit and waste dump mining including in-pit dumping, with the selection of shortest haulage from possible haul-road networks. Solution methodologies have been developed using exact and meta-heuristic methods and applied on several cases

Modelo matemático e algoritmo de apoio para auxílio ao sequenciamento e à programação de lavra com alocação de equipamentos de carga

This paper focuses on the sequencing and scheduling problem of open pit mining,\ud with the allocation of loading equipment considering a medium-term horizon.\ud This study considers the existence of a heterogeneous loading equipment fleet and two\ud types of mineable material, namely ore or waste rock. For the mining of ore, the following\ud requirements are taken under consideration: the mixture quality, a crusher, the\ud processing plant capacity and a stockpile, called ROM stockpile. In this context, we\ud present a mathematical model in mixed integer linear programming, supported by an\ud algorithm that is responsible for moving the time horizon at each model run, aiming\ud to generate mining orders resolved with optimality. Together, these orders describe the\ud loading equipment mining plan.Esse trabalho tem seu foco no problema de sequenciamento e programação da\ud lavra em mina a céu aberto com a alocação de equipamentos de carregamento, considerando\ud um período de médio prazo. Nesse estudo, considera-se a existência de uma\ud frota heterogênea de equipamentos de carga e de dois tipos de materiais lavráveis,\ud sendo minério ou estéril. Para a lavra de minério, são contemplados requisitos de\ud qualidade da mistura, um britador, capacidade da usina de beneficiamento e uma pilha\ud de estoque, denominada pilha de ROM. Nesse contexto, apresenta-se um modelo\ud matemático em programação linear inteira mista, apoiado por um algoritmo responsável\ud por mover o horizonte de tempo, a cada execução do modelo, com intuito de\ud gerar ordens de lavra resolvidas com otimalidade. Juntas, essas ordens descreverão o\ud plano de lavra dos equipamentos de carga

Presidential address: Optimization in underground mine planning-developments and opportunities.

Presidential address presented at the The Southern African Institute of Mining and Metallurgy Annual General Meeting on 11 August 2016.The application of mining-specific and generic optimization techniques in the mining industry is deeply rooted in the discipline of operations research (OR). OR has its origins in the British Royal Air Force and Army around the early 1930s. Its development continued during and after World War II. The application of OR techniques to optimization in the mining industry started to emerge in the early 1960s. Since then, optimization techniques have been applied to solve widely different mine planning problems. Mine planning plays an important role in the mine value chain as operations are measured against planned targets in order to evaluate operational performance. An optimized mine plan is expected to be sufficiently robust to ensure that actual outcomes are close or equal to planned targets, provided that variances due to poor performance are minimal. Despite the proliferation of optimization techniques in mine planning, optimization in underground mine planning is less extensively developed and applied than in open pit mine planning. This is due to the fact that optimization in underground mine planning is far more complex than open pit optimization. Optimization in underground mine planning has been executed in four broad areas, namely: development layouts, stope envelopes, production scheduling, and equipment selection and utilization. This paper highlights commonly applied optimization techniques, explores developments and opportunities, and makes a case for integrated three-dimensional (3D) stochastic optimization, in underground mine planning.MvdH201

Optimised decision-making under grade uncertainty in surface mining

Mining schedule optimisation often ignores geological and economic risks in favour of simplistic deterministic methods. In this thesis a scenario optimisation approach is developed which uses MILP optimisation results from multiple conditional simulations of geological data to derive a unique solution. The research also generated an interpretive framework which incorporates the use of the Coefficient of Variation allowing the assessment of various optimisation results in order to find the solution with the most attractive risk-return ratio