A twostep approach to incorporate cutoff grade and. Solving a large sip model for production scheduling at a gold. A study of the bienstockzuckerberg algorithm, applications in. T in this paper we discuss some branch and bound methods implemented in the umpire mathematical programming system for solving practical integer pro. Mixedinteger programming techniques for strategic open. Integrated pit, dump and haulage network optimisation for mine scheduling a linear programming approach introduction mine planning and production scheduling are fundamental to realising the value of an in situ asset.
Open pit mine planning with degradation due to stockpiling, computers and operations research, accepted. A mine productionscheduling model and critical path analysis. Production schedule optimisation in underground hard rock. In the stochastic mine planning arena, he has worked on the development of new stochastic models and algorithms to solve these models for optimal open pit production phase design, optimal production scale of mining operations, and cutoff grade optimization for open pit mining operations with multiple processing streams considering geological. Open pit mine production scheduling opmps is a decision problem involving which blocks, within the final pit limits, should be mined in each year, and where the blocks should be sent, e. The openpit mine production scheduling problem has received a great deal of attention in recent years, both in the academic literature, and in the mining industry. Absi and kedadsidhoum 18 presented a mixed integer mathematical formulation for solving the capacitated multi product lotsizing problem when shortage costs and setup times were assumed. However, a deposit usually contains more than one metal and sometimes a contaminant. Mixed integer programming mip models are used for longterm production scheduling of open pit mines. Stockpiling linear and integer programming mine planning open pit mining a b s t r a c t the seeksopen topit determinemine if ever,scheduling to problem when, ex tract each notional, threedimensional block of ore andor waste in a deposit and what to do with each, e. The model incorporates buffer and blending stockpiles, horizontal directional. The objective of this work is to develop, implement, and verify deterministic milp formulations for longterm largescale open pit production scheduling problems. Hooman askarinasab, university of alberta edmonton. Largescale open pit production scheduling using mixed.
In this article we study a wellknown integer programming formulation of the problem that we refer to as cpit. Gold mine problem programming interview question ideserve. Demand vertical and horizontal sequencing between machine placements shaft group newman largescale mining 8 29. Optimization online minimum cost flow problems with value. Based on the model formulation, a progressive timeoriented decomposition heuristic framework is. Classical and stochastic mine planning techniques, state of the art. Mixed integer programming in production planning with bill. Linear models for stockpiling in openpit mine production. However, solving realistic mip production planning problems is nphard. He can move only right, right up, right down that is from a given cell, the miner can move to the cell diagonally up towards the right or right or diagonally down towards the right. A new algorithm for the openpit mine production scheduling. We tackle this by solving the relaxed problem of a tight linear formulation and we round the resulting near. We develop a mixed integer programming model to determine a multitime period.
Applications using aggregation to optimize longterm production planning at an underground mine alexandra m. Solving largescale open pit mining production scheduling. Using aggregation to optimize longterm production planning at an underground mine alexandra m. A mixed integer linear programming algorithm is formulated to find the mining sequence of blocks from a predefined pit shell and their respective destinations. Open pit mine planning with degradation due to stockpiling. We discuss the application of a mip to mediumterm planning based on a 60month production schedule. Longterm room and pillar mine production planning based on.
Pdf a twostep approach to incorporate cutoff grade and. The model is solved by branchandcut algorithm using tomlabcplex optimiser. Practical performance of an open pit mine scheduling model. Mining is the extraction of valuable minerals or other geological materials from the earth, usually from an ore body, lode, vein, seam, reef or placer deposit. Scheduling is typically driven by feasibility and focuses on shortterm time horizon. A mixed integer linear programming model for shortterm open pit. Pdf cutoff grade optimization algorithm with stockpiling. He notes that correctly capturing the contents of the stockpile requires nonlinear constructs, and enhances tractability of the original model by introducing piecewise linear constructs to approximate separable terms after reformulation representing the product of the average grade in the stockpile. Smith 1999 uses mixed integer programming to solve a short term production scheduling problem with blending, considering stockpiles both at the mine and. A mixed integer programming model extended the wagnerwhitin model. The thrust of this thesis is the investigation of a new mixed integer programming formulation for the open pit mining production scheduling problem, which allows for processing decisions to be made at block level, while the ac. Solving mixed integer programming production planning. Production scheduling at lkabs kiruna mine using mixedinteger programming. Combining this with a quick rounding algorithm based on topological sorting, we obtain integer feasible solutions to the more general problem where multiple capacity constraints per.
Using integer programming for strategic underground and. Despite the models remarkable success, lp and milp have not become the preferred method for mine planning due to computational difficulties gershon, 1983. Since the 1960s, it has been known that this problem can be cast as an integer programming model. A linear programming model for longterm mine planning in. The objective of the model is to maximize the net present value, while. What are the various open source minlp mixed integer non.
A mixed integer linear programming model for planning at. Waste rock dumping optimisation using mixed integer programming mip, international journal of mining. Milp is almost identical to linear programming in the. Mixed integer linear programming for oil sands production planning and tailings management, journal of environmental informatics, international society for environmental information sciences, regina, canada, vol 33, 2, pp. Sep 17, 2011 one of the main obstacles in using mixed integer linear programming milp formulations for largescale open pit production scheduling is the size of the problem. Mediumterm production scheduling of the lumwana mining. Solving largescale production scheduling problems in. However, formulations based on binary variables for mining blocks require too many variables and are often difficult or impossible to solve. Mine planning engineers do not have a wide variety of controls that can be. Stochastic minimum cost flow smcf problems have been studied for applications involving random arc capacities or demand uncertainty. Solving mixed integer nonlinear programming problems for mine production planning with stockpiling andreas bley, natashia boland, gary froyland, mark zuckerberg on the relative strength of different generalizations of split cuts sanjeeb dash, oktay gunluk, marco molinaro linear, cone and semidefinite programming. That is, how crushers, loaders and trucks should be used to realise the short term plan.
A new algorithm for the openpit mine production scheduling problem. A mixed integer programming based solution methodology for a scheduling problem in tissue paper. Production scheduling on practical problems 159 this chapter is specifically related to the discrete time and static production scheduling problems. Mine production plan, linear programming, optimum mining program, lingo software. This paper proposes a mixed integer programming formulation for modeling the capacitated multilevel lot sizing problem with both backlogging and linked lot sizes. A method is presented to calculate the cost of uncertainty in a production schedule based on deviations from the target production. Mixed integer programming techniques for strategic openpit mine planning gonzalo munoz polytechnique montreal cosmo mcgill university may 16, 2018. Absi and kedadsidhoum 18 presented a mixed integer. We propose a new decomposition method for solving the linear programming relaxation lp of cpit. In our production plan, we maximize recovered copper metal based on a mixed integer program mip formulation with reserve aggregations that approximate those used in operational mine planning. Comparing miqcp solvers to a specialised algorithm for.
Scheduling with fixed maintenance, shared resources and nonlinear feedrate constraints. In this section we provide mixedinteger quadratically constrained programming miqcp formulations of the open pit mine production scheduling problem with one attribute metal and a single, in. The objective is to provide to the mine feasible goals for quality and quantity production of rom run of mine. Our computations show that we can solve, in minutes, the lp relaxation of realsized mine planning applications with up to five million blocks and 20 time periods. The main objective of this paper is to develop, implement, and verify a mathematical programming framework for the optimal mediumterm openpit mine production scheduling using mixed integer. The objective of the model is to maximize the net present value.
Nov 19, 2010 this textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming mip models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. Strategic mine planning flexible mine planning to meet. Heuristic methods are required to obtain good solutions efficiently. Zuckerberg bz algorithm can be used to solve lp relaxations. However, the large size of some real instances 310 million blocks, 1520 time periods has made these models impractical for use in real planning applications, thus leading to the use of numerous heuristic methods. Shortterm production scheduling in open pit mines usually generates a scheme to. Comparing miqcp solvers to a specialised algorithm for mine. The open pit mine production scheduling opmps problem seeks to determine when, if ever, to extract each notional, threedimensional block of ore andor waste in a deposit and what to do with each, e.
We compare the solvers baron, couenne, sbb, and scip to a problem speci. Linear models for stockpiling in openpit mine production scheduling problems, european journal of operational research, 260. This scheduling model maximizes net present value subject to spatial precedence constraints, and resource capacities. An american gold mine longterm integer programming model determine the start date for each machine placement minimize deviation from preplanned production levels for each ore type in each month observe operational constraints. Good processes in data management and using the data effectively are vital to realising value from technology. A multidestination mixed integer linear programming milp model is. A strengthened formulation and cutting planes for the open. Using aggregation to optimize longterm production planning. Using aggregation to optimize longterm production planning at an. We propose a new decomposition method for solving the linear programming relaxation lp of cpit when there is a single capacity constraint per time period. In this research, a theoretical and conceptual mine planning framework based on mixed integer linear goal programming milgp for oil sands production scheduling and waste management is presented.
Preprocessing specialized linear programming solvers heuristics cuttingplanes. Linear models for stockpiling in openpit mine production scheduling problems. Strategic mine planning is the process where the mine planning process is integrated and aligned with the strategic objectives of the company which involves continuous adjustments to changes in the business environment. This paper presents and tests alternative mip scheduling models that have reduced the number of binary variables and solution times, thus increasing.
Linear models for stockpiling in openpit mine production scheduling. The illustrated method is a simple example of modeling, and it is possible to include stockpiles. Annual production plan of mine based on linear programming. Aprof mohammad waqar asad curtin university, perth. A number of problems in underground mine design that are.
Recent applications of operations research and efficient. A mixed integer programming model formulation for solving the. Based on the model formulation, a progressive timeoriented decomposition heuristic framework is then proposed, where improvement and construction. A mixed integer linear programming model for planning at operative level in a meat packing plant 3 type of carcass. A mixed integer programming based solution methodology. These deposits form a mineralized package that is of economic interest to the miner. Subsequently, a mixed integer linear goal programming milgp model was developed to generate a detailed production schedule for removal of ore, waste and dyke materials from the final pit limit.
The openpit mine production scheduling problem has received a great deal of attention in recent years, both in. Solving mixed integer nonlinear programming problems for mine production planning with stockpiling. A holistic approach to mine planning 6 this study took the concept one step further by incorporating the schedule and landform together in order to make a seamless mine plan including all factors from mine production, truck scheduling, rehabilitation, stockpiling and final landform. According to, the open pit mine production scheduling problem studied in recent years is usually. Integrated pit, dump and haulage network optimisation for. The solution of this problem provides a basis for the strategic future. Mixed integer linear programming formulations for open pit. Stochastic mine planning 1 introduction the problem of production scheduling in open pit mining is determining the parts of. Newman a, mark kuchta b a division of economics and business, colorado school of mines, 1500 illinois street, golden, co 80401, usa. One of the most critical aspects of the production scheduling process is to determine a feasible mining sequence.
This problem in an isolated way could be tackled trough a data analysis, but in practical implementation, its interaction with the demand makes it much more complex to solve. Mixed integer programming in production planning with billofmaterials structures. The use of stockpiling to blend extracted material in these cases has not been treated in previous linear and mixed integer programming models. Similar to the mixed integer programming library miplib, we present a library of publicly available test problem instances for three classical types of open pit mining problems. Initially the miner is in first column but can be at any row i. Minimum cost flow problems with valueatrisk and conditional valueatrisk flow losses under topological uncertainty. Mining projects are complex systems including dynamic digging locations, haul routes and waste dumping locations. A mixed integer programming model formulation for solving. The mixed integer programming model that we solve in the rst. Solving mixed integer nonlinear programming problems for. It is important to achieve both grade targets by blending and maximise the utilisation i. Such production planning with setup decisions can be formulated as a mixed integer programming mip problem. Smith 1999 uses mixed integer programming to solve a shortterm production scheduling problem with blending, considering stockpiles both at the mine and at the mill. Production scheduling at lkabs kiruna mine using mixed.
Mine production management and improvement by numbers amc. It also presents control features for individual operation units, and discusses the technical viability of a mining production realtime optimization mprto system for underground mines, with possible benefits and. Practical solution of large mixed integer programming. This is critical, because a goal lower than possible.
Optimal mine waste rock dump planning and design, paper presented to 21st international symposium on mine planning and equipment selection, new delhi, india, 2830 november 2012. The second reflects the opportunity cost involved when the ore is stockpiled rather than. Mixed integer programming in production planning with billof. Solving largescale open pit mining production scheduling problems by integer programming diplomarbeit bei prof. A mine production scheduling model and critical path analysis of mine development work for longrange mine planning mathias, adrian j. We develop a mixed integer programming model to determine a multitime. Actionable insights from analytics help mine production managers make decisions when controlling and improving their operations. The resulting problem is a nonlinear scheduling problem with maintenance constraints, blending and shared resources. Relaxations and discretizations for the pooling problem. Creating an integer programming solution to the linear programming relaxation with the largest objective function value results in a schedule that cannot be implemented. One of the main obstacles that these authors encountered was solving large integer programming problems. Various industrial software packages facilitate open pit mine planning with. Jan 19, 2018 solving a large sip model for production scheduling at a gold mine with multiple processing streams and uncertain geology. A mixed integer programming based solution methodology for a.
The computational results presented show that generalpurpose. Direct sequencing of blocks in stochastic models with multimines. This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming mip models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. Pdf a new algorithm for the openpit mine production. Major uncertainty affecting optimization is uncertainty in the mineralized materials resource available in the ground which constitutes an uncertain supply for mine production. The problem that is discussed in this paper has a grade con. Production scheduling and mine fleet assignment using integer. This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and related supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming mip models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. Optimization approaches to strategic planning for mine exploitation have. The use of optimization model associated with a simulation model can be used to solve these types of problem merschmann 2002. Abstract the complexity of an open pit production scheduling problem is increased by grade uncertainty.
Lpbased disaggregation approaches to solving the open pit mining production scheduling problem with block processing selectivity. Production scheduling is typically a mixed integer programming mip type problem containing uncertainty in the geologic input data and economic parameters involved. The goal of scheduling is to orchestrate an optimized behavior of a resources. The ultimate pit limit problem determines a set of notional three. Production planning by mixed integer programming springer. Solving a large sip model for production scheduling at a. Lpbased disaggregation approaches to solving the open pit. The pooling problem is a folklore nphard global optimization problem that finds applications in industries such as petrochemical refining, wastewater treatment and. Maximizing the total profit of production and sales over a finite planning horizon was considered as objective while a singleitem has been assumed and backordered was not allowed 17. Each field in this mine contains an integer which is the amount of gold in tons. One of the main obstacles in using mixed integer linear programming milp formulations for largescale open pit production scheduling is the size of the problem.
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