Incorporating geo-metallurgical information into mine production scheduling

Economic characterization of mining parcels depends upon geo-metallurgical properties, which vary throughout orebody. Mine production scheduling should aim to obtain maximum utility from orebody in such a way as to ensure mine–mill reconciliation. As heterogeneity of geo-metallurgical variables increases, the scheduling will be a very complicated task. Geo-metallurgical and financial data used in the mine production scheduling are based on simulation and/or estimation generated from sparse drilling and unknown future events. Therefore, the scheduling process involves a significant degree of uncertainty. In order to deal with the uncertainty stemmed from geo-metallurgical and financial variables, two approaches are recommended in this paper. Firstly, mine production scheduling is formulated as a problem of stochastic programming with recourse. The extraction periods of mining blocks are treated as the first-stage variables and the block destinations represents a recourse vector. It is observed that the solution is implicitly robust. Secondly, the scheduling is expressed as a maximin problem to extract more uniform metal quantity in periods to coincide with mill requirements instead of maximization of net present value because the blending constraint in the traditional approach forces more uniform production. In the case where there is correlation between grade and geo-metallurgical variables, this model generates reasonably good results.     

A new MIP model for mine equipment scheduling by minimizing maintenance cost

Mining investment has been recognized as capital intensive due mainly to the cost of large equipment. Equipment capital costs for a given operation are usually within the order of hundreds of million dollars but may reach to billion dollars for large companies operating multiple mines. Such large investments require the optimum usage of equipment in a manner that the operating costs are minimized and the utilization of equipment is maximized through optimal scheduling. This optimum usage is required to ensure that the business remains sustainable and financially stable. Most mining operations utilize trucks to haul the mined material. Maintenance is one of the major operating cost items for these fleets as it can reach approximately one hundred million dollars yearly. There is no method or application in the literature that optimizes the utilization for truck fleet over the life of mine. A new approach based on mixed integer programming (MIP) techniques is used for annually scheduling a fixed fleet of mining trucks in a given operation, over a multi-year time horizon to minimize maintenance cost. The model uses the truck age (total hours of usage), maintenance cost and required operating hours to achieve annual production targets to produce an optimum truck schedule. While this paper focuses on scheduling trucks for mining operation, concept can be used in most businesses using equipment with significant maintenance costs. A case study for a large scale gold mine showed an annual discounted (10% rate) maintenance cost saving of over $2M and more than 16% ($21M) of overall maintenance cost reduction over 10 years of mine life, compared with the spreadsheet based approach used currently at the operation.     

Optimization-based heuristics for underground mine scheduling

Underground mine production scheduling possesses mathematical structure similar to and yields many of the same challenges as general scheduling problems. That is, binary variables represent the time at which various activities are scheduled. Typical objectives seek to minimize costs or some measure of production time, or to maximize net present value; two principal types of constraints exist: (i) resource constraints and (ii) precedence constraints. In our setting, we maximize “discounted metal production” for the remaining life of an underground lead and zinc mine that uses three different underground methods to extract the ore. Resource constraints limit the grade, tonnage, and backfill paste (used for structural stability) in each time period, while precedence constraints enforce the sequence in which extraction (and backfill) is performed in accordance with the underground mining methods used. We tailor exact and heuristic approaches to reduce model size, and develop an optimization-based decomposition heuristic; both of these methods transform a computationally intractable problem to one for which we obtain solutions in seconds, or, at most, hours for problem instances based on data sets from the Lisheen mine near Thurles, Ireland.     

可拓数据挖掘研究进展

可拓学研究用形式化模型解决矛盾问题的理论与方法,可拓数据挖掘是可拓学和数据挖掘结合的产物,它探讨利用可拓学方法和数据挖掘技术,去挖掘数据库中与可拓变换有关的知识,包括可拓分类知识、传导知识等可拓知识.随着经济全球化的推进,环境的多变促使了信息和知识的更新周期缩短,创新和解决矛盾问题越来越成为各行各业的重要工作.因此,如何挖掘可拓知识就成为数据挖掘研究的重要任务.研究表明,可拓数据挖掘将具有广阔的应用前景.将介绍可拓数据挖掘的集合论基础、基本知识和目前研究的主要内容,并提出今后需要进一步探讨的问题及其发展前景.     

MineLib: a library of open pit mining problems

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: the ultimate pit limit problem and two variants of open pit production scheduling problems. The ultimate pit limit problem determines a set of notional three-dimensional blocks containing ore and/or waste material to extract to maximize value subject to geospatial precedence constraints. Open pit production scheduling problems seek to determine when, if ever, a block is extracted from an open pit mine. A typical objective is to maximize the net present value of the extracted ore; constraints include precedence and upper bounds on operational resource usage. Extensions of this problem can include (i) lower bounds on operational resource usage, (ii) the determination of whether a block is sent to a waste dump, i.e., discarded, or to a processing plant, i.e., to a facility that derives salable mineral from the block, (iii) average grade constraints at the processing plant, and (iv) inventories of extracted but unprocessed material. Although open pit mining problems have appeared in academic literature dating back to the 1960s, no standard representations exist, and there are no commonly available corresponding data sets. We describe some representative open pit mining problems, briefly mention related literature, and provide a library consisting of mathematical models and sets of instances, available on the Internet. We conclude with directions for use of this newly established mining library. The library serves not only as a suggestion of standard expressions of and available data for open pit mining problems, but also as encouragement for the development of increasingly sophisticated algorithms.     

金属矿山企业生产计划优化方法

针对金属矿山企业的单位开采与运输成本大、优化求解结果偏差大问题, 首先, 依据金属矿山企业编制开采计划的基本原则, 以矿石开采与运输成本最小化为优化目标, 利用整数规划方法, 构建了金属矿山企业生产计划数学模型, 其次, 为了精准快速求解金属矿山企业生产计划模型, 提出了改进的量子粒子群优化算法, 采用进化速度和聚集度因子对算法中的惯性权重进行动态调整, 并设计了双层可行域搜索策略, 提高了算法的局部和全局搜索能力。最后, 以某大型金属矿山企业采运生产作业为案例, 通过与矿山实际生产指标、非线性规划结果以及粒子群优化结果进行比较分析。结果表明:在相同经济指标和参数环境下, 本文算法优于其它两种优化方法, 且每吨矿石的开采和运输成本减少了0.05元左右, 降低了金属矿山企业的开采运输成本, 提高了企业的整体经济效益。     

Algorithms for railway crew management

Crew management is concerned with building the work schedules of crews needed to cover a planned timetable. This is a well-known problem in Operations Research and has been historically associated with airlines and mass-transit companies. More recently, railway applications have also come on the scene, especially in Europe. In practice, the overall crew management problem is decomposed into two subproblems, called crew scheduling and crew rostering. In this paper, we give an outline of different ways of modeling the two subproblems and possible solution methods. Two main solution approaches are illustrated for real-world applications. In particular we discuss in some detail the solution techniques currently adopted at the Italian railway company, Ferrovie dello Stato SpA, for solving crew scheduling and rostering problems.     

Mathematical programming applied to cement-plant and quarry operations

A large linear-programming model is developed that describes cement operations from the quarry to the market. Separate optimization of clinker composition and quarry scheduling leads to inconsistencies, thereby creating a need for simultaneous optimization. By including both problems and their interfaces in the mode, simultaneous optimization is accomplished. Other factors included in the model are equipment acquisition and assignment, hauling distances and capacities, plant capacities, market prices and demands, and operational costs. Optimization objectives are maximization of net present value, life of mine, or production. Time periods are organized so that long-range profits guide short-range scheduling. Computer implementation of the model is also discussed.     

Survey on fuzzy shop scheduling

The real life scheduling problems often have several uncertainties. The solutions of these problems can provide deeper insights to the decision maker than those of deterministic problems. Fuzzy set theory as most important tool to model uncertainty represents an attractive tool to aid research in the production management. Since to the best of our knowledge, there is not a comprehensive review on the fuzzy scheduling literature, the goal of this paper is to provide an extensive review for the fuzzy machine scheduling which it covers more than 140 papers. For this purpose, first, this paper classifies and reviews the literature according to shop environments, including single machine, parallel machines, flowshop, job shop and open shop. Then the reviewed literature is quantified and measured. At the end the paper concludes by presenting some problems receiving less attention than the others and proposing some research opportunities in the field.     

A genetic algorithm for flow shop scheduling problems

Many scheduling problems are NP-hard problems. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we develop a genetic algorithm-based heuristic for the flow shop scheduling problem with makespan as the criterion. The performance of the algorithm is compared with the established NEH algorithm. Computational experience indicates that genetic algorithms can be good techniques for flowshop scheduling problems.     

Airport runway scheduling

Airport runway optimization is an ongoing challenge for air traffic controllers. Since demand for air-transportation is predicted to increase, there is a need to realize additional take-off and landing slots through better runway scheduling. In this paper, we review the techniques and tools of operational research and management science that are used for scheduling aircraft landings and take-offs. The main solution techniques include dynamic programming, branch and bound, heuristics and meta-heuristics.     

Airport runway scheduling

Airport runway optimization is an ongoing challenge for air traffic controllers. Since demand for air-transportation is predicted to increase, there is a need to realize additional take-off and landing slots through better runway scheduling. In this paper, we review the techniques and tools of operational research and management science that are used for scheduling aircraft landings and take-offs. The main solution techniques include dynamic programming, branch and bound, heuristics and meta-heuristics.     

Integrated production and material handling scheduling using mathematical programming and constraint programming

In this article, we propose an integrated formulation of the combined production and material handling scheduling problems. Traditionally, scheduling problems consider the production machines as the only constraining resource. This is however no longer true as material handling vehicles are becoming more and more valuable resources requiring important investments. Their operations should be optimized and above all synchronized with machine operations. In the problem addressed in this paper, a job shop context is considered. Machines and vehicles are both considered as constraining resources. The integrated scheduling problem is formulated as a mathematical programming model and as a constraint programming model which are compared for optimally solving a series of test problems. A commercial software (ILOG OPLStudio) was used for modeling and testing both models.     

A review of planning and scheduling systems and methods for integrated steel production

Iron and steel industry is an essential and sizable sector for industrialized economies. Since it is capital and energy extensive, companies have been putting consistent emphasis on technology advances in the production process to increase productivity and to save energy. The modern integrated process of steelmaking, continuous casting and hot rolling (SM–CC–HR) directly connects the steelmaking furnace, the continuous caster and the hot rolling mill with hot metal flow and makes a synchronized production. Such a process has many advantages over the traditional cold charge process. However, it also brings new challenges for production planning and scheduling. In this paper we first give a comparative analysis of the production processes and production management problems for the SM–CC–HR and the traditional cold charge process. We then review planning and scheduling systems developed and methods used for SM–CC–HR production. Finally some key issues for further research in this field are discussed.     

Robust Planning for an Open-Pit Mining Problem under Ore-Grade Uncertainty

Open-pit mining production planning is a risky problem: operation costs are considerable, many parameters are inherently subject to uncertainty and, moreover, the mining operation can only be done once. In this work we address uncertainty in the ore-grade, where we only assume the availability of an i.i.d. sample of the joint distribution of ore-grade in the blocks of the mining site. We consider an open-pit mining problem involving extraction and processing decisions under capacity constraints. We apply and compare the risk-hedging performance of three approaches for optimization under uncertainty: Value-at-Risk, Conditional Value-at-Risk and a proposed robust optimization approach. The latter is shown to have desirable risk-averse properties. Computational results on one small size vein-type mine are shown.     

Scheduling coordination problems in supply chain planning

Scheduling algorithms and their role in supply chain planning are topics that have been discussed in scheduling literature for many years. Based on examples and experience with commercial supply chain planning software, this paper presents background information about production planning and scheduling functionality in commercial supply chain planning software and interesting scheduling coordination problems in supply chain planning for researchers. We first provide an overview of different planning activities in supply chain planning, while taking into consideration existing functionalities that are available in commercial supply chain planning software. As a second step, we show three scheduling coordination problems in supply chain planning, namely the integration of production planning and production scheduling, the integration of sales order confirmation and production scheduling and the integration of VMI planning and production scheduling. We conclude this paper with a detailed discussion of an implementation of a supply chain planning solution at the tissue producer SCA Hygiene in Sweden. This paper expresses the authors opinion and does not represent an official statement from SAP.     

Decomposition approaches in permutation scheduling problems with application to the M-machine flow shop scheduling problems

In this article, we consider three decomposition techniques for permutation scheduling problems. We introduce a general iterative decomposition algorithm for permutation scheduling problems and apply it to the permutation flow shop scheduling problem. We also develop bounds needed for this iterative decomposition approach and compare its computational requirements to that of the traditional branch and bound algorithms. Two heuristic algorithms based on the iterative decomposition approach are also developed. extensive numerical study indicates that the heuristic algorithms are practical alternatives to very costly exact algorithms for large flow shop scheduling problems.     

Games,Critical Paths and Assignment Problems in Permutation Flow Shops and Cyclic Scheduling Flow Line Environments

In this paper we address the non-pre-emptive flow shop scheduling problem for makespan minimization in a new modelling framework. A lower bound generation scheme is developed by using appropriately defined linear assignment problems and, based on this new approach, a special class of permutation flow shop problems is identified. We present a game theoretic interpretation of our modelling approach which leads to an integer programming formulation of the scheduling problem. A new branch and bound scheme is developed based on these results. The major advantage of our modelling framework and branch-and- bound approach is that it can be easily extended to address a general class of cyclic scheduling problems for production flow lines with blocking. After a discussion of this extension, we report on computational experience that indicates the very satisfactory performance of the new optimal solution procedure for cyclic scheduling problems with finite capacity buffers.     

Lagrangian heuristics for instructor scheduling in executive development programmes

In this paper we present the problem of scheduling instructors in a university management development programme. Problems of similar structure arise in a number of scheduling applications like assigning officials to athletic competitions, inspectors to sites and maintenance crews to jobs. The problem is formulated as a zero-one linear integer programme but is difficult to solve in real life situations because of problem size. The bounds on total assignments for different nested time periods give sub-problems that can be solved as network flow problems. Four Lagrangian relaxation heuristics are developed using different relaxations of the problem. Computational results are reported on 1350 random problems. In over 85% of these problems, the heuristics find solutions within 1% of the optimal. Heuristic performance is also analyzed in terms of average percent deviation from optimal, percent of times optimal solution is found and the cpu time. Computational results on two significantly larger real problems indicate that the heuristics are capable of solving real sized problems with tolerable deviations of around 4% from the optimal. An integrated strategy utilizing the strengths of the optimal and heuristic approaches is described for schedule generation and updating.