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Optimization of cut-off grades considering grade uncertainty in narrow, tabular gold deposits

JOURNAL OF THE SOUTHERN AFRICAN INSTITUTE OF MINING AND METALLURGY 2017年第2期117卷 149-156页

作者： Birch, C. Univ Witwatersrand Sch Min Engn Johannesburg South Africa

Mineral reserve statements as well as optimizing mine planning require a block model with grades for each mining block. A cut-off grade is determined by considering the mining costs as well as the expected revenue for each block. These grades are estimated using various techniques, but in reality there is uncertainty in the grade values. These uncertainties result in two types of error. A type I error is where material is classified as ore and mined, but the true value is below the cut-off grade and the material is therefore waste. This material constitutes dilution. The type II error is where material is estimated to be below the cut-off grade and is classified as waste, whereas the true grade is actually above the cut-off grade. This material is not mined and the value is lost. This research considers the value of the lost ore and the costs of dilution under various degrees of uncertainty. Simulation using @ Risk and mixed integer linear programing (Excel Solver) is used in a financial optimizer model to maximize either profit or net present value. This is applied to four Witwatersrand tabular gold deposits to investigate the impact of block grade uncertainty on cut-off grades. When optimizing for profit, value may be added by adjusting the cutoff grade slightly downwards. When optimizing for NPV, value may be added by lowering the cut-off grade significantly for the lower discounting rates. At higher discount rates, the lowering of the cut-off grades should be reduced, and in some cases an increase in cut-off grade may be required. Each mine reacted differently to the optimization and thus there is no single rule that can be applied across all tabular Witwatersrand gold deposits.

关键词： uncertainty type I error type II error cut-off grade optimization profit NPV simulation mixed integer linear programing

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A simulation-optimization approach to integrate process design and planning decisions under technical and market uncertainties: A case from the chemical-pharmaceutical industry

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COMPUTERS & CHEMICAL ENGINEERING 2017年 106卷 796-813页

作者： Marques, Catarina M. Moniz, Samuel de Sousa, Jorge Pinho Barbosa-Povoa, Ana Paula Univ Porto Fac Engn Rua Dr Roberto Frias Oporto Portugal INESC TEC Rua Dr Roberto Frias Oporto Portugal Univ Lisbon Inst Super Tecn Ctr Estudos Gestao Ave Rovisco Pais Lisbon Portugal

This study addresses the product-launch planning problem in the chemical-pharmaceutical industry under technical and market uncertainties, and considering resource limitations associated to the need of processing in the same plant products under development and products in commercialization. A novel approach is developed by combining a mixed integer linear programming (MILP) model and a Monte Carlo simulation (MCS) procedure, to deal with the integrated process design and production planning decisions during the New Product Development (NPD) phase. The Monte Carlo simulation framework was designed as a two-step sampling procedure based on Bernoulli and Normal distributions. Results show the unquestionable influence of the uncertainty parameters on the decision variables and objective function, thus highlighting the inherent risks associated to the deterministic models. Process designs and scale-ups that maximize expected profit were determined, providing a valuable knowledge frame to support the long-term decision-making process, and enabling earlier and better decisions during NPD. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Process design Capacity planning Scale-ups mixed integer linear programing Monte carlo simulation Uncertainty

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Locating charging infrastructure for electric buses in Stockholm

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2017年 78卷 183-200页

作者： Xylia, Maria Leduc, Sylvain Patrizio, Piera Kraxner, Florian Silveira, Semida KTH Royal Inst Technol Energy & Climate Studies Unit Stockholm Sweden KTH Royal Inst Technol ITRL Stockholm Sweden Int Inst Appl Syst Anal Laxenburg Austria

Charging infrastructure requirements are being largely debated in the context of urban energy planning for transport electrification. As electric vehicles are gaining momentum, the issue of locating and securing the availability, efficiency and effectiveness of charging infrastructure becomes a complex question that needs to be addressed. This paper presents the structure and application of a model developed for optimizing the distribution of charging infrastructure for electric buses in the urban context, and tests the model for the bus network of Stockholm. The major public bus transport hubs connecting to the train and subway system show the highest concentration of locations chosen by the model for charging station installation. The costs estimated are within an expected range when comparing to the annual bus public transport costs in Stockholm. The model could be adapted for various urban contexts to promptly assist in the transition to fossil-free bus transport. The total costs for the operation of a partially electrified bus system in both optimization cases considered (cost and energy) differ only marginally from the costs for a 100% biodiesel system. This indicates that lower fuel costs for electric buses can balance the high investment costs incurred in building charging infrastructure, while achieving a reduction of up to 51% in emissions and up to 34% in energy use in the bus fleet. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Electric bus Charging infrastructure Optimization mixed integer linear programing Public transport Sweden

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Impact of the South African mineral resource royalty on cut-off grades for narrow, tabular Witwatersrand gold deposits

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JOURNAL OF THE SOUTHERN AFRICAN INSTITUTE OF MINING AND METALLURGY 2016年第3期116卷 237-246页

作者： Birch, C. Univ Witwatersrand Sch Min Engn Johannesburg South Africa

A mineral resource royalty is payment to the holder of mineral rights for the utilization of the mineral resource. In South Africa, this payment is made to the State as holder of the mineral rights (The Mineral and Petroleum Resources Royalty Act of 2008). The principle purpose of this research paper is to identify if the State is benefitting from the mineral resource royalty by considering its impact on seven individual Witwatersrand gold mines. For this study, a simple financial optimiser model was created in Microsoft Excel that links the ore flow, block listing and the cash flow (excluding or including the cost of the mineral resource royalty). mixed integer linear programing (the Excel Solver function) is utilised to optimise either profit or NPV (at 9% and 12%) by adjusting the cut-off grade. The impact on each of the seven mines mine was different but overall R7.9 billion is estimated to be paid in mineral resource royalty over their expectedremaining lives. Due to the cost of the mineral resource royalty andincreasing the cut-off grades, the total revenue decreases by R10 billion. Asignificant portion of this lost revenue would have been paid to the State inthe forms of other taxation including company income tax which decreasesby R2.8 billion. It is recommended that an industry wide investigation beconducted to determine if the resource royalty is adding to the State'srevenue, or destroying value including premature job losses.

关键词： Mineral and Petroleum Resources Royalty Act of 2008 cut-off grade optimization net present value (NPV) mixed integer linear programing excel solver

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Management of loads in residential buildings installed with PV system under intermittent solar irradiation using mixed integer linear programming

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ENERGY AND BUILDINGS 2016年第Oct.期130卷 253-271页

作者： Ogunjuyigbe, A. S. O. Ayodele, T. R. Oladimeji, O. E. Univ Ibadan Power Energy Machine & Drive Res Grp Dept Elect & Elect Engn Fac Technol Ibadan Nigeria

One of the challenges of utilizing solar PV in residential buildings is the management of load in accordance to the intermittent nature of solar resource. In this paper, mixed integer linear Programming (MILP) is proposed to effectively plan and allocate load for consumption in such a way that the user defined priority of loads are conserved. In this way, the loads are made to follow the battery state of charge in accordance to the intermittent nature of solar resource without adversely affecting the quality of life of the user. In doing this, energy audit of a typical 4-bedroom residential building belonging to a medium-income family is carried out and classified into controllable and non-controllable loads. The energy audit is also used to size the PV system and the battery bank taking into consideration the financial status of the user (i.e. adequately sized and under-sized PV system based on financial status of the user). A load manager based on MILP with solar resource load following capability is thereafter developed and implemented in a computational program to manage the load based on user's priority. Six scenarios are created to gain insights into the effectiveness of the proposed load manager. The results reveal that the proposed technique is effective in allocating loads based on the available solar resource in such a way that the user priority is maintained. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Load management PV system Battery state of charge Load following capability mixed integer linear programing

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Cogeneration systems optimization: Comparison of multi-step and mixed integer linear programming approaches

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INTERNATIONAL JOURNAL OF GREEN ENERGY 2016年第8期13卷 781-792页

作者： Bischi, Aldo Perez-Iribarren, Estibaliz Campanari, Stefano Manzolini, Giampaolo Martelli, Emanuele Silva, Paolo Macchi, Ennio Pedro Sala-Lizarraga, Jose Maria Politecn Milan Dipartimento Energia Via Lambruschini 4 I-20156 Milan Italy Univ Basque Country ENEDI Res Grp Bilbao Spain

The presented work compares two optimization models for combined heat and power (CHP) energy systems scheduling. Both models are focused on the evaluation of the best operating strategy to run a defined cogeneration system that is dealing with time-variable loads and tariffs. The simultaneous usage of different prime movers operating in parallel is taken into consideration as well as their part load performance, the influence of ambient temperature, and the usage of a heat storage system. One of the models is heuristic and adopts an optimization strategy based on a multi-step approach: it simulates several cases according to a pre-defined path exploring the most reasonable operational modes and comparing them systematically. The other one relies on a mathematical approach. A mixed integer linear Programming (MILP) algorithm has been developed in order to deal with more complex systems without the need of predefining a too large variety of optimization paths according to the case. Results of the two models are compared against a test case based on real plant specifications, discussing their performance, by the point of view of simulation capabilities, quality of the optimization results, and calculation time.

关键词： Cogeneration heat storage mixed integer linear programing multi-step optimization two temperature levels

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Efficient Benders cuts for transmission expansion planning

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ELECTRIC POWER SYSTEMS RESEARCH 2016年第Feb.期131卷 275-284页

作者： Alizadeh-Mousavi, Omid Zima-Bockarjova, Marija ABB Corp Res Ctr Baden Switzerland

This paper studies the problem of optimal transmission grid expansion planning. Deterministic formulations are developed for a single time period planning problem, while the operation costs (including total energy, reserve procurement, and load and wind curtailment costs) and N-1 security constraints are taken into consideration. Benders decomposition approach is employed to decompose the large optimization problem into smaller subproblems. New and more efficient Benders cuts are proposed, which are specifically tailored to the binary decision variables of transmission planning problem. The advantages of the proposed Benders cuts to the regular cuts used in the literature are demonstrated, in terms of the increase in convergence speed, decrease in the computational time and required number of iterations, and the scalability of the solution approach. Besides, the proposed Benders cuts are extended to include multiple operation scenarios (similar to stochastic formulations), where the optimization problem considers multiple power demand and wind production scenarios. The proposed optimization models are investigated using Graver's 6-bus, IEEE 24-bus, IEEE 73-bus, and IEEE 118-bus test systems and compared to ones reported in the literature. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Transmission network planning Disjunctive model mixed integer linear programing Deterministic optimization model

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An iterative approach for reducing the impact of infrastructure maintenance on the performance of railway systems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2016年第1期252卷 39-53页

作者： Vansteenwegen, Pieter Dewilde, Thijs Burggraeve, Sofie Cattrysse, Dirk Katholieke Univ Leuven Leuven Mobil Res Ctr CIB Celestijnenlaan 300 B-3001 Leuven Belgium Conundra Guldensporenpk 120 B-9820 Merelbeke Belgium

Planned infrastructure works reduce the available capacity of a railway system and make it more vulnerable to conflicts and delay propagation. The starting point of this paper is a published timetable that needs to be adapted due to the temporary unavailability of some resources. Since the timetable is in operation, changed arrival or departure times and cancelations have an impact on the passengers who need to adapt their travel behavior. In the light of passenger service, a trade-off is made between these inconveniences and the delays that occur in practice due to the reduced capacity. Taking the robustness of the adapted railway timetable into account is a new approach to rescheduling in case of a planned infrastructure unavailability. In this paper, an algorithm that adjusts the train routing and the train schedule to the planned maintenance interventions and keeps the level of passenger service as high as possible is presented. To avoid large inconveniences, the developed algorithm tries to minimize the number of cancelations. Computational results show that by allowing small modifications to the routing and the timetable, the robustness of the resulting solution can improve by more than 10 percent and only few trains need to be canceled. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Transportation Railway timetabling Robustness Maintenance mixed integer linear programing

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