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A dynamic stochastic programming approach for open-pit mine planning with geological and commodity price uncertainty

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RESOURCES POLICY 2020年第0期65卷 101570-000页

作者： Rimele, Adrien Dimitrakopoulos, Roussos Gamache, Michel McGill Univ Dept Min & Mat Engn COSMO Stochast Mine Planning Lab Montreal PQ H3A 0E8 Canada Polytech Montreal Dept Math & Ind Engn Montreal PQ H3T 1J4 Canada

Over the last decade, geological uncertainty and its effects on long-term or strategic mine planning and methods for related risk management have been studied. However, the combined effect of geological and commodity price uncertainty has received relatively less attention in the technical literature. A research experiment that addresses both these sources of uncertainty is presented herein and accounts for their differences. In particular, while the current commodity price is known at the beginning of every new mining period, the geology, including the mineral grades, metal content, material types and so on, remain uncertain, even when additional information becomes available. The proposed method first uses a two-stage model to manage the geological uncertainty that leads to a scenario-independent extraction sequence. Based on different metal production targets, a pool of subsets of mining blocks is also precomputed for every period. Then, a stochastic dynamic programming algorithm is developed and employed to define the best policy in terms of metal production targets to follow, depending on the evolution of the related commodity price. This policy follows the scenario tree of the commodity price, as it is scenario-dependent (price only) with non-anticipativity constraints, which is similar to an operator that adapts to a fluctuating market. This new approach is tested through a case study that reveals the counter-intuitive combined effects of both sources of uncertainty. For instance, based on the previous evolution of the commodity price, the obtained policy suggests adaptations of the metal production target that go against common practices of mining operators.

关键词： Open pit mine planning Geological and market uncertainty stochastic model stochastic dynamic programming

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Exploring the effects of reductions in krill biomass in the Southern Ocean on blue whales using a state-dependent foraging model

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ECOLOGICAL MODELLING 2011年第18期222卷 3366-3379页

作者： Wiedenmann, John Cresswell, Katherine A. Goldbogen, Jeremy Potvin, Jean Mangel, Marc Univ Calif Santa Cruz Dept Ocean Sci Santa Cruz CA 95064 USA Univ Calif Santa Cruz Dept Appl Math & Stat Ctr Stock Assessment Res CSTAR Santa Cruz CA 95064 USA Cascadia Res Collect Olympia WA 98501 USA St Louis Univ Dept Phys St Louis MO 63103 USA Univ Bergen Dept Biol Bergen Norway

Many species of baleen whales were hunted to near extinction in the Southern Hemisphere. The recovery of these populations will be affected by the availability of krill, a major dietary component, in the Southern Ocean. We combine a novel energetics model for baleen whales with a state dependent foraging model to explore the impacts of an expanding krill fishery on baleen whales. We parameterize the model for blue whales, but with simple modifications it could be applied to most baleen whales. We predict that an expanding fishery will have a small but significant impact on the blue whale population through decreased birth rates. However, spreading the catch limit throughout the range of krill can reduce these effects. In addition, whales may be able to reduce these impacts through adaptive changes in foraging behavior. The relationship between krill abundance and blue whale foraging and reproductive success is nonlinear, such that larger reductions in krill biomass, potentially following a loss of sea ice due to climate change, could have a much larger negative impact on the recovery of blue whales. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Blue whales Antarctic krill Energetics Climate change stochastic dynamic programming Fishing impact

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Pricing to accelerate demand learning in dynamic assortment planning for perishable products

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第2期237卷 555-565页

作者： Talebian, Masoud Boland, Natashia Savelsbergh, Martin Univ Newcastle Callaghan NSW 2308 Australia

Retailers, from fashion stores to grocery stores, have to decide what range of products to offer, i.e., their product assortment. Frequent introduction of new products, a recent business trend, makes predicting demand more difficult, which in turn complicates assortment planning. We propose and study a stochastic dynamic programming model for simultaneously making assortment and pricing decisions which incorporates demand learning using Bayesian updates. We show analytically that it is profitable for the retailer to use price reductions early in the sales season to accelerate demand learning. A computational study demonstrates the benefits of such a policy and provides managerial insights that may help improve a retailer's profitability. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Assortment planning Demand learning Bayesian updating stochastic dynamic programming Retailing

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AN ANALYSIS OF A dynamic PROJECT COST PROBLEM

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1992年第6期43卷 591-604页

作者： MEHREZ, A SNIEDOVICH, M CSIR NATL RES INST MATH SCIPRETORIASOUTH AFRICA

This paper presents a stochastic allocation model for a sequential financial problem involving the allocation of funds to uncertain future payments. It is shown that under certain conditions the optimal allocation policies are piece-wise linear with the budget available, and that there exists an intimate relationship between these policies and the myopic policies obtained from the solution of a sequence of single-payment problems. A numerical example is provided and, finally, certain technical and methodological issues associated with a chance constraint version of the problem are discussed.

关键词： stochastic dynamic programming FINANCIAL COST PROBLEM CHANCE CONSTRAINT

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Supply contracts, profit sharing, switching, and reaction options

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MANAGEMENT SCIENCE 2004年第1期50卷 64-82页

作者： Kamrad, B Siddique, A Georgetown Univ McDonough Sch Business Washington DC 20057 USA Off Comptroller Currency Risk Anal Div Washington DC 20219 USA

A common theme in the studies of flexible supply contracts has been the producer's profit-maximization problem without regard to the suppliers' reactions. However, suppliers do react and protect their downside against producer's operating policies by revising their strategies in a manner consistent with their profit-maximization objectives. This fact motivates our work. Using a real-options (contingent claims) approach, we analyze and value supply contracts in a setting characterized by exchange rate uncertainty, supplier-switching options, order-quantity flexibility, profit sharing, and supplier reaction options. We also use basic diversification concepts, from portfolio theory, to analyze risk reduction in a unique framework. Given this setup, we explicitly model how flexibility can be mutually beneficial to both the producer and the suppliers. Using this model, we concurrently solve and examine the dual optimization problem for the suppliers and the producer. Our approach also endogenizes the extent and degree of profit sharing through the resulting optimal policies. We also analyze what induces the producer and the suppliers to accept flexibility in their contracts.

关键词： valuation supply contracts real options reaction options stochastic dynamic programming

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Predictive control of a diesel electric wheel loader powertrain

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CONTROL ENGINEERING PRACTICE 2015年 41卷 47-56页

作者： Nilsson, T. Froberg, A. Aslund, J. Linkoping Univ S-58183 Linkoping Sweden Volvo Construct Equipment Gothenburg Sweden

Wheel loaders often have a highly repetitive pattern of operation, which can be used for creating a rough prediction of future operation. As the present torque converter based transmission is replaced with an infinitely variable device, such as an electric or hydraulic transmission, a freedom in the choice of engine speed is introduced. This choice is far from trivial in the extremely transient operation of these machines, but the availability of a load prediction should be utilized. In this paper, a predictive engine and generator controller, based on stochastic dynamic programming, is described, implemented and evaluated. The evaluation is performed against non-predictive controllers in the same system, to lift out any possible benefits of utilizing the repetition based prediction. Simulations and field tests show that the controllers are able to handle disturbances introduced from model errors, the machine environment and the human operator, and that the predictive controller gives around 5% lower fuel consumption than the non-predictive reference controllers. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Diesel engine Continuously variable transmission Predictive control stochastic dynamic programming

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The stability of an optimal maintenance strategy for repairable assets

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART E-JOURNAL OF PROCESS MECHANICAL ENGINEERING 2004年第E2期218卷 77-82页

作者： Archibald, TW Ansell, JI Thomas, LC Univ Edinburgh Dept Business Studies Edinburgh EH8 9JY Midlothian Scotland Univ Southampton Dept Accounting & Management Sci Southampton SO9 5NH Hants England

Equipment in the process industry is often subject to decay and requires maintenance, repair and eventual replacement. The challenge of competition and the accompanying regulatory regime requires that actions be integrated and cost effective. Ansell and colleagues in 2001 explored an approach to the assessment of asset life of maintained equipment in the process industry using a semiparametric approach. Using stochastic dynamic programming techniques an approach to find the optimal strategy was also developed by Ansell and colleagues. The approach was illustrated using data from the water industry. A major aspect in the development of optimal strategy for repair and replacement is the cost of these activities. Often the costs can. only be ascertained roughly in terms of hours expended on the activity. Detailed costings are rarely available. The discount factor will depend on the interest rate in place. Generally a conservatively high level has been taken but with current low rates one needs to explore the sensitivity of solution to the discount factor. Also there is a need to explore the sensitivity of the solution to changes in the costs of the maintenance activities involved. In this paper we explore the stability of the results to changes in the relative costs. It is seen that two costs seem to be more important than the others;hence the accounting effort appears to be best directed towards these costs. One concern that arises from these results is the impact of the maintenance events. In past modelling the impact of maintenance has been assumed to have a fixed effect. This was derived from study of data. It is felt that this assumption may be too simple and so a differing model is explored to examine this issue.

关键词： optimal maintenance strategy non-homogeneous Poisson process proportional hazard model stochastic dynamic programming

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Optimal avian migration: A dynamic model of fuel stores and site use

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EVOLUTIONARY ECOLOGY 1998年第4期12卷 377-401页

作者： Weber, TP Ens, BJ Houston, AI Univ Oxford Dept Zool Ecol & Behav Grp BBSRCNERC Oxford OX1 3PS England DLO IBN Inst Forestry & Nat Res NL-1790 AD Den Burg Texel Netherlands Univ Bristol Sch Biol Sci Bristol BS8 1UG Avon England

Birds migrating between widely separated wintering and breeding grounds may choose among a number of potential stopover sites by using different itineraries. Our aim is to predict the optimal migration schedule in terms of (1) rates of fuel deposition, (2) departure fuel loads and (3) stopover site use, when only a handful of such sites are available. We assume that reproductive success depends on the date and fuel load at arrival on the breeding grounds. On migration, the birds face a trade-off between gaining fuel and avoiding predation. To allow the optimal decision at any given moment to depend on the fuel load and the location of the bird, as well as on unpredictability in conditions, we employed stochastic dynamic programming. This technique assumes that the birds know the probability distribution of conditions in all sites, but not the particular realization they will encounter. We examined the consequences of varying aspects of the model, like (1) the shape of the relationship between arrival date and fitness, (2) the presence of stochasticity in fuel deposition rates and wind conditions, and (3) the nature of predation (i.e. whether predation risk depends on the fuel load of the birds or their feeding intensity). Optimal fuel deposition rates are predicted to be constant if there are either only predation risks of maintaining stores or only risks of acquiring fuel stores. If only fuel acquisition is risky, fuel deposition rates can be below maximum, especially if there also is an intermediate best arrival time at the breeding ground. The fuel deposition rate at a site then depends not just on the site's quality but on the qualities of all visited sites. In contrast, rates of fuel deposition are not constant if both the acquisition and the maintenance of fuel stores carry risk. Optimal departure fuel loads are just enough to reach the next site if the environment is deterministic and are simply set by the energetic cost of covering the distance. As with time

关键词： avian migration departure fuel loads fuel deposition rates stochastic dynamic programming stopover site use

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dynamic expediting of an urgent order with uncertain progress

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第1期267卷 78-85页

作者： Bertazzi, Luca Mogre, Riccardo Univ Brescia Dept Econ & Management Contrada Santa Chiara 50 I-25122 Brescia Italy Univ Durham Business Sch Millhill Ln Durham DH1 3LB England

A supplier manages an urgent order with uncertain progress for which her client has set a deadline for its completion. The supplier observes in real time the order progress and chooses dynamically the effort level, such as manpower level, to expedite the order. Her problem is to identify expediting policies to minimise her expected cost, given by two costs in trade-off with each other: an effort level cost and a one-time penalty cost for late completion of the order. We formulate this problem using a discrete stochastic dynamic programming framework and obtain an optimal expediting policy for it. By conducting a worst-case analysis, we show that decreasing the level of flexibility, interpreted as the supplier's ability to update effort levels more often, may lead to a large increase in the costs of managing the order. We refine the problem formulation by modelling the case in which the supplier takes into account the negative effects of late order completion on her client using a penalty cost charged every period the order is delayed. We find an optimal policy for this case, by solving two dynamic programming problems sequentially. For both problems, we show that in presence of certain assumptions, there is an optimal expediting policy for which effort levels are non-increasing in the order progress. Finally, using a simulation study based on a car seat assembly case, we compare the performance of the two policies. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Supply chain management Tracking technologies Supply chain risk management stochastic dynamic programming Worst-case analysis

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Multi-Agent Learning-Based Nearly Non-Iterative stochastic dynamic Transactive Energy Control of Networked Microgrids

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IEEE TRANSACTIONS ON SMART GRID 2022年第1期13卷 688-701页

作者： Pan, Zhenning Yu, Tao Li, Jie Wu, Yufeng Chen, Junbin Lu, Jidong Zhang, Xiaoshun South China Univ Technol Coll Elect Power Guangzhou 510640 Peoples R China Guangdong Prov Key Lab Intelligent Measurement & Guangzhou Peoples R China Northeastern Univ Foshan Grad Sch Foshan 528311 Peoples R China

Coordination of networked microgrids (MGs) offers a promising solution to utilize distributed resources flexibilities and accommodate renewable energy. This paper studies real-time coordination of distribution system operation (DSO) and MGs considering multivariate uncertainty. Current researches suffer from inadaptability to dynamic system uncertainty, extensive iterations, and dependence on prediction. To fill these gaps, A novel multi-agent learning based stochastic dynamic programming (MASDP) is proposed to obtain the optimal policy for entities. Specifically, transactive energy control (TEC) mechanism, which requires only market-based information interactions, is employed to facilitate coordination between MG and DSO. A data-driven offline self-learning is proposed for entities to learn how to manage resources in response to system uncertainty. After sufficient offline learning, online operation of MASDP can be run in both non-iterative and iterative manners, by which near-optimal/optimal real-time solutions of DSO and MGs can be given sequentially and distributedly. Numerical comparisons with state-of-art policies and TEC algorithms verify the optimality, efficiency, adaptability, and scalability of MASDP.

关键词： Uncertainty Real-time systems dynamic programming Distribution networks stochastic processes Power demand Microgrids Microgrids distribution networks transactive energy control stochastic optimization real-time optimization stochastic dynamic programming multi-agent learning

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