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stochastic stope design optimisation under grade uncertainty and dynamic development costs

INTERNATIONAL JOURNAL OF MINING RECLAMATION AND ENVIRONMENT 2022年第2期36卷 81-103页

作者： Faria, Matheus Furtado e Dimitrakopoulos, Roussos Pinto, Claudio McGill Univ Dept Min & Mat Engn Cosmo Stochast Mine Planning Lab Montreal PQ Canada Univ Fed Minas Gerais Dept Min Engn Belo Horizonte MG Brazil

Stope design optimisation defines three-dimensional extraction volumes aiming to maximise cashflows, subject to geotechnical and operational constraints. Available stope layout methods are deterministic, failing to account for grade uncertainty and variability that affect stope locations and sizes, as well as value. A two-stage stochastic integer programming model for stope design optimisation is proposed, integrating grade uncertainty quantified through geostatistical simulations, level allocation, variable stope and pillar sizes for different geotechnical zones, and development costs. An application at an underground gold mine employing sublevel open stoping highlights the integration and management of grade uncertainty to define risk-resilient stope design.

关键词： Stope design optimisation stochastic integer programming underground mine planning geological uncertainty

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stochastic PROGRAMS WITH FIRST-ORDER DOMINANCE CONSTRAINTS INDUCED BY MIXED-integer LINEAR RECOURSE

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SIAM JOURNAL ON OPTIMIZATION 2008年第2期19卷 552-571页

作者： Gollmer, Ralf Neise, Frederike Schultz, Ruediger Univ Duisburg Essen Dept Math D-47048 Duisburg Germany

We propose a new class of stochastic integer programs whose special features are dominance constraints induced by mixed-integer linear recourse. For these models, we establish closedness of the constraint set mapping with the underlying probability measure as a parameter. In the case of finite probability spaces, the models are shown to be equivalent to large-scale, block-structured, mixed-integer linear programs. We propose a decomposition algorithm for the latter and discuss computational results.

关键词： stochastic integer programming stochastic dominance mixed-integer optimization

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The stochastic critical node problem over trees

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NETWORKS 2020年第3期76卷 381-401页

作者： Hosteins, Pierre Scatamacchia, Rosario Univ Gustave Eiffel COSYS ESTAS F-59666 Lille France Politecn Torino Dipartimento Ingn Gest & Prod Turin Italy

We tackle a stochastic version of the critical node problem (CNP) where the goal is to minimize the pairwise connectivity of a graph by attacking a subset of its nodes. In the stochastic setting considered, the outcome of attacks on nodes is uncertain. In our work, we focus on trees and demonstrate that over trees the stochastic CNP actually generalizes to the stochastic critical element detection problem where the outcome of attacks on edges is also uncertain. We prove the NP-completeness of the decision version of the problem when connection costs are one, while its deterministic counterpart was proved to be polynomial. We then derive a nonlinear model for the considered CNP version over trees and provide a corresponding linearization based on the concept ofprobability chains. Moreover, given the features of the derived linear model, we devise an exact Benders decomposition (BD) approach where we solve the slave subproblems analytically. A strength of our approach is that it does not rely on any statistical approximation such as the sample average approximation, which is commonly employed in stochastic optimization. We also introduce an approximation algorithm for the problem variant with unit connection costs and unit attack costs, and a specific integer linear model for the case where all the survival probabilities of the nodes in case of an attack are equal. Our methods are capable of solving relevant instances of the problem with hundreds of nodes within 1 hour of computational time. With this work, we aim to foster research on stochastic versions of the CNP, a problem tackled mainly in deterministic contexts so far. Interestingly, we also show a successful application of the concept of probability chains for problem linearizations significantly improved by decomposition methods such as the BD.

关键词： approximation algorithm Benders decomposition critical element detection critical node problem network interdiction probability chains stochastic integer programming trees

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Joint stochastic optimisation of open-pit mine production scheduling with ramp design

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INTERNATIONAL JOURNAL OF MINING RECLAMATION AND ENVIRONMENT 2024年第6期38卷 480-495页

作者： Cutler, Jacob Dimitrakopoulos, Roussos McGill Univ Dept Min & Mat Engn Montreal PQ Canada

stochastic optimisation of open-pit mine production scheduling maximises the NPV of a mine's extraction sequence while satisfying production constraints and minimising deviations from targets. Past approaches consider mining block access based on slope constraints, thus providing no guarantee that the infrastructure required for equipment access is feasible. To address this issue, a joint stochastic optimisation of life-of-mine production scheduling and ramp design is proposed, ensuring feasible equipment access to the related mining blocks. An application at a gold mine demonstrates the value of considering the complex relationship that exists between ramp design, equipment access and production scheduling during optimisation.

关键词： Open-pit mine production scheduling optimisation stochastic integer programming ramp design

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Capacity allocation problem with random demands for the rail container carrier

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第1期217卷 214-221页

作者： Cao, Chengxuan Gao, Ziyou Li, Keping Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China

In this paper, we consider the formulation and heuristic algorithm for the capacity allocation problem with random demands in the rail container transportation. The problem is formulated as the stochastic integer programming model taking into account matches in supply and demand of rail container transportation. A heuristic algorithm for the stochastic integer programming model is proposed. The solution to the model is found by maximizing the expected total profit over the possible control decisions under the uncertainty of demands. Finally, we give numerical experiments to demonstrate the efficiency of the heuristic algorithm. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Transportation Capacity allocation Rail container stochastic integer programming Heuristic algorithm

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An algorithm for stochastic programs with first-order dominance constraints induced by linear recourse

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DISCRETE APPLIED MATHEMATICS 2010年第4期158卷 291-297页

作者： Drapkin, Dimitri Schultz, Ruediger Univ Duisburg Essen Dept Math D-47048 Duisburg Germany

We derive a cutting plane decomposition method for stochastic programs with first-order dominance constraints induced by linear recourse models with continuous variables in the second stage. (C) 2009 Elsevier B.V. All... 详细信息

关键词： stochastic integer programming stochastic dominance Mixed-integer optimization

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Single-ratio fractional integer programs with stochastic right-hand sides

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IISE TRANSACTIONS 2017年第6期49卷 579-592页

作者： Zhang, Junlong Ozaltin, Osman Y. North Carolina State Univ Edward P Fitts Dept Ind & Syst Engn Raleigh NC 27695 USA

We present an equivalent value function reformulation for a class of single-ratio Fractional integer Programs (FIPs) with stochastic right-hand sides and propose a two-phase solution approach. The first phase constructs the value functions of FIPs in both stages. The second phase solves the reformulation using a global branch-and-bound algorithm or a level-set approach. We derive some basic properties of the value functions of FIPs and utilize them in our algorithms. We show that in certain cases our approach can solve instanceswhose extensive forms have the same order ofmagnitude as the largest stochastic quadratic integer programs solved in the literature.

关键词： Fractional integer programming stochastic integer programming value functions superadditive duality

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Semi liner Shipping Service Design

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TRANSPORTATION SCIENCE 2020年第5期54卷 1288-1306页

作者： Wang, Yadong Meng, Qiang Nanjing Univ Sci & Technol Sch Econ & Management Nanjing 210094 Peoples R China Natl Univ Singapore Dept Civil & Environm Engn Singapore 117576 Singapore Natl Univ Singapore Inst Operat Res & Analyt Singapore 119077 Singapore

Semi-liner shipping transports various types of cargo, such as containers, break-bulk cargo, and heavy-lift project cargo, between different ports. Similar to liner shipping, semi-liner shipping publishes shipping routes for customers' reference. However, it does not strictly follow the published route and usually makes some adjustments for each ship voyage by adding some port calls to transport more cargo considering the excess ship capacity. This study first proposes the semi-liner shipping service design (SILSSD) problem that aims to maximize the shipping profit by determining a shipping route subject to the potential adjustments. The proposed SI SSD problem is subsequently formulated as a two-stage stochastic mixed integer programming model with integer recourse variables. The first stage determines the visit sequence of a set of compulsory ports under shipping demand uncertainty. The second stage decides whether to add or remove some ports in the route in view of the realized shipping demand for each ship voyage. To effectively solve the model, two decomposition methods are developed, namely, the stage decomposition method and the scenario decomposition method, that decompose the problem by stage and demand scenario, respectively. in addition, two novel acceleration techniques are also provided to expedite the scenario decomposition method. Numerical experiments reveal satisfactory efficiency of these two methods to solve the semi-liner shipping service design problem, especially the scenario decomposition method, which is generally better than the stage decomposition method and can be thousands of times faster than the classic branch-and-cut algorithm.

关键词： semi-liner shipping service design stochastic integer programming integer recourse variable scenario decomposition

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A hybrid evolutionary algorithm for solving two-stage stochastic integer programs in chemical batch scheduling

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COMPUTERS & CHEMICAL ENGINEERING 2007年第5-6期31卷 630-647页

作者： Till, Jochen Sand, Guido Urselmann, Maren Engell, Sebastian Univ Dortmund Proc Control Lab BCI AST D-44221 Dortmund Germany ABB Corp Res Ctr D-68526 Ladenburg Germany

This contribution deals with the solution of two-stage stochastic integer programs with discrete scenarios (2-SIPs) that arise in chemical batch scheduling under uncertainty. Since the number of integer variables in the second-stage increases linearly with the number of scenarios considered, the real world applications usually give rise to large scale deterministic equivalent mixed-integer linear programs (MILPs) which cannot be solved easily without incorporating decomposition methods or problem specific knowledge. In this paper a new hybrid algorithm is proposed to solve 2-SIPs based on stage decomposition: an evolutionary algorithm performs the search on the first-stage variables while the second-stage subproblems are solved by mixed-integer programming. The algorithm is tested for a real-world scheduling problem with uncertainties in the demands and in the production capacity. Numerical experiments have shown, that the new algorithm is robust and superior to state-of-the-art solvers if good solutions are needed in short CPU-times. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： stochastic integer programming evolutionary algorithms hybrid algorithms chemical batch scheduling uncertainty

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A stochastic model for scheduling elective surgeries in a cyclic Master Surgical Schedule

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COMPUTERS & INDUSTRIAL ENGINEERING 2019年 129卷 156-168页

作者： M'Hallah, Rym Visintin, Filippo Kuwait Univ Dept Stat & Operat Res Coll Sci Safat Kuwait Univ Florence IBIS Lab Dept Ind Engn Florence Italy

In this study we propose a stochastic model that determines the number and type of surgeries to schedule in a two-week planning horizon where each operating session is assigned to a surgical specialty according to a fixed grid (Master Surgical Schedule). Our model considers surgery times, intensive care unit times and post-surgery lengths of stays stochastic and accounts for the availability of both intensive care unit beds and post-surgery beds. It aims to maximise the expected operating theatre's throughput. The assignment problem, modelled as a stochastic problem, is solved via a sample average approximation. It gets an estimate of the optimum expected throughput for each specialty and of the operating theatre. We illustrate the application of the model on a real case study with real data from a leading European Children's Hospital, study the sensitivity of obtained results to the two-week planned grid, and highlight the importance of considering the stochastic nature of the problem.

关键词： Sample average approximation stochastic integer programming Length of stay Post-surgery beds Operating room

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