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Decomposition of test sets in stochastic integer programming

MATHEMATICAL programming 2003年第2-3期94卷 323-341页

作者： Hemmecke, R Schultz, R Univ Calif Davis Dept Math Davis CA 95616 USA Univ Duisburg Gesamthsch Inst Math D-47048 Duisburg Germany

We study Graver test sets for linear two-stage stochastic integer programs and show that test sets can be decomposed into finitely many building blocks whose number is independent on the number of scenarios of the stochastic program. We present a finite algorithm to compute the building blocks directly, without prior knowledge of test set vectors. Once computed, building blocks can be employed to solve the stochastic program by a simple augmentation scheme, again without explicit knowledge of test set vectors. Finally, we report preliminary computational experience.

关键词： test sets stochastic integer programming decomposition methods

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On multistage stochastic integer programming for incorporating logical constraints in asset and liability management under uncertainty

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COMPUTATIONAL MANAGEMENT SCIENCE 2009年第3期6卷 307-327页

作者： Escudero, Laureano F. Garin, Araceli Merino, Maria Perez, Gloria Univ Miguel Hernandez Ctr Invest Operat Elche Alicante Spain Univ Basque Country Dept Econ Aplicada 3 Bilbao Vizcaya Spain Univ Basque Country Dept Matemat Aplicada Estadist & IO Leioa Vizcaya Spain

We present a model for optimizing a mean-risk function of the terminal wealth for a fixed income asset portfolio restructuring with uncertainty in the interest rate path and the liabilities along a given time horizon. Some logical constraints are considered to be satisfied by the assets portfolio. Uncertainty is represented by a scenario tree and is dealt with by a multistage stochastic mixed 0-1 model with complete recourse. The problem is modelled as a splitting variable representation of the Deterministic Equivalent Model for the stochastic model, where the 0-1 variables and the continuous variables appear at any stage. A Branch-and-Fix Coordination approach for the multistage 0-1 program solving is proposed. Some computational experience is reported.

关键词： Multistage scenario tree Assets and liabilities stochastic integer programming Branch-and-Fix Coordination Mean-risk function

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A two-stage stochastic integer programming model for a thermal power system expansion

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International Transactions in Operational Research 2004年第3期11卷 243-257页

作者： Albornoz, Víctor M. Benario, Pablo Rojas, Manuel E. Departamento de Industrias Universidad Técnica Federico Santa María Chile Mega Red Ingenieros Ltds Santiago Chile

In this paper the obtaining of an optimum policy in the capacity expansion planning of a particular thermal-electric power system is proposed. Therefore, a two-stage stochastic integer programming is formulated. The model includes, through a finite group of scenarios, the existent uncertainty related to the future availability of the thermal plants currently under operation. The resultant model is solved numerically by the application of the L-shaped method, whose implementation and development were executed using the software AMPL, with CPLEX as a solver. The results reached are shown, which validate the use of the methodology adopted in this work. © 2004 Wiley Periodicals, Inc.

关键词： Capacity expansion Decomposition stochastic integer programming

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Modeling and solving real-time scheduling problems by stochastic integer programming

Modeling and solving real-time scheduling problems by stocha...

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International Conference on Foundations of Computer-Aided Process Operations

作者： Sand, G Engell, S Univ Dortmund Proc Control Lab D-44221 Dortmund Germany

This contribution deals with scheduling problems of flexible chemical batch processes with a special emphasis on their real-time character. This implies not only the need for sufficiently short response times, but in particular the burden of in-complete knowledge about the future. To solve such problems, the application of two-stage stochastic integer programming techniques on moving horizons is proposed. They reflect the need for immediately applicable decisions and the potential of later recourse actions to cope with realized uncertainties. In addition to the classical expected value objective, simple measures of risk can be included. Motivated by an example process, some essential modeling prerequisites are discussed. As an important first step, the master scheduling problem is studied and a number of master scheduling models are presented. Large mixed-integer linear problems arise, which are well-suited for a dual decomposition approach. Numerical experiments with a problem-specific solution algorithm demonstrate the applicability of the method to real-world problems. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： batch scheduling uncertainty stochastic integer programming

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The DNA genetic algorithm applied for solving stochastic integer programming expected value models

The DNA genetic algorithm applied for solving stochastic int...

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7th International Conference on Machine Learning and Cybernetics

作者： Wang, Ming-Chun Tang, Wan-Sheng Liu, Xin Tianjin Univ Syst Engn Inst Tianjin 300072 Peoples R China Tianjin Univ Technol & Educ Tianjin 300072 Peoples R China

ISBN: (纸本)9781424420957

In this paper, how to use DNA genetic algorithm to solve stochastic integer programming expected value models is discussed. Since DNA Genetic algorithm has the merits of plentiful coding, and decoding, conveying complex knowledge flexibly. These merits and the technique of stochastic simulation are combined, which for estimating the random variables of stochastic integer programming expected value models problem. Base on them, a best solution of this problem can be found. The classical newspaper-selling boy problem is calculated for testifying the feasibility and effectiveness of this method.

关键词： stochastic integer programming expected value models DNA genetic algorithm stochastic simulation

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stochastic integer programming BY DYNAMIC programming

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Statistica Neerlandica 1985年第2期39卷 97-113页

作者： Lageweg, B.J. Lenstra, J.K RinnooyKan, A.H.G. Stougie, L. Kan, A.H.G. Rinnooy Centre for Mathematics and Computer Science Amsterdam 1009 AB P.O. Box 4079 Netherlands Econometric Institute Erasmus University Rotterdam Rotterdam 3000 DR P.O. Box 1738 Netherlands

stochastic integer programming is a suitable tool for modeling hierarchical decision situations with combinatorial features. In continuation of our work on the design and analysis of heuristics for such problems, we now try to find optimal solutions. Dynamic programming techniques can be used to exploit the structure of two–stage scheduling, bin packing and multiknapsack problems. Numerical results for small instances of these problems are presented. Copyright © 1985, Wiley Blackwell. All rights reserved

关键词： bin packing distribution model dynamic programming multiknapsack scheduling stochastic integer programming two–stage decision model

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AN ASYNCHRONOUS BUNDLE-TRUST-REGION METHOD FOR DUAL DECOMPOSITION OF stochastic MIXED-integer programming

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SIAM JOURNAL ON OPTIMIZATION 2019年第1期29卷 318-342页

作者： Kim, Kibaek Petra, Cosmin G. Zavala, Victor M. Argonne Natl Lab Math & Comp Sci Div Lemont IL 60439 USA Lawrence Livermore Natl Lab Livermore CA 94550 USA Univ Wisconsin Dept Chem & Biol Engn Madison WI 53706 USA

We present an asynchronous bundle-trust-region algorithm within the context of Lagrangian dual decomposition for stochastic mixed-integer programs. The approach solves the Lagrangian master problem by using a bundle method with a trust-region constraint. This scheme enables asynchronous computations and can thus help mitigate severe load imbalance issues (associated with the solution of scenario subproblems) and improve parallel efficiency. We provide a convergence analysis and an implementation of the proposed scheme. We also present extensive numerical results on eighty instances of a large-scale stochastic unit commitment problem, and demonstrate that the proposed approach provides significant reductions in solution time and achieves strong scaling.

关键词： stochastic integer programming bundle methods asynchronous parallel computing

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THE DNA GENETIC ALGORITHM APPLIED FOR SOLVING stochastic integer programming EXPECTED VALUE MODELS

THE DNA GENETIC ALGORITHM APPLIED FOR SOLVING STOCHASTIC INT...

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2008 International Conference on Machine Learning and Cybernetics(2008机器学习与控制论国际会议)

作者： MING-CHUN WANG WAN-SHENG TANG XIN LIU System Engineering Institute of Tianjin University Tianjin 300072 China Tianjin University of Tec System Engineering Institute of Tianjin University Tianjin 300072 China Tianjin University of Technology and Education Tianjin 300222 China

关键词： stochastic integer programming Ezpected value models DNA genetic algorithm stochastic simulation

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Supply Chain Design Optimization With Heterogeneous Risk-Aware Agents

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 9872-9883页

作者： Estrada-Garcia, Juan-Alberto Tilbury, Dawn M. Barton, Kira Shen, Siqian Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA Univ Michigan Robot Dept Ann Arbor MI 48109 USA Univ Michigan Dept Mech Engn Ann Arbor MI 48109 USA

Modern supply chain networks (SCN) are becoming increasingly complex, with vulnerable entities exposed to uncertain disruptions that affect local or global supply chain attributes. We model a stochastic mixed-integer program to minimize the overall cost of SCN design and operations, in response to lead-time and demand uncertainties following given probability distributions. We formulate a heterogeneous risk-aware model to trade off between cost and delay/shortage by considering different risk-attitudes amongst supply chain agents. In particular, we employ the Conditional Value-at-Risk (CVaR) as a coherent risk measure for quantifying risk while attaining solution tractability. We derive managerial insights from our numerical studies, finding the most benefit from diversifying agents in the root tier, since their disruptions affect all other tiers in the SCN. We find that as agents become more risk averse, the optimal solutions for key agents (such as assemblers), seek more backup suppliers and allocate extra capacities to achieve resiliency and reliability. Practitioners can use the outcomes of our framework and studies to guide SCN design considering heterogeneous risk attitudes between agents. Note to Practitioners-With growing uncertainties in global supply chains, inefficient responses to disruptions can lead to large penalties and long-term impacts such as customer dissatisfaction. This research is motivated by the challenges arising during the operations of supply chains under both lead-time and demand uncertainties. We employ optimization and centralized control approaches to optimize supply-chain network design as well as response strategies to disruptions, and our framework can handle heterogeneous risk preferences as it models the risk attitude of each individual entity or agent in supply chains. Our model can be utilized to completely or partially re-design resilient supply chains, to better prepare for unknown features and uncertainties. Our case study p

关键词： Costs Supply chains Uncertainty stochastic processes Lead Optimization Termination of employment Optimization models Design optimization Vectors Supply chain network design risk-averse optimization conditional value-at-risk (CVaR) stochastic integer programming

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Underground mine scheduling under uncertainty

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第1期294卷 340-352页

作者： Nesbitt, Peter Blake, Lewis R. Lamas, Patricio Goycoolea, Marcos Pagnoncelli, Bernardo K. Newman, Alexandra Brickey, Andrea Naval Postgrad Sch Operat Res Dept Monterey CA 93943 USA Colorado Sch Mines Dept Appl Math & Stat Golden CO 80401 USA Univ Adolfo Ibanez Sch Business Santiago Chile Colorado Sch Mines Dept Mech Engn Golden CO 80401 USA South Dakota Sch Mines & Technol Dept Min Engn & Management Rapid City SD 57701 USA

Underground mine schedules seek to determine start dates for activities related to the extraction of ore, often with an objective of maximizing net present value;constraints enforce geotechnical precedence be-tween activities, and restrict resource consumption on a per-time-period basis, e.g., development footage and extracted tons. Strategic schedules address these start dates at a coarse level, whereas tactical sched-ules must account for the day-to-day variability of underground mine operations, such as unanticipated equipment breakdowns and ground conditions, both of which might slow production. At the time of this writing, the underground mine scheduling literature is dominated by a deterministic treatment of the problem, usually modeled as a Resource Constrained Project Scheduling Problem (RCPSP), which pre-cludes mine operators from reacting to unforeseen circumstances. Therefore, we propose a stochastic integer programming framework that: (i) characterizes uncertainty in duration and economic value for each underground mining activity;(ii) formulates a new stochastic variant of the RCPSP;(iii) suggests an optimization-based heuristic;and, (iv) produces implementable, tactical schedules in a practical amount of time and provides corresponding managerial insights. (c) 2021 Elsevier B.V. All rights reserved.

关键词： OR in natural resources stochastic integer programming Optimization-based heuristics Project scheduling Underground mining

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