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Quantitative stability of fully random mixed-integer two-stage stochastic programs

W. Römisch, S. Vigerske
2007 Optimization Letters  
Mixed-integer two-stage stochastic programs with fixed recourse matrix, random recourse costs, technology matrix, and right-hand sides are considered.  ...  Quantitative continuity properties of its optimal value and solution set are derived when the underlying probability distribution is perturbed with respect to an appropriate probability metric.  ...  These results are used in Section 3 to obtain the desired quantitative stability result (Theorem 3.3) for fully random mixed-integer two-stage stochastic programs with fixed recourse.  ... 
doi:10.1007/s11590-007-0066-1 fatcat:aeasxydfsjfibfhdgn7gqlt4pe

A Review of Stochastic Programming Methods for Optimization of Process Systems Under Uncertainty

Can Li, Ignacio E. Grossmann
2021 Frontiers in Chemical Engineering  
The mathematical formulations and algorithms for two-stage and multistage stochastic programming are reviewed with illustrative examples from process industries.  ...  stochastic programming.  ...  One common type of two-stage stochastic program is mixed-integer linear program presented in Eq. 2.  ... 
doi:10.3389/fceng.2020.622241 fatcat:32gnbbfemrh6hlbrcorxvnrksa

SDDP for multistage stochastic programs: preprocessing via scenario reduction

Jitka Dupačová, Václav Kozmík
2016 Computational Management Science  
Stage-wise backward reduction of single scenarios applied to a fixed branching structure of the tree is a promising tool for efficient algorithms like SDDP.  ...  We provide computational results which show an acceptable precision of the results for the reduced problem and a substantial decrease of the total computation time.  ...  Acknowledgements The research was partly supported by the project of the Czech Science Foundation P/402/12/G097 'DYME/Dynamic Models in Economics'.  ... 
doi:10.1007/s10287-016-0261-6 fatcat:ivue3fybbbgp5l3vimvp76xuqa

Stochastic Optimization for Unit Commitment—A Review

Qipeng P. Zheng, Jianhui Wang, Andrew L. Liu
2015 IEEE Transactions on Power Systems  
The first wave has made mixed integer programming stand out from the early solution and modeling approaches for deterministic UC, such as priority list, dynamic programming, and Lagrangian relaxation.  ...  Since UC's birth, there have been two major waves of revolution on UC research and real life practice.  ...  stochastic mixed integer problems (MIPs).  ... 
doi:10.1109/tpwrs.2014.2355204 fatcat:5hyp3avcszdzhhq43qzfkhd5ra

Simultaneous Optimal Control and Discrete Stochastic Sensor Selection [chapter]

D. Bernardini, D. Muñoz de la Peña, A. Bemporad, E. Frazzoli
2009 Lecture Notes in Computer Science  
The problem is formulated using stochastic programming ideas with decision-dependent scenario trees, and a solution based on mixed-integer linear programming is presented.  ...  We assume that the decision maker has the ability to choose among a discrete set of sources of information, where the outcome of each source is stochastic.  ...  This class of problems was posed as a two-stage mixed integer stochastic optimization problems with endogenous uncertainty, that can be solved recursively in time for optimal performance of systems subject  ... 
doi:10.1007/978-3-642-00602-9_5 fatcat:ie7k2ywzvneknplctvaqqq34ia

A Study of Demand Stochasticity in Service Network Design

Arnt-Gunnar Lium, Teodor Gabriel Crainic, Stein W. Wallace
2009 Transportation Science  
Stochastic programming, scheduled service network design, flexibility, robustness. Acknowledgements.  ...  Why and how are solutions to stochastic models better than those from deterministic ones? Answers to these two questions are the main contributions of this paper.  ...  Partial funding for this research has been provided by the Natural sciences and Engineering Research Council of Canada (NSERC) through its Discovery Grants and Chairs and Faculty Support programs.  ... 
doi:10.1287/trsc.1090.0265 fatcat:xjdt2sascjh77m6bt7zv2k5bui

Optimal Monitoring and Mitigation of Systemic Risk in Financial Networks

Zhang Li, Xiaojun Lin, Borja Peleato-Inarrea, Ilya Pollak
2014 Social Science Research Network  
With such extensions, the linear program turns into mixed-integer linear programs.  ...  We show that in this case, Problem I is an NP-hard mixed-integer linear program.  ... 
doi:10.2139/ssrn.2506326 fatcat:opwla6rgpjfphboc5si5gfxr5e

Portfolio optimization via stochastic programming: Methods of output analysis

Jitka Dupačová
1999 Mathematical Methods of Operations Research  
Selected methods for analysis of results obtained by solving stochastic programs are presented and their scope illustrated on generic examples ± the Markowitz model, a multiperiod bond portfolio management  ...  The approaches are based on asymptotic and robust statistics, on the moment problem and on results of parametric optimization.  ...  was in the case of the two-stage stochastic program.  ... 
doi:10.1007/s001860050097 fatcat:wfe555gf2bdpvegckoytu2srqm

Opportunities and Challenges of AC/DC Transmission Network Planning Considering High Proportion Renewable Energy

Arslan Habib, Chan Sou, Adeel Arshad, Hafiz Muhammad Hafeez
2018 European Journal of Sustainable Development Research  
These two features of renewable energy directly impede the integration of new energy into the grid.  ...  With the distribution network in conjunction with the transmission network planning, transmission planning program comprehensive evaluation and decision-making methods.  ...  Then, the whole planning model is transformed into a Mixed Integer Linear Programming (MILP) model.  ... 
doi:10.20897/ejosdr/83707 fatcat:q6h2ioc5efdcrh3z2mqf4nccn4

Stochastic multi-objective optimization: a survey on non-scalarizing methods

Walter J. Gutjahr, Alois Pichler
2013 Annals of Operations Research  
Part of the existing quantitative approaches to deal with problems of this class apply scalarization techniques in order to reduce a given stochastic multi-objective problem to a stochastic single-objective  ...  Currently, stochastic optimization on the one hand and multi-objective optimization on the other hand are rich and well-established special fields of Operations Research.  ...  Often, also stochastic mixed-integer problems occur.  ... 
doi:10.1007/s10479-013-1369-5 fatcat:tkit6o7xlfc4ppjcb77q53kauq

Approximation and contamination bounds for probabilistic programs

Martin Branda, Jitka Dupačová
2010 Annals of Operations Research  
Development of applicable robustness results for stochastic programs with probabilistic constraints is a demanding task.  ...  Therefore we explore approximations and reformulations of stochastic programs with probabilistic constraints by stochastic programs with suitably chosen recourse or penalty-type objectives and fixed constraints  ...  The second author acknowledges the support by the project "Methods of modern mathematics and their applications" -MSM 0021620839 and by the grant 402/08/0107 of the Czech Science Foundation.  ... 
doi:10.1007/s10479-010-0811-1 fatcat:6nefxqtjmnfpdg4slbuspk5ybe

Risk analysis methods of the water resources system under uncertainty

Zeying GUI, Chenglong ZHANG, Mo Li, Ping GUO
2015 Frontiers of Agricultural Science and Engineering  
Finally, this paper focuses on the various methods of risk analysis under uncertainty, which are summarized as random, fuzzy and mixed methods.  ...  In this paper the inherent stochastic uncertainty and cognitive subjective uncertainty of the WRS are discussed first, from both objective and subjective perspectives.  ...  This article does not contain any studies with human or animal subjects performed by any of the authors.  ... 
doi:10.15302/j-fase-2015073 fatcat:mf44jdwgs5hyralfcrvtfb7kqe

Stochastic network models for logistics planning in disaster relief

Douglas Alem, Alistair Clark, Alfredo Moreno
2016 European Journal of Operational Research  
This paper develops a new two-stage stochastic network flow model to help decide how to rapidly supply humanitarian aid to victims of a disaster within this context.  ...  location and needs of victims, possible random supplies and donations, precarious transport links, scarcity of resources, and so on.  ...  In the first phase, we still have a two-stage stochastic mixed-integer programming model, but with only |R| integer decisions.  ... 
doi:10.1016/j.ejor.2016.04.041 fatcat:tov7rpdsf5a6fmcqbj5sos6wim

Agent-Based Modelling: An Overview with Application to Disease Dynamics [article]

Affan Shoukat, Seyed M. Moghadas
2020 arXiv   pre-print
Modelling and computational methods have been essential in advancing quantitative science, especially in the past two decades with the availability of vast amount of complex, voluminous, and heterogeneous  ...  However, any well-established quantitative method relies on theoretical frameworks for both construction and analysis.  ...  Of course, if the system is stochastic in nature, then capturing randomness is of particular importance.  ... 
arXiv:2007.04192v1 fatcat:wkhfrty43zbhlniwz3buwliobu

Liquefied Natural Gas Ship Route Planning Model Considering Market Trend Change

Jaeyoung Cho, Gino J. Lim, Taofeek Biobaku, Selim Bora, Hamid Parsaei
2014 Transactions on Maritime Science  
The model is then extended to consider BOG using a two-stage stochastic modeling approach in which BOG is a random variable.  ...  The solutions are evaluated using expected value of perfect information (EVPI) and value of stochastic solution (VSS).  ...  We formulate this problem as LNG VRP model in mixed integer programming considering the rate of BOG.  ... 
doi:10.7225/toms.v03.n02.003 fatcat:y3eoefly2bhxflvkj7sdztzfby
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