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A probability metrics approach for reducing the bias of optimality gap estimators in two-stage stochastic linear programming

Rebecca Stockbridge, Güzin Bayraksan
2012 Mathematical programming  
In this paper, we present a method for reducing the bias of the optimality gap estimators for two-stage stochastic linear programs with recourse via a probability metrics approach, motivated by stability  ...  Monte Carlo sampling-based estimators of optimality gaps for stochastic programs are known to be biased.  ...  This work has been partially supported by the National Science Foundation through grants DMS-0602173, EFRI-0835930, and CMMI-1151226. Probability metrics for bias reduction  ... 
doi:10.1007/s10107-012-0563-6 fatcat:ndujaatxqzf23ciilyjbnxjkwq

Assessing Solution Quality in Stochastic Programs via Sampling [chapter]

Güzin Bayraksan, David P. Morton
2009 Decision Technologies and Applications  
An alternative approach in stochastic programming is to use Monte Carlo sampling-based estimators on the optimality gap.  ...  We then discuss methods to reduce the computational effort, bias, and variance of our simplest estimator.  ...  Acknowledgments Section 5 is based on the doctoral thesis of Partani [48] .  ... 
doi:10.1287/educ.1090.0065 fatcat:6tofe76lpje4bol2n6lrkjfxnu

Data-driven multi-stage scenario tree generation via statistical property and distribution matching

B.A. Calfa, A. Agarwal, I.E. Grossmann, J.M. Wassick
2014 Computers and Chemical Engineering  
In this paper, we focus on a general, data-driven optimization-based method for generating scenario trees, which does not require strict assumptions on the probability distributions of the uncertain parameters  ...  We present two approaches for generating multi-stage scenario trees by considering time series modeling and forecasting.  ...  They also are grateful to Alex Kalos for the fruitful discussions regarding the incorporation of (E)CDF information to the moment matching method, and to the Advanced Analytics team, especially Joe Czyzyk  ... 
doi:10.1016/j.compchemeng.2014.04.012 fatcat:5i5kk4rqbncoha6a5lys22w43e

The empirical behavior of sampling methods for stochastic programming

Jeff Linderoth, Alexander Shapiro, Stephen Wright
2006 Annals of Operations Research  
We investigate the quality of solutions obtained from sample-average approximations to two-stage stochastic linear programs with recourse.  ...  of the computed solutions in various ways.  ...  An Algorithm for Two-Stage Stochastic Linear Programs with Recourse In this section, we focus our attention on two-stage stochastic linear programs with recourse over a discrete scenario space, which are  ... 
doi:10.1007/s10479-006-6169-8 fatcat:eqfepudhmvdgdhjx74wr5iq3xq

Monte Carlo sampling-based methods for stochastic optimization

Tito Homem-de-Mello, Güzin Bayraksan
2014 Surveys in Operations Research and Management Science  
This paper surveys the use of Monte Carlo sampling-based methods for stochastic optimization problems.  ...  a stochastic optimization problem with sampling.  ...  They are also grateful to Bernardo Pagnoncelli, Hamed Rahimian, two anonymous referees and the associate editor for their comments.  ... 
doi:10.1016/j.sorms.2014.05.001 fatcat:wxcytmx6urbyng6q2hsm3tmbtq

New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

F.D. Munoz, B.F. Hobbs, J.-P. Watson
2016 European Journal of Operational Research  
We propose a novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems that have to consider a large number  ...  Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system.  ...  Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S.  ... 
doi:10.1016/j.ejor.2015.07.057 fatcat:7iwqbyzgrvdoth6fktjpuyw5wq

Sample average approximation for risk-averse problems: A virtual power plant scheduling application

Ricardo M. Lima, Antonio J. Conejo, Loïc Giraldi, Olivier Le Maître, Ibrahim Hoteit, Omar M. Knio
2021 EURO Journal on Computational Optimization  
The problem is modeled using a risk-neutral and two risk-averse two-stage stochastic programming formulations, where the conditional value at risk is used to represent risk.  ...  The numerical results include an analysis of the computational performance of the methodology for two case studies, estimators for the bounds of the true optimal solutions of the problems, and an assessment  ...  We would like to thank two referees for their comments and contributions that helped to improve the presentation of this work.  ... 
doi:10.1016/j.ejco.2021.100005 fatcat:led6hocoqba2hcqoyg5fduzkvy

Variance Reduction for Sequential Sampling in Stochastic Programming [article]

Jangho Park and Rebecca Stockbridge and Güzin Bayraksan
2020 arXiv   pre-print
It computationally compares their use in both the sequential and non-sequential settings through a collection of two-stage stochastic linear programs with different characteristics.  ...  , AV and LHS sequential procedures present attractive alternatives in practice for a class of stochastic programs.  ...  All test problems are two-stage stochastic linear programs with recourse, and they all satisfy (A SP ).  ... 
arXiv:2005.02458v2 fatcat:sv6g3oht5zhwdgmxvqrwnv34b4

Distributionally Robust Optimization: A review on theory and applications

Fengming Lin, Xiaolei Fang, Zheming Gao
2022 Numerical Algebra, Control and Optimization  
<p style='text-indent:20px;'>In this paper, we survey the primary research on the theory and applications of distributionally robust optimization (DRO).  ...  We start with reviewing the modeling power and computational attractiveness of DRO approaches, induced by the ambiguity sets structure and tractable robust counterpart reformulations.  ...  Acknowledgement The authors are grateful to the editors and referees for their valuable comments and suggestions, which have significantly improved the quality of this paper.  ... 
doi:10.3934/naco.2021057 fatcat:cluvjzkrhfbc7o2446fhjrmbji

A multi-stage stochastic programming approach in master production scheduling

Ersin Körpeoğlu, Hande Yaman, M. Selim Aktürk
2011 European Journal of Operational Research  
We use a multi-stage stochastic programming approach in order to come up with the maximum expected profit given the demand scenarios.  ...  The classical approach for generating MPS assumes infinite capacity, fixed processing times, and a single scenario for demand forecasts.  ...  Huang and Ahmed (2009) provide analytical bounds for the value of multi-stage stochastic programming over the two-stage approach for a general class of capacity planning problems under uncertainty.  ... 
doi:10.1016/j.ejor.2011.02.032 fatcat:otdccdvvynbtzgemaiet3azm7a

A stochastic programming model for scheduling call centers with global Service Level Agreements

Thomas R. Robbins, Terry P. Harrison
2010 European Journal of Operational Research  
Our model has two distinctive features. Firstly, we combine the server sizing and staff scheduling into a single optimization program.  ...  We show that the stochastic formulation in general calculates a higher cost optimal schedule than a model which ignores variability, but that the expected cost of this schedule is lower.  ...  In some of our empirical analysis we found that over 80% of the abandonment in a 24 hour day occurred in a two hour window. We formulate the model as a two stage mixed integer stochastic program.  ... 
doi:10.1016/j.ejor.2010.06.013 fatcat:ztlb2vjsevf45dpzume4mjtjkm

Optimal scenario tree reductions for the stochastic Unit Commitment Problem

Ali Koc, Soumyadip Ghosh
2012 Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC)  
Scenario tree reductions of multi-period stochastic processes have been used as an important technique in obtaining good approximate solutions of multi-period convex stochastic programs.  ...  The scenario reduction step is aimed often at optimal approximation of the underlying stochastic process.  ...  LIMITATIONS OF SCENARIO-TREE REDUCTION APPROACHES The procedures described in this article approximate the optimal solution of original multi-stage stochastic program (1) by solving the same problem for  ... 
doi:10.1109/wsc.2012.6465238 dblp:conf/wsc/KocG12 fatcat:reqkjq4ctvbwbkzvufdtijjt7u

A scalable solution framework for stochastic transmission and generation planning problems

Francisco D. Munoz, Jean-Paul Watson
2015 Computational Management Science  
Although convergence of PH to an optimal solution is not guaranteed for mixed-integer linear optimization models, we find that it is possible to obtain solutions with acceptable optimality gaps for practical  ...  The resulting stochastic optimization model is decomposed on a scenario basis and solved using a variant of the Progressive Hedging (PH) algorithm.  ...  The specialization of this approach for stochastic programs is known as the L-shaped method [10] .  ... 
doi:10.1007/s10287-015-0229-y fatcat:j3a672fnofelnc3xejgmlevkyu

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.  ...  , the problem reduces to a two-stage multiperiod stochastic program.  ... 
doi:10.1007/s001860050097 fatcat:wfe555gf2bdpvegckoytu2srqm

Electric sector capacity planning under uncertainty: Climate policy and natural gas in the US

John E. Bistline
2015 Energy Economics  
Using a two-stage stochastic programming approach, model results suggest that the two most critical risks in the nearterm planning process of the uncertainties considered here are natural gas prices and  ...  The stochastic solution is especially valuable if decision-makers do not sufficiently account for the potential of climate constraints in future decades or if fuel price projections are outdated.  ...  The views expressed in this paper do not necessarily reflect those of EPRI or its members. Morgan, M.G., Henrion, M., 1990  ... 
doi:10.1016/j.eneco.2015.07.008 fatcat:ydohgvcaxrhzxdmwkaeqbj2bei
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