Topic
Stochastic programming
About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.
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01 Dec 1992
TL;DR: It is shown how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo sampling techniques.
Abstract: For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving two-stage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multi-computer and derive the theory for solving a general class of multi-stage problems with dependency of the stochastic parameters within a stage and between different stages.
250 citations
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TL;DR: A scheme based on a blending of classical Benders decomposition techniques and a special technique, called importance sampling, is used to solve this general class of multi-stochastic linear programs.
Abstract: The paper demonstrates how multi-period portfolio optimization problems can be efficiently solved as multi-stage stochastic linear programs. A scheme based on a blending of classical Benders decomposition techniques and a special technique, called importance sampling, is used to solve this general class of multi-stochastic linear programs. We discuss the case where stochastic parameters are dependent within a period as well as between periods. Initial computational results are presented.
249 citations
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TL;DR: The objective of this research is to propose a manufacturing/remanufacturing policy that would minimize the sum of the holding and backlog costs for manufacturing and remanufacturing products.
249 citations
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TL;DR: This paper proposes tractable methods of addressing a general class of multistage stochastic optimization problems, which assume only limited information of the distributions of the underlying uncertainties, such as known mean, support, and covariance, and proposes several new decision rules that improve upon linear decision rules, while keeping the approximate models computationally tractable.
Abstract: Stochastic optimization, especially multistage models, is well known to be computationally excruciating. Moreover, such models require exact specifications of the probability distributions of the underlying uncertainties, which are often unavailable. In this paper, we propose tractable methods of addressing a general class of multistage stochastic optimization problems, which assume only limited information of the distributions of the underlying uncertainties, such as known mean, support, and covariance. One basic idea of our methods is to approximate the recourse decisions via decision rules. We first examine linear decision rules in detail and show that even for problems with complete recourse, linear decision rules can be inadequate and even lead to infeasible instances. Hence, we propose several new decision rules that improve upon linear decision rules, while keeping the approximate models computationally tractable. Specifically, our approximate models are in the forms of the so-called second-order cone (SOC) programs, which could be solved efficiently both in theory and in practice. We also present computational evidence indicating that our approach is a viable alternative, and possibly advantageous, to existing stochastic optimization solution techniques in solving a two-stage stochastic optimization problem with complete recourse.
248 citations
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26 Oct 2013TL;DR: This work presents two algorithms whose reward is close to the information-theoretic optimum: one is based on a novel "balanced exploration" paradigm, while the other is a primal-dual algorithm that uses multiplicative updates that is optimal up to polylogarithmic factors.
Abstract: Multi-armed bandit problems are the predominant theoretical model of exploration-exploitation tradeoffs in learning, and they have countless applications ranging from medical trials, to communication networks, to Web search and advertising. In many of these application domains the learner may be constrained by one or more supply (or budget) limits, in addition to the customary limitation on the time horizon. The literature lacks a general model encompassing these sorts of problems. We introduce such a model, called "bandits with knapsacks", that combines aspects of stochastic integer programming with online learning. A distinctive feature of our problem, in comparison to the existing regret-minimization literature, is that the optimal policy for a given latent distribution may significantly outperform the policy that plays the optimal fixed arm. Consequently, achieving sub linear regret in the bandits-with-knapsacks problem is significantly more challenging than in conventional bandit problems. We present two algorithms whose reward is close to the information-theoretic optimum: one is based on a novel "balanced exploration" paradigm, while the other is a primal-dual algorithm that uses multiplicative updates. Further, we prove that the regret achieved by both algorithms is optimal up to polylogarithmic factors. We illustrate the generality of the problem by presenting applications in a number of different domains including electronic commerce, routing, and scheduling. As one example of a concrete application, we consider the problem of dynamic posted pricing with limited supply and obtain the first algorithm whose regret, with respect to the optimal dynamic policy, is sub linear in the supply.
247 citations