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 Jan 2004TL;DR: This book emphasises the dos and don'ts of stochastic calculus, cautioning the reader that certain results and intuitions cherished by many economists do not extend to stochastics models.
Abstract: List of figures Preface 1. Probability theory 2. Wiener processes 3. Stochastic calculus 4. Stochastic dynamic programming 5. How to solve it 6. Boundaries and absorbing barriers Appendix. Miscellaneous applications and exercises Bibliography Index.
129 citations
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29 Jul 2010
TL;DR: This work presents a generalization of the classic Differential Dynamic Programming algorithm that assumes the existence of state and control multiplicative process noise, and proceeds to derive the second-order expansion of the cost-to-go.
Abstract: Although there has been a significant amount of work in the area of stochastic optimal control theory towards the development of new algorithms, the problem of how to control a stochastic nonlinear system remains an open research topic. Recent iterative linear quadratic optimal control methods iLQG [1], [2] handle control and state multiplicative noise while they are derived based on first order approximation of dynamics. On the other hand, methods such as Differential Dynamic Programming expand the dynamics up to the second order but so far they can handle nonlinear systems with additive noise. In this work we present a generalization of the classic Differential Dynamic Programming algorithm. We assume the existence of state and control multiplicative process noise, and proceed to derive the second-order expansion of the cost-to-go. We find the correction terms that arise from the stochastic assumption. Despite having quartic and cubic terms in the initial expression, we show that these vanish, leaving us with the same quadratic structure as standard DDP.
129 citations
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18 Jul 1996
TL;DR: Stochastic Programming Models with Probability and Quantile Objective Functions and Methods and Algorithms for Solving Probabilistic Problems.
Abstract: Stochastic Programming Models with Probability and Quantile Objective Functions. Basic Properties of Probabilistic Problems. Estimates and Bounds for Probabilities and Quantiles. Methods and Algorithms for Solving Probabilistic Problems. Notation List. Index.
129 citations
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TL;DR: The approach provides a theoretical justification for the widely held maxim that adding a small number of links to the process flexibility structure can significantly enhance the ability of the system to match (fixed) production capacity with (random) demand.
Abstract: The concept of chaining, or in more general terms, sparse process structure, has been extremely influential in the process flexibility area, with many large automakers already making this the cornerstone of their business strategies to remain competitive in the industry. The effectiveness of the process strategy, using chains or other sparse structures, has been validated in numerous empirical studies. However, to the best of our knowledge, there have been relatively few concrete analytical results on the performance of such strategies vis-a-vis the full flexibility system, especially when the system size is large or when the demand and supply are asymmetrical. This paper is an attempt to bridge this gap.
We study the problem from two angles: (1) For the symmetrical system where the (mean) demand and plant capacity are balanced and identical, we utilize the concept of a generalized random walk to evaluate the asymptotic performance of the chaining structure in this environment. We show that a simple chaining structure performs surprisingly well for a variety of realistic demand distributions, even when the system size is large. (2) For the more general problem, we identify a class of conditions under which only a sparse flexible structure is needed so that the expected performance is already within e optimality of the full flexibility system.
Our approach provides a theoretical justification for the widely held maxim: In many practical situations, adding a small number of links to the process flexibility structure can significantly enhance the ability of the system to match (fixed) production capacity with (random) demand.
129 citations
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TL;DR: This study carefully examines the trade-off between computation time and the aggregation level of demand uncertainty with examples of a multi-leg flight and a single-hub network.
129 citations