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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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Journal ArticleDOI
TL;DR: By leveraging the combination of a high-level programming language (Python) and the embedding of the base deterministic model in that language (Pyomo), the package is able to provide completely generic and highly configurable solver implementations.
Abstract: Although stochastic programming is a powerful tool for modeling decision-making under uncertainty, various impediments have historically prevented its wide-spread use. One factor involves the ability of non-specialists to easily express stochastic programming problems as extensions of their deterministic counterparts, which are typically formulated first. A second factor relates to the difficulty of solving stochastic programming models, particularly in the mixed-integer, non-linear, and/or multi-stage cases. Intricate, configurable, and parallel decomposition strategies are frequently required to achieve tractable run-times on large-scale problems. We simultaneously address both of these factors in our PySP software package, which is part of the Coopr open-source Python repository for optimization; the latter is distributed as part of IBM’s COIN-OR repository. To formulate a stochastic program in PySP, the user specifies both the deterministic base model (supporting linear, non-linear, and mixed-integer components) and the scenario tree model (defining the problem stages and the nature of uncertain parameters) in the Pyomo open-source algebraic modeling language. Given these two models, PySP provides two paths for solution of the corresponding stochastic program. The first alternative involves passing an extensive form to a standard deterministic solver. For more complex stochastic programs, we provide an implementation of Rockafellar and Wets’ Progressive Hedging algorithm. Our particular focus is on the use of Progressive Hedging as an effective heuristic for obtaining approximate solutions to multi-stage stochastic programs. By leveraging the combination of a high-level programming language (Python) and the embedding of the base deterministic model in that language (Pyomo), we are able to provide completely generic and highly configurable solver implementations. PySP has been used by a number of research groups, including our own, to rapidly prototype and solve difficult stochastic programming problems.

125 citations

Journal ArticleDOI
TL;DR: Two new stochastic linear programming formulations of appointment scheduling problems that are motivated by the management of health services, where customers are scheduled dynamically, one at a time, as they request appointments, are formulated.
Abstract: We formulate and solve two new stochastic linear programming formulations of appointment scheduling problems that are motivated by the management of health services. We assume that service durations and the number of customers to be served on a particular day are uncertain. In the first model, customers may fail to show up for their appointments “no-show”. This model is formulated as a two-stage stochastic linear program. In the second model, customers are scheduled dynamically, one at a time, as they request appointments. This model is formulated as a multistage stochastic linear program with stages defined by customer appointment requests. We analyze the structure of the models and adapt decomposition-based algorithms to solve the problems efficiently. We present numerical results that illustrate the impact of uncertainty on dynamic appointment scheduling, and we identify useful insights that can be applied in practice. We also present a case study based on real data for an outpatient procedure center.

125 citations

Journal ArticleDOI
TL;DR: In this article, a stochastic averaging-based nonlinear feedback control strategy was proposed for a randomly excited structural system and the control forces were divided into conservative and dissipative parts.
Abstract: A strategy for optimal nonlinear feedback control of randomlyexcited structural systems is proposed based on the stochastic averagingmethod for quasi-Hamiltonian systems and the stochastic dynamicprogramming principle. A randomly excited structural system isformulated as a quasi-Hamiltonian system and the control forces aredivided into conservative and dissipative parts. The conservative partsare designed to change the integrability and resonance of the associatedHamiltonian system and the energy distribution among the controlledsystem. After the conservative parts are determined, the system responseis reduced to a controlled diffusion process by using the stochasticaveraging method. The dissipative parts of control forces are thenobtained from solving the stochastic dynamic programming equation. Boththe responses of uncontrolled and controlled structural systems can bepredicted analytically. Numerical results for a controlled andstochastically excited Duffing oscillator and a two-degree-of-freedomsystem with linear springs and linear and nonlinear dampings, show thatthe proposed control strategy is very effective and efficient.

124 citations

Book ChapterDOI
01 Jan 2007
TL;DR: The paper starts with decribing how to model natural gas transportation and storage, and at the end it presents a stochastic portfolio optimization model for the natural gas value chain in a liberalized market.
Abstract: In this paper we give an introduction to modelling the natural gas value chain including production, transportation, processing, contracts, and markets. The presentation gives insight in the complexity of planning in the natural gas supply chain and how optimization can help decision makers in a natural gas company coordinate the different activities. We present an integrated view from the perspective of an upstream company. The paper starts with decribing how to model natural gas transportation and storage, and at the end we present a stochastic portfolio optimization model for the natural gas value chain in a liberalized market.

124 citations

01 Jan 2005
TL;DR: This paper presents an introduction to stochastic programming models and methodology at a level that is intended to be accessible to the breadth of members within the INFORMS community.
Abstract: Stochastic Programming (SP) was first introduced by George Dantzig in the 1950's. Since that time, tremendous progress toward an understanding of properties of SP models and the design of algorithmic approaches for solving them has been made. As a result, SP is gaining recognition as a viable approach for large scale models of decisions under uncertainty. In this paper, we present an introduction to stochastic programming models and methodology at a level that is intended to be accessible to the breadth of members within the INFORMS community.

124 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532