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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: Computational results on a real-life case study demonstrate the proposed optimization tools’ applicability as well as the effect of disruption risk and sustainability dimensions on biofuel SC planning.
Abstract: We focus on design and planning of a biofuel supply chain (SC) network from biomass to demand centers where biomass supply is stochastic and seasonal, and facilities’ capacity varies randomly because of possible disruptions. We propose a cost-efficient multi-stage stochastic program in which the greenhouse gas emissions are mitigated and the social impact of the SC is considered. A rolling horizon procedure is presented to implement and evaluate the stochastic model solution. Computational results on a real-life case study demonstrate the proposed optimization tools’ applicability as well as the effect of disruption risk and sustainability dimensions on biofuel SC planning.

111 citations

Journal ArticleDOI
TL;DR: The scenario-based optimization approach provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled outcomes of the uncertainty ( ``scenarios'').
Abstract: The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled outcomes of the uncertainty (`scenarios'). A key merit of this approach is that it neither assumes knowledge of the uncertainty set, as it is common in robust optimization, nor of its probability distribution, as it is usually required in stochastic optimization. Moreover, the scenario approach is computationally efficient as its solution is based on a deterministic optimization program that is canonically convex, even when the original chance-constrained problem is not. Recently, researchers have obtained theoretical foundations for the scenario approach, providing a direct link between the number of scenarios and bounds on the constraint violation probability. These bounds are tight in the general case of an uncertain optimization problem with a single chance constraint. However, this paper shows that these bounds can be improved in situations where the constraints have a limited `support rank', a new concept that is introduced for the first time. This property is typically found in a large number of practical applications---most importantly, if the problem originally contains multiple chance constraints (e.g. multi-stage uncertain decision problems), or if a chance constraint belongs to a special class of constraints (e.g. linear or quadratic constraints). In these cases the quality of the scenario solution is improved while the same bound on the constraint violation probability is maintained, and also the computational complexity is reduced.

110 citations

Journal ArticleDOI
TL;DR: In this paper, a risk-averse stochastic modeling approach for a pre-disaster relief network design problem under uncertain demand and transportation capacities is introduced, where the sizes and locations of the response facilities and the inventory levels of relief supplies at each facility are determined while guaranteeing a certain level of network reliability.
Abstract: This article introduces a risk-averse stochastic modeling approach for a pre-disaster relief network design problem under uncertain demand and transportation capacities. The sizes and locations of the response facilities and the inventory levels of relief supplies at each facility are determined while guaranteeing a certain level of network reliability. A probabilistic constraint on the existence of a feasible flow is introduced to ensure that the demand for relief supplies across the network is satisfied with a specified high probability. Responsiveness is also accounted for by defining multiple regions in the network and introducing local probabilistic constraints on satisfying demand within each region. These local constraints ensure that each region is self-sufficient in terms of providing for its own needs with a large probability. In particular, the Gale–Hoffman inequalities are used to represent the conditions on the existence of a feasible network flow. The solution method rests on two pillars. A ...

110 citations

Journal ArticleDOI
TL;DR: A Branch-and-Fix Coordi- nation approach is introduced for coordinating the selection of the branching nodes and branching variables in the scenario subproblems to be jointly optimized.

110 citations

Journal ArticleDOI
TL;DR: Recent advances in deterministic methods for solving signomial programming problems and mixed-integer nonlinear programming problems are introduced and important applications of these methods are reviewed to reveal the usefulness of the optimization methods.
Abstract: With the increasing reliance on modeling optimization problems in practical applications, a number of theoretical and algorithmic contributions of optimization have been proposed. The approaches developed for treating optimization problems can be classified into deterministic and heuristic. This paper aims to introduce recent advances in deterministic methods for solving signomial programming problems and mixed-integer nonlinear programming problems. A number of important applications in engineering and management are also reviewed to reveal the usefulness of the optimization methods.

110 citations


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