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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: The approach adopted in this paper applies not only to optimization, but also to generic decision problems where the solution is obtained according to a rule that is not necessarily the optimization of a cost function.
Abstract: The scenario approach is a general methodology for data-driven optimization that has attracted a great deal of attention in the past few years. It prescribes that one collects a record of previous cases (scenarios) from the same setup in which optimization is being conducted and makes a decision that attains optimality for the seen cases. Scenario optimization is by now very well understood for convex problems, where a theory exists that rigorously certifies the generalization properties of the solution, that is, the ability of the solution to perform well in connection to new situations. This theory supports the scenario methodology and justifies its use. This paper considers nonconvex problems. While other contributions in the nonconvex setup already exist, we here take a major departure from previous approaches. We suggest that the generalization level is evaluated only after the solution is found and its complexity in terms of the length of a support subsample (a notion precisely introduced in this paper) is assessed. As a consequence, the generalization level is stochastic and adjusted case by case to the available scenarios. This fact is key to obtain tight results. The approach adopted in this paper applies not only to optimization, but also to generic decision problems where the solution is obtained according to a rule that is not necessarily the optimization of a cost function. Accordingly, in our presentation we adopt a general stance of which optimization is just seen as a particular case.

138 citations

Journal ArticleDOI
TL;DR: In this article, a multi-product, multi-period production planning problem with uncertainty in the quality of raw materials and consequently in processes yields, as well as uncertainty in products demands is studied.
Abstract: Motivated by the challenges encountered in sawmill production planning, we study a multi-product, multi-period production planning problem with uncertainty in the quality of raw materials and consequently in processes yields, as well as uncertainty in products demands. As the demand and yield own different uncertain natures, they are modelled separately and then integrated. Demand uncertainty is considered as a dynamic stochastic data process during the planning horizon, which is modelled as a scenario tree. Each stage in the demand scenario tree corresponds to a cluster of time periods, for which the demand has a stationary behaviour. The uncertain yield is modelled as scenarios with stationary probability distributions during the planning horizon. Yield scenarios are then integrated in each node of the demand scenario tree, constituting a hybrid scenario tree. Based on the hybrid scenario tree for the uncertain yield and demand, a multi-stage stochastic programming (MSP) model is proposed which is full ...

138 citations

Journal ArticleDOI
TL;DR: This work develops a detailed formal description of project portfolio management as a multistage stochastic integer program with endogenous uncertainty, and proposes an efficient solution approach, which involves the development of a formulation technique that is amenable to scenario decomposition.

137 citations

01 Jan 2008
TL;DR: This tutorial discusses a fam- ily valid inequalities for a integer programming formulations for a special but large class of chance-constrained problems that have demonstrated significant computa- tional advantages.
Abstract: Various applications in reliability and risk management give rise to optimization prob- lems with constraints involving random parameters, which are required to be satisfied with a prespecified probability threshold. There are two main difficulties with such chance-constrained problems. First, checking feasibility of a given candidate solution exactly is, in general, impossible because this requires evaluating quantiles of random functions. Second, the feasible region induced by chance constraints is, in general, nonconvex, leading to severe optimization challenges. In this tutorial, we discuss an approach based on solving approximating problems using Monte Carlo samples of the random data. This scheme can be used to yield both feasible solutions and statistical optimality bounds with high confidence using modest sample sizes. The approximat- ing problem is itself a chance-constrained problem, albeit with a finite distribution of modest support, and is an NP-hard combinatorial optimization problem. We adopt integer-programming-based methods for its solution. In particular, we discuss a fam- ily valid inequalities for a integer programming formulations for a special but large class of chance-constrained problems that have demonstrated significant computa- tional advantages.

137 citations

Journal ArticleDOI
TL;DR: For a particular class of minimax stochastic programming models, it is shown that the problem can be equivalently reformulated into a standard stochastics programming problem, which permits the direct use of standard decomposition and sampling methods developed for stochastically programming.
Abstract: For a particular class of minimax stochastic programming models, we show that the problem can be equivalently reformulated into a standard stochastic programming problem. This permits the direct use of standard decomposition and sampling methods developed for stochastic programming. We also show that this class of minimax stochastic programs is closely related to a large family of mean-risk stochastic programs where risk is measured in terms of deviations from a quantile.

137 citations


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