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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: This approach relaxes the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and imposes a “penalty” that punishes violations of nonant anticipativity.
Abstract: We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a “penalty” that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values.

228 citations

BookDOI
01 Jan 1996
TL;DR: The problem of optimal decisions can be seen as getting simulation and optimization effectively combined, and Optimization of Stochastic Models: The Interface Between Simulation andoptimization is suitable as a text for a graduate level course on Stochastics, or as a secondary text for an undergraduate level course in Operations Research.
Abstract: Stochastic models are everywhere. In manufacturing, queuing models are used for modeling production processes, realistic inventory models are stochastic in nature. Stochastic models are considered in transportation and communication. Marketing models use stochastic descriptions of the demands and buyer's behaviors. In finance, market prices and exchange rates are assumed to be certain stochastic processes, and insurance claims appear at random times with random amounts. To each decision problem, a cost function is associated. Costs may be direct or indirect, like loss of time, quality deterioration, loss in production or dissatisfaction of customers. In decision making under uncertainty, the goal is to minimize the expected costs. However, in practically all realistic models, the calculation of the expected costs is impossible due to the model complexity. Simulation is the only practicable way of getting insight into such models. Thus, the problem of optimal decisions can be seen as getting simulation and optimization effectively combined. The field is quite new and yet the number of publications is enormous. This book does not even try to touch all work done in this area. Instead, many concepts are presented and treated with mathematical rigor and necessary conditions for the correctness of various approaches are stated. Optimization of Stochastic Models: The Interface Between Simulation and Optimization is suitable as a text for a graduate level course on Stochastic Models or as a secondary text for a graduate level course in Operations Research.

228 citations

Journal ArticleDOI
TL;DR: Multivariate verification tools, as well as diagnostic approaches based on event-based verification are presented, and their application to the evaluation of various sets of scenarios of short-term wind power generation demonstrates them as valuable discrimination tools.

228 citations

Journal ArticleDOI
TL;DR: An algorithm for calculating optimal operating strategies in a multi-reservoir hydroelectric system, which can take into account inflow stochasticity and does not require discretization of the state space is described.

228 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a stochastic dynamic programming model that captures the essential elements of this problem, and a numerical example further demonstrates the optimal mode switching decision rules, where the value derived from the ability to better cope with uncertainty is considered.
Abstract: The author studies the topical issue of flexible manufacturing system (FMS) justification. He contends that current evaluation methods fall short of capturing a key advantage of an FMS: the value of flexibility. He identifies various benefits of FMS that arise from the ability to switch between modes of production, and in particular, he models the value derived from the ability to better cope with uncertainty. A model to capture this value must solve for the value of flexibility together with the dynamic operating schedule of the production process. He presents a stochastic dynamic programming model that captures the essential elements of this problem. A numerical example further demonstrates the optimal mode switching decision rules. >

227 citations


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