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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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TL;DR: In this paper, the convergence of ordinal comparison has been studied in the context of regenerative simulations and it has been shown that ordinal contrast converges monotonically in the case of averaging normal random variables.
Abstract: Recent research has demonstrated that ordinal comparison has fast convergence despite the possible presence of large estimation noise in the design of discrete event dynamic systems. In this paper, we address the fundamental problem of characterizing the convergence of ordinal comparison. To achieve this goal, an indicator process is formulated and its properties are examined. For several performance measures frequently used in simulation, the rate of convergence for the indicator process is proven to be exponential for regenerative simulations. Therefore, the fast convergence of ordinal comparison is supported and explained in a rigorous framework. Many performance measures of averaging type have asymptotic normal distributions. The results of this paper show that ordinal comparison converges monotonically in the case of averaging normal random variables. Such monotonicity is useful in simulation planning.

154 citations

Journal ArticleDOI
TL;DR: A stochastic programming approach to solve a multi-period multi-product multi-site aggregate production planning problem in a green supply chain for a medium-term planning horizon under the assumption of demand uncertainty.

154 citations

Journal ArticleDOI
TL;DR: The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure.
Abstract: Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

154 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduce an efficient stochastic dynamic programming model to optimally charge an electric vehicle while accounting for the uncertainty inherent to its use, and show that the randomness intrinsic to driving needs has a substantial impact on the charging strategy to be implemented.

153 citations

Book
18 Aug 2011
TL;DR: In this article, it was shown that if performance measures in stochastic and dynamic scheduling problems satisfy generalized conservation laws, then the feasible region of achievable performance is a polyhedron called an extended polymatroid that generalizes the classical polymatroids introduced by Edmonds.
Abstract: We show that if performance measures in stochastic and dynamic scheduling problems satisfy generalized conservation laws, then the feasible region of achievable performance is a polyhedron called an extended polymatroid, that generalizes the classical polymatroids introduced by Edmonds. Optimization of a linear objective over an extended polymatroid is solved by an adaptive greedy algorithm, which leads to an optimal solution having an indexability property indexable systems. Under a certain condition the indices possess a stronger decomposition property decomposable systems. The following problems can be analyzed using our theory: multiarmed bandit problems, branching bandits, scheduling of multiclass queues with or without feedback, scheduling of a batch of jobs. Consequences of our results include: 1 a characterization of indexable systems as systems that satisfy generalized conservation laws, 2 a sufficient condition for indexable systems to be decomposable, 3 a new linear programming proof of the decomposability property of Gittins indices in multiarmed bandit problems, 4 an approach to sensitivity analysis of indexable systems, 5 a characterization of the indices of indexable systems as sums of dual variables, and an economic interpretation of the branching bandit indices in terms of retirement options, 6 an analysis of the indexability of undiscounted branching bandits, 7 a new algorithm to compute the indices of indexable systems in particular Gittins indices, as fast as the fastest known algorithm, 8 a unification of Klimov's algorithm for multiclass queues and Gittms' algorithm for multiarmed bandits as special cases of the same algorithm, 9 a closed formula for the maximum reward of the multiarmed bandit problem, with a new proof of its submodularity and 10 an understanding of the invariance of the indices with respect to some parameters of the problem. Our approach provides a polyhedral treatment of several classical problems in stochastic and dynamic scheduling and is able to address variations such as: discounted versus undiscounted cost criterion, rewards versus taxes, discrete versus continuous time, and linear versus nonlinear objective functions.

153 citations


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