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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: In this article, an interactive procedure is described to obtain a best compromise for such a MOSLP problem, which involves in particular, the concepts of stochastic programming with recourse, and the efficiency projection techniques are used to provide the decisionmaker with detailed graphical information on efficient solution families.

150 citations

Proceedings ArticleDOI
08 May 2002
TL;DR: In this paper, an approach based on stochastic dynamic programming is proposed to develop optimal operating policies for automotive powertrain systems, aiming to minimize fuel consumption and tailpipe emissions.
Abstract: An approach based on stochastic dynamic programming is proposed to develop optimal operating policies for automotive powertrain systems. The goal is to minimize fuel consumption and tailpipe emissions. Unlike in the conventional approach, the minimization is performed not for a predetermined drive cycle, but in a stochastic "average" sense over a class of trajectories from an underlying Markov chain drive cycle generator. The objective of this paper is to introduce the approach and illustrate its applications. with several examples.

150 citations

Journal ArticleDOI
TL;DR: This work considers the problem of determining (for a short lifecycle) retail product initial and replenishment order quantities that minimize the cost of lost sales, back orders, and obsolete inventory, and proposes a heuristic, establishes conditions under which the heuristic finds an optimal solution, and reports results of the application at a catalog retailer.
Abstract: We consider the problem of determining (for a short lifecycle) retail product initial and replenishment order quantities that minimize the cost of lost sales, back orders, and obsolete inventory. We model this problem as a two-stage stochastic dynamic program, propose a heuristic, establish conditions under which the heuristic finds an optimal solution, and report results of the application of our procedure at a catalog retailer. Our procedure improves on the existing method by enough to double profits. In addition, our method can be used to choose the optimal reorder time, to quantify the benefit of leadtime reduction, and to choose the best replenishment contract.

150 citations

Journal ArticleDOI
TL;DR: This paper describes a method for estimating the future value function by multivariate adaptive regression splines (MARS) fit over a discretization scheme based on orthogonal array (OA) experimental designs and shows that this method is accurately able to solve higher dimensional SDP problems than previously possible.
Abstract: In stochastic dynamic programming (SDP) with continuous state and decision variables, the future value function is computed at discrete points in the state spac e. Interpolation can be used to approximate the values of the future value function between these discrete points. However, for large dimensional problems the number of discrete points required to obtain a good approximation of the future value function can be prohibitively large. Statistical methods of experimental design and function estimation may be employed to overcome this "curse of dimensionality." In this paper, we describe a method for estimating the future value function by multivariate adaptive regression splines (MARS) fit over a discretization scheme based on orthogonal array (OA) experimental designs. Because orthogonal arrays only grow polynomially in the state-space dimension, our OA/MARS method is accurately able to solve higher dimensional SDP problems than previously possible. To our knowledge, the most efficient method published prior to this work employs tensor-product cubic splines to approximate the future value function (Johnson et al. 1993). The computational advantages of OA/MA RS are demonstrated in comparisons with the method using tensor-product cubic splines for applications of an inventory forecasting SDP with up to nine state variables computed on a small workstation. In particular, the storage of an adequate tensor-product cubic spline for six dimensions exceeds the memory of our workstation, and the run time for an accurate OA/MARS SDP solution would be at least an order of magnitude faster than using tensor-product cubic splines for higher than six dimensions.

150 citations

Journal ArticleDOI
TL;DR: This paper considers production planning when inputs have different and uncertain quality levels, and there are capacity constraints, and formulate the problem as a stochastic program that can be solved easily using Cplex.
Abstract: In this paper, we consider production planning when inputs have different and uncertain quality levels, and there are capacity constraints. This situation is typical of most remanufacturing environments, where inputs are product returns (also called cores). Production (remanufacturing) cost increases as the quality level decreases, and any unused cores may be salvaged at a value that increases with their quality level. Decision variables include, for each period and under a certain probabilistic scenario, the amount of cores to grade, the amount to remanufacture for each quality level, and the amount of inventory to carry over for future periods for ungraded cores, graded cores, and finished remanufactured products. Our model is grounded with data collected at a major original equipment manufacturer that also remanufactures. We formulate the problem as a stochastic program; although it is a large linear program, it can be solved easily using Cplex. We provide a numeric study to generate insights into the nature of the solution.

150 citations


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