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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: It is demonstrated that for a certain class of convex stochastic programs these bounds are comparable in quality with similar bounds computed by the sample average approximation method, while their computational cost is considerably smaller.
Abstract: The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing stochastic approximation (SA) type algorithms. To this end we show that while running a Mirror Descent Stochastic Approximation procedure one can compute, with a small additional effort, lower and upper statistical bounds for the optimal objective value. We demonstrate that for a certain class of convex stochastic programs these bounds are comparable in quality with similar bounds computed by the sample average approximation method, while their computational cost is considerably smaller.

151 citations

Posted Content
TL;DR: In this article, the problem of managing demand risk in tactical supply chain planning for a particular global consumer electronics company is considered, where the company follows a deterministic replenishment-and-planning process despite considerable demand uncertainty.
Abstract: We consider the problem of managing demand risk in tactical supply chain planning for a particular global consumer electronics company. The company follows a deterministic replenishment-and-planning process despite considerable demand uncertainty. As a possible way to formally address uncertainty, we provide two risk measures, “demand-at-risk” (DaR) and “inventory-at-risk” (IaR) and two linear programming models to help manage demand uncertainty. The first model is deterministic and can be used to allocate the replenishment schedule from the plants among the customers as per the existing process. The other model is stochastic and can be used to determine the “ideal” replenishment request from the plants under demand uncertainty. The gap between the output of the two models as regards requested replenishment and the values of the risk measures can be used by the company to reallocate capacity among different products and to thus manage demand/inventory risk.

151 citations

Journal ArticleDOI
TL;DR: The paper presents computational results that were obtained by employing a Rolling Horizon Procedure to simulate the operation of the truckload carrier and indicates the superiority of the new algorithm over other approaches tested.
Abstract: The Stochastic Dynamic Vehicle Allocation problem involves managing a fleet of vehicles over time in an uncertain demand environment to maximize expected total profits. The problem is formulated as a Stochastic Programming problem. A new heuristic algorithm is developed and is contrasted to various deterministic approximations. The paper presents computational results that were obtained by employing a Rolling Horizon Procedure to simulate the operation of the truckload carrier. Results indicate the superiority of the new algorithm over other approaches tested.

151 citations

Journal ArticleDOI
TL;DR: An optimal dynamic solution is presented that simplifies the structure of the control mechanism by exercising ground-holding on groups of aircraft instead of individual flights by using stochastic linear programming with recourse.
Abstract: Existing probabilistic solutions to the ground-holding problem in air traffic control are of a static nature, with ground-holds assigned to aircraft at the beginning of daily operations. In this paper we present an optimal dynamic solution that simplifies the structure of the control mechanism by exercising ground-holding on groups of aircraft instead of individual flights. Using stochastic linear programming with recourse, we have been able to solve problem instances for one of the largest airports in the U.S. with just a powerful PC. We illustrate the advantage of the probabilistic dynamic solution over: (a) the static solution; (b) a deterministic solution; and (c) the passive strategy of no ground-holding.

151 citations

Journal ArticleDOI
TL;DR: The problem of finding valuable scenario approximations can be viewed as the problem of optimally approximating a given distribution with some distance function and it is shown that for Lipschitz continuous cost/profit functions it is best to employ the Wasserstein distance.
Abstract: The quality of multi-stage stochastic optimization models as they appear in asset liability management, energy planning, transportation, supply chain management, and other applications depends heavily on the quality of the underlying scenario model, describing the uncertain processes influencing the profit/cost function, such as asset prices and liabilities, the energy demand process, demand for transportation, and the like. A common approach to generate scenarios is based on estimating an unknown distribution and matching its moments with moments of a discrete scenario model. This paper demonstrates that the problem of finding valuable scenario approximations can be viewed as the problem of optimally approximating a given distribution with some distance function. We show that for Lipschitz continuous cost/profit functions it is best to employ the Wasserstein distance. The resulting optimization problem can be viewed as a multi-dimensional facility location problem, for which at least good heuristic algorithms exist. For multi-stage problems, a scenario tree is constructed as a nested facility location problem. Numerical convergence results for financial mean-risk portfolio selection conclude the paper.

151 citations


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