Topic
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 authors investigated a production planning problem in a periodic review environment with variable production capacity, random yields, and uncertain demand, and they proved that the objective function is quasi-convex and that the structure of the optimal policy is characterized by a single critical point for the initial stock level at each period.
Abstract: We investigate a production planning problem in a periodic review environment with variable production capacity, random yields, and uncertain demand. The implications of random yields and variable capacity for lot sizing previously have been explored separately, but not jointly. Many production environments are likely to be subject to both types of uncertainties. To minimize the total discounted expected costs production, holding, and shortage costs, we formulate the problem as a stochastic dynamic program. For the finite-horizon problem, we prove that the objective function is quasi-convex and that the structure of the optimal policy is characterized by a single critical point for the initial stock level at each period. That is, if the initial stock is greater than this critical point, the optimal planned production is zero; otherwise, it is greater than zero. Expressions for solving the critical point and the optimal planned production are obtained. We further show that the solution for the finite-horizon problem converges to that of the infinite-horizon problem.
225 citations
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01 Nov 1969
TL;DR: A unifying framework of concepts central to the optimization of large structured systems is developed and used in the organization of the literature.
Abstract: : A unifying framework of concepts central to the optimization of large structured systems is developed and used in the organization of the literature. The basic concepts are divided in two groups, (1) problem manipulations, in which a given problem is restated in an alternative form more amenable to solution, and (2) solution strategies which reduce an optimization problem to a related sequence of simpler problems that can be solved by specialized methods.
225 citations
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01 Jan 2003TL;DR: In this paper, continuity properties of optimal values and solution sets relative to changes of the original probability distribution, varying in some space of probability measures equipped with some convergence and metric, are studied.
Abstract: The behaviour of stochastic programming problems is studied in case of the underlying probability distribution being perturbed and approximated, respectively. Most of the theoretical results provide continuity properties of optimal values and solution sets relative to changes of the original probability distribution, varying in some space of probability measures equipped with some convergence and metric, respectively. We start by discussing relevant notions of convergence and distances for probability measures. Then we associate a distance with a stochastic program in a natural way and derive (quantitative) continuity properties of values and solutions by appealing to general perturbation results for optimization problems. Later we show how these results relate to stability with respect to weak convergence and how certain ideal probability metrics may be associated with more specific stochastic programs. In particular, we establish stability results for two-stage and chance constrained models. Finally, we present some consequences for the asymptotics of empirical approximations and for the construction of scenario-based approximations of stochastic programs.
225 citations
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TL;DR: A continuous global optimization heuristic for a stochastic approximation of an objective function, which is not globally convex, is introduced and some results of the estimation of the parameters for a specific agent based model of the DM/US-$ foreign exchange market are presented.
224 citations
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TL;DR: In this paper, a technique based on stochastic programming is proposed to optimally solve the electricity procurement problem faced by a large consumer, where risk aversion is explicitly modeled using the conditional value-at-risk methodology.
Abstract: This paper provides a technique based on stochastic programming to optimally solve the electricity procurement problem faced by a large consumer. Supply sources include bilateral contracts, a limited amount of self-production and the pool. Risk aversion is explicitly modeled using the conditional value-at-risk methodology. Results from a realistic case study are provided and analyzed
224 citations