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: Using the concept of comparison of fuzzy numbers, a very effective method for solving linear programming problems with fuzzy variables is introduced.
319 citations
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01 Jan 1995TL;DR: In this paper, the authors present a general framework for formulating and solving stochastic, dynamic network problems, including shortest paths, traveling salesman-type problems and vehicle routing.
Abstract: Publisher Summary This chapter discusses stochastic and dynamic networks and routing. The chapter discusses priori optimization in routing, shortest paths, traveling salesman-type problems and vehicle routing. These problems arise when decisions must be made before random outcomes (typically customer demands) are known. The chapter covers dynamic models of problems arising in transportation and logistics, and includes a discussion of important modeling issues, as well as a summary of dynamic models for a number of key problem areas. Dynamic networks provide an important foundation for addressing many problems in logistics planning. Algorithms that have been specialized for dynamic networks are presented. The results for solving infinite networks, including both exact results for stationary infinite networks, and model truncation techniques are briefly discussed. The chapter presents basic results and concepts from the field of stochastic programming, oriented toward their application to network problems. This discussion provides a general framework for formulating and solving stochastic, dynamic network problems. That framework is used to present two stochastic programming models.
319 citations
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TL;DR: In this article, a game theoretical model for the Stackelberg relationship between retailers (leaders) and consumers (followers) in a dynamic price environment is proposed, where both players in the game solve an economic optimisation problem subject to stochasticity in prices, weather-related variables and must-serve load.
316 citations
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TL;DR: In this paper, the existence and stability of invariant distributions for stochastically monotone Markov processes are studied. And the existence of fixed points of mappings on compact sets of measures that are increasing with respect to a stochastic ordering is established.
Abstract: The existence and stability of invariant distributions for stochastically monotone processes is studied. The Knaster-Tarski fixed point theorem is applied to establish existence of fixed points of mappings on compact sets of measures that are increasing with respect to a stochastic ordering. Global convergence of a monotone Markov process to its unique invariant distribution is established under an easily verified assumption. Topkis' theory of supermodular functions is applied to stochastic dynamic optimization, providing conditions under which optimal stationary decisions are monotone functions of the state and induce a monotone Markov process. Applications of these results to investment theory, stochastic growth, and industry equilibrium dynamics are given.
314 citations