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: By using a finite set to define the visitation angle of a vehicle over a target, this work poses the integrated problem of task assignment and path optimization in the form of a graph, and proposes genetic algorithms for the stochastic search of the space of solutions.
170 citations
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01 Jan 1995TL;DR: A stochastic programming model is a model that specifies the assumptions made concerning the system in mathematical terms and identifies system parameters with mathematical objects and forms a problem to be solved and uses the obtained result for descriptive or operative purposes.
Abstract: When formulating a stochastic programming problem, we usually start from a deterministic problem that we call underlying deterministic problem. Then, observing that some of the parameters are random, we formulate another problem, the stochastic programming problem, by taking into account the probability distribution of the random elements in the underlying problem. When decision can or has to be made in the presence of randomness, at one single step, i.e., we do not wait for the occurrence of any event or realization of some random variable(s), then we say that the stochastic programming model is static. The two words: model and problem are used as synonyms. In the strict sense, the model specifies the assumptions made concerning the system in mathematical terms and identifies system parameters with mathematical objects. Having these, we formulate a problem to be solved and use the obtained result for descriptive or operative purposes.
170 citations
01 Jan 2011
TL;DR: Based on a stochastic programming with recourse framework, the authors incorporates different probabilistic scenarios in the rolling horizon decision process to recognize the input data uncertainty associated with predicted segment running time and segment recovery times, and the possibilities of rescheduling decisions after receiving status updates.
Abstract: After a major service disruption, dispatchers need to continuously generate train meet-pass plans that can recover the impacted train schedule from the current and future disturbances and minimize the expected additional delay under different forecasted operational conditions. Based on a stochastic programming with recourse framework, this paper incorporates different probabilistic scenarios in the rolling horizon decision process to recognize (1) the input data uncertainty associated with predicted segment running time and segment recovery times, and (2) the possibilities of rescheduling decisions after receiving status updates. The proposed model periodically optimizes schedules for a relatively long rolling horizon, while selecting and disseminating a robust meet-pass plan for every roll period. A multi-layer branching solution procedure is developed to systematically generate and select meet-pass plans under different stochastic scenarios. Illustrative examples and numerical experiments are used to demonstrate the importance of robust disruption handling under a dynamic and stochastic environment.
170 citations
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01 Jan 2002TL;DR: The MARKAL family of models has been contributing to energy/environmental planning since the early J980’s and was enlarged by members to model material flows, to employ stochastic programming (SP) to address future uncertainties, and to model endogenous technology learning using mixed integer programming (MIP) techniques.
Abstract: This article presents an overview and a flavour of almost two decades of MARKAL model developments and selected applications. The MARKAL family of models has been contributing to energy/environmental planning since the early J980’s. Under the auspices of the International Energy Agency’s (IEA) Energy Technology Systems Analysis Programme (ETSAP) the model started as a linear programming (LP) application focused strictly on the integrated assessment of energy systems. It was followed by a non-linear programming (NLP) formulation which combines the ‘bottom-up’ technology model with a ‘top-down’ simplified macro-economic model. In recent years, the family was enlarged by members to model material flows, to employ stochastic programming (SP) to address future uncertainties, to model endogenous technology learning using mixed integer programming (MIP) techniques, and to model multiple regions (NLP/LP).
170 citations
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TL;DR: A design and planning approach is proposed for addressing general multi-period, multi-product closed-loop supply chains (CLSCs), structured as a 10-layer network, with uncertain levels in the amount of raw material supplies and customer demands.
169 citations