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, a stochastic linear programming formulation of a firm's short-term financial planning problem is presented, which allows a more realistic representation of the uncertainties fundamental to this problem than previous models.
Abstract: This paper presents a stochastic linear programming formulation of a firm's short term financial planning problem. This framework allows a more realistic representation of the uncertainties fundamental to this problem than previous models. In addition, using Wets's algorithm for linear simple recourse problems, this formulation has approximately the same computational complexity as the mean approximation i.e., the deterministic program obtained by replacing all random elements by their means. Using this formulation we empirically investigate the effects of differing distributions and penalty costs. We conclude that even with symmetric penalty costs and distributions the mean model is significantly inferior to the stochastic linear programming formulation. Thus we are able to demonstrate that ignoring the stochastic components in linear programming formulations can be very costly without having significant computational savings.
108 citations
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TL;DR: A utility maximizing algorithm that uses explicit delay information from the head-of-line packet at each user is designed to ensure deterministic worst-case delay guarantees and to yield a throughput-utility that differs from the optimally fair value by an amount that is inversely proportional to the delay guarantee.
Abstract: It is well known that max-weight policies based on a queue backlog index can be used to stabilize stochastic networks, and that similar stability results hold if a delay index is used. Using Lyapunov optimization, we extend this analysis to design a utility maximizing algorithm that uses explicit delay information from the head-of-line packet at each user. The resulting policy is shown to ensure deterministic worst-case delay guarantees and to yield a throughput utility that differs from the optimally fair value by an amount that is inversely proportional to the delay guarantee. Our results hold for a general class of 1-hop networks, including packet switches and multiuser wireless systems with time-varying reliability .
108 citations
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TL;DR: Simulation results demonstrate that even for a moderate number of antennas at each link, the new approach provides indistinguishable results as those obtained by the complex stochastic programming approach.
Abstract: In this paper, we study the capacity-achieving input covariance matrices for the multiuser multiple-input multiple-output (MIMO) uplink channel under jointly-correlated Rician fading when perfect channel state information (CSI) is known at the receiver, or CSIR while only statistical CSI at the transmitter, or CSIT, is available. The jointly-correlated MIMO channel (or the Weichselberger model) accounts for the correlation at two link ends and is shown to be highly accurate to model real channels. Classically, numerical techniques together with Monte-Carlo methods (named stochastic programming) are used to resolve the problem concerned but at a high computational cost. To tackle this, we derive the asymptotic sum-rate of the multiuser (MU) MIMO uplink channel in the large-system regime where the numbers of antennas at the transmitters and the receiver go to infinity with constant ratios. Several insights are gained from the analytic asymptotic sum-rate expression, based on which an efficient optimization algorithm is further proposed to obtain the capacity-achieving input covariance matrices. Simulation results demonstrate that even for a moderate number of antennas at each link, the new approach provides indistinguishable results as those obtained by the complex stochastic programming approach.
108 citations
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TL;DR: In this paper, an integrated optimization method is developed for supporting agriculture water management and planning in Tarim River Basin, Northwest China, where two-stage stochastic programming (TSP) with inexact quadratic program (IQP) is used for forecasting the available irrigation water.
108 citations
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TL;DR: The authors develop a stochastic optimization model under demand uncertainty, where the inherent risk is modeled by scenarios, and propose solution methods for the stochastically optimization problem based on L-shaped algorithm within an e-optimality framework.
Abstract: The authors consider the design of a two-echelon production distribution network with multiple manufacturing plants, customers and a set of candidate distribution centers. The main contribution of the study is to extend the existing literature by incorporating the demand uncertainty of customers within the distribution center location and transportation mode allocation decisions, as well as providing a network design satisfying the both economical and service quality objectives of the decision maker within two levels supply network setting. The authors formulate the problem as two stage integer recourse problem to find a set of optimal network configuration and assignment of transportation modes and the respective flows in order to minimize total cost and total service time, simultaneously. The authors develop a stochastic optimization model under demand uncertainty, where the inherent risk is modeled by scenarios. Finally, they propose solution methods for our stochastic optimization problem based on L-shaped algorithm within an e-optimality framework and present numerical results demonstrating the computational effectiveness.
108 citations