Stochastic programming is an optimization technique used in the presence of uncertainty and it typically leads to very large problem sizes. In this paper, a modified version of the L-shaped method was used to solve tw...
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Stochastic programming is an optimization technique used in the presence of uncertainty and it typically leads to very large problem sizes. In this paper, a modified version of the L-shaped method was used to solve two-stage stochastic linear programs with recourse, based on the projection method and the augmented Lagrangian method. Using this modified version of the L-shaped method allows us to reduce the number of iterations and the time of solving a two-stage stochastic linear program with fixed recourse, in comparison with traditional methods. (C) 2015 Elsevier Inc. All rights reserved.
In this paper, stochastic programming problems are viewed as parametric programs with respect to the probability distributions of the random coefficients. General results on quantitative stability in parametric optimi...
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In this paper, stochastic programming problems are viewed as parametric programs with respect to the probability distributions of the random coefficients. General results on quantitative stability in parametric optimization are used to study distribution sensitivity of stochastic programs. For recourse and chance constrained models quantitative continuity results for optimal values and optimal solution sets are proved (with respect to suitable metrics on the space of probability distributions). The results are useful to study the effect of approximations and of incomplete information in stochastic programming.
We consider the optimal value of a pure minimum cost network flow problem as a function of supply, demand and arc capacities. We present a new piecewise linear upper bound on this function, which is called the network...
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We consider the optimal value of a pure minimum cost network flow problem as a function of supply, demand and arc capacities. We present a new piecewise linear upper bound on this function, which is called the network recourse function. The bound is compared to the standard Madansky bound, and is shown computationally to be a little weaker, but much faster to find. The amount of work is linear in the number of stochastic variables, not exponential as is the case for the Madansky bound. Therefore, the reduction in work increases as the number of stochastic variables increases. Computational results are presented.
We present a construction which gives deterministic upper bounds for stochastic programs in which the randomness appears on the right-hand-side and has a multivariate Gaussian distribution. Computation of these bounds...
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We present a construction which gives deterministic upper bounds for stochastic programs in which the randomness appears on the right-hand-side and has a multivariate Gaussian distribution. Computation of these bounds requires the solution of only as many linear programs as the problem has variables.
This paper analyses decision models with an uncertain set of alternatives defined by a deterministic objective function and constraints with uncertain coefficients. Here, in contrast to decisions under risk, the stoch...
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This paper analyses decision models with an uncertain set of alternatives defined by a deterministic objective function and constraints with uncertain coefficients. Here, in contrast to decisions under risk, the stochastic distribution of uncertain coefficients is not known. On the basis of an uncertain multiobjective decision model, we define efficient alternatives and formulate deterministic surrogate models. Uncertain decision models with recourse are introduced, and we present solution concepts that combine approaches from both multiobjective decision making and decision models with uncertain objective functions. These approaches are discussed in relation to stochastic and fuzzy programming and to models with linear partial information. In addition, ramifications of this particular approach are explored.
We study the new problem of stochastic programs over trees with dependent random arc capacities. This problem can be used as a subproblem in decomposition methods that solve multi-stage networks with independent rando...
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We study the new problem of stochastic programs over trees with dependent random arc capacities. This problem can be used as a subproblem in decomposition methods that solve multi-stage networks with independent random arc capacities and random travel times. An efficient algorithm is provided to compute the expected total cost. (C) 2007 Wiley Periodicals, Inc.
Multiple ecological, economic, social, and political facets influence forest-planning decisions. Decision models have been widely used in forest management planning, but most are deterministic models. However, long-te...
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Multiple ecological, economic, social, and political facets influence forest-planning decisions. Decision models have been widely used in forest management planning, but most are deterministic models. However, long-term forest planning problems are surrounded by potential uncertainties. To begin to account for uncertainty surrounding growth and yield under climate change conditions, a stochastic forest planning model was developed and tested. The intent of the model is to help identify potential current forest management actions that will perform well over a range of plausible climate change scenarios (futures). The stages of the model address how uncertainty about the future might unfold, with model solutions providing immediate management actions plus detailed contingency (recourse) plans for each future. The use of specialized decomposition methods of operations research has allowed for testing the model in a detailed and large application. Results from the case study showed that planning for an average deterministic case produces a misleading solution, underestimating the potential impact of climate change. On the other hand, only planning for a worst-case scenario ignores the potential value of management opportunities under other likely futures in which harvesting benefits could be greater. Overall, results advance our understanding of recognizing forest-wide uncertainty in forest management planning models. Study Implications Stand-level decisions often have forest-wide implications. Forest planning helps coordinate management of stands to address ecological, economic, and social aspects. Decision models are often used, but most assume all the information is known. However, long-term forest planning is surrounded by potential uncertainties, such as climate change. We developed a model to identify current forest management actions that will perform well over a range of plausible climate change scenarios instead of just one. The novelty lies in how we solve the
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