Computational and Applied Aspects of Multiperiod Stochastic Programming

小行星9523275 这项研究是以前的NSF资助的随机规划项目的延续。具体来说，这个项目将继续发展的解决方案的方法，近似程序，模型和结构的结果，多期随机程序。这些目标将通过为分布式处理器开发新的分解方法来实现，包括整数变量和非线性函数，具有内点技术的新方法，其专注于分布式解，随机解和近似解的值的新界限，用于定界随机整数规划问题的新技术，以及使用特定模型特征的新的近似和方法，以实现准确的结果。Cmmparisons将考虑计算工作量，误差分析，信息和模型复杂性的价值的替代方法。这些模型将被应用于从制造，金融，车辆路径，电力系统规划和能源政策中提取的各种问题。我们的目标是获得有效的实际解决方案与已知的错误特性。 许多优化问题的特点是参数值不确定。随机规划识别参数的不确定性，以建模和解决问题。在这项研究中开发的算法将提供额外的能力，解决复杂的决策问题，通常具有更大的数量与不确定值的参数。明确识别模型构建中的不确定性，并结合更有效的算法来求解模型，将导致更高的决策质量。从经济角度来看，提高决策质量的影响可能非常显著。此外，所研究的模型和所产生的解决方案技术将有助于推进该领域的知识。

9523275 Birge This research is a continuation of a previous NSF funded project on stochastic programming. Specifically, this project will continue the development of solution methods, approximation procedures, models , and structural results for multiperiod stochastic programs. These objectives will be accomplished through the development of new decomposition methods for distributed processors, including integer variables and nonlinear functions, new methods with interior point techniques that focus on distributed solutions, new bounds on the value of the stochastic solution and approximation solutions, new techniques for bounding stochastic integer programming problems, and new approximations and methods using specific model characteristics to enable accurate results. Cmmparisons will consider alternative approaches with computational effort, error analysis, and the value of information and model complexity. The models will be applied to a variety of problems drawn from manufacturing, finance, vehicle routing, power systems planning, and energy policy. The goals are to obtain efficient practical solutions with known error characteristics. Many optimization problems are characterized by parameter values that are not known with certainty. Stochastic programming recognizes the uncertain nature of parameters to model and solve problems. The algorithms developed in this research will provide additional capabilities for solving complex decision problems which generally possess greater number of parameters with uncertain values. The explicit recognition of uncertainty in model building combined with more efficient algorithms for solving the models will lead to higher decision quality. The impact of improved decision quality from an economic point of view can be very significant. Further, the models investigated and the solution techniques produced will help to advance the knowledge in the area.