Computational and Applied Aspects of Multiperiod Stochastic Programming

9523275伯杰这项研究是美国国家科学基金会先前资助的随机规划项目的继续。具体地说，该项目将继续发展多周期随机规划的求解方法、近似过程、模型和结构结果。这些目标将通过开发用于分布式处理器的新的分解方法来实现，包括整数变量和非线性函数，具有内点技术的专注于分布式解决方案的新方法，随机解和近似解的值的新界限，约束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。Cmm parison将考虑计算工作量、误差分析以及信息价值和模型复杂性的替代方法。这些模型将应用于制造、金融、车辆路径、电力系统规划和能源政策等方面的各种问题。目标是获得具有已知误差特性的有效实用解决方案。许多优化问题的特点是参数值不确定。随机规划通过识别参数的不确定性来建模和解决问题。本研究开发的算法将为解决复杂的决策问题提供额外的能力，这些问题通常具有更多的参数和不确定的值。明确地认识到建模过程中的不确定性，结合更高效的模型求解算法，将会带来更高的决策质量。从经济角度来看，决策质量提高的影响可能是非常显著的。此外，所调查的模型和产生的解决方案技术将有助于促进该领域的知识。

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.