基于时间限制与组合近似的模具项目群监控方法

Mold product deliverability is one of the core competitiveness of the mold companies. Mold projects monitoring has become a worldwide problem due to the great number of random factors occur during the mold production, large number of projects and other characteristics. In preliminary studies, the Markov decision processes theory is used to build the model of mold projects monitoring problems that with uncertain resource availability and activity duration, and moreover, a space approximation based method is proposed. On this groundwork, this program will further study the modeling of mold projects monitoring problems by considering random reworks, as well as other efficient methods. The study includes constructing the mathematical model of the mold projects monitoring problem with random rework cycles and both resources and durations under uncertainty by using the Markov decision process theory; proposing a time restriction based method which define the project's short-term performance objective and efficiently solving the short-term decision problem; introducing a combinatorial approximation based method that combined the space approximation and time restriction, which is used to solve the original problem. The characteristics and innovation of this program lies in the establishment of a mathematical model of mold projects monitoring problem where the project network topology is uncertain due to the random rework cycles, and proposed the time restriction and combinatorial approximation based efficient solution methods. This program aims to establish a complete methodology that can efficiently approximate solve large-scale mold projects monitoring problems, and provide a scientific basis for the decision-making of project management in mold companies.

模具产品的交付能力是模具企业的核心竞争力之一。因模具制造过程中随机因素多、项目群规模大等特征，模具项目群监控已成为世界性难题。在前期研究中，已采用马尔可夫决策过程理论对资源和任务工期不确定下的模具项目群监控问题建模，并提出了空间近似方法。在此基础上，本项目进一步研究考虑随机返修的模具项目群监控问题建模及其高效求解方法，包括：利用马尔可夫决策过程理论构建具有随机返修循环的模具项目群监控数学模型；提出一种时间限制的方法，设定项目群短期执行目标，高效求解短期决策问题；将空间近似与时间限制相结合，提出新的组合近似方法求解原问题。其特色与创新之处在于：建立了因随机返修循环而导致项目网络拓扑结构不确定的模具项目群监控数学模型；提出了基于时间限制与组合近似的高效求解方法。本项目旨在建立一套面向大规模模具项目群监控问题的建模与高效求解方法体系，为模具企业提供科学的项目管理决策依据。

本项目以模具项目群监控问题为研究对象，对具有随机任务工期和随机返修的模具项目群监控建模方法和近似求解方法进行系统深入的研究，旨在建立一套面向大规模模具项目群监控问题的建模与高效求解方法体系，为模具企业提供科学的项目管理决策依据。围绕上述研究目标，并结合课题组前期对模具企业的调研，对以下内容展开了研究：.1. 具有随机返修的模具项目完工时间预测解析模型。针对模具项目因设计和制造过程中存在的随机返修循环导致完工时间难以预测问题，提出基于马尔可夫理论构建解析模型。根据模具任务工期分布类型，分别提出了基于连续时间马尔可夫链、相型分布、以及离散时间马尔可夫链的建模方法。所构建的解析模型不仅能够更加高效准确的获得带返修模具项目完工时间概率分布，用于分析不同设计评审策略的优劣，还为后续优化建模打下了坚实基础。.2. 具有随机返修的模具项目调度优化建模方法。在模具项目完工时间预测解析模型的基础上，进一步考虑资源约束。提出采用连续时间马尔可夫决策过程理论构建具有随机返修的资源受限项目调度模型，并将其转化成离散时间马尔可夫决策过程，从而使用随机动态规划方法求解最优调度策略。实验结果表明，所得最优动态调度策略明显优于传统确定性近似方法。.3. 大规模模具项目群近似决策方法。在上述建模方法的基础上，构建能够高效求解大规模模具项目群决策问题的近似方法。从空间维度构建了基于资源解耦的分解方法，从时间维度构建了基于分时段决策的分解方法。此外，还探索了基于嵌套分解动态规划的方法，以及基于近似动态规划的决策方法。实验结果表明，所构建的方法能够有效提高模具项目群优化决策能力和效率，可应用于工程实际。