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Sequential Decision Making under System-inherent Uncertainty: Mathematical Optimization Methods for Time-dynamic Applications

系统固有不确定性下的顺序决策：时间动态应用的数学优化方法

基本信息

批准号：
354864080
负责人：
Dr. Fabian Dunke, Ph.D.
金额：
--
依托单位：
Informatik 1 - Lehrstuhl Algorithmen und Komplexität
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2017
资助国家：
德国
起止时间：
2016-12-31 至 2020-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/354864080?language=en
关键词：
Sequential Decision Making under System

项目摘要

In mathematical optimization it is often assumed that a problem's data is known entirely. In practice however this assumption is often not met because data is made known over the course of time requiring iterative decision making under uncertainty. Applications for time-dynamic optimization problems arise on different levels: For instance, in strategic supply chain planning data is made available quarterly, whereas in operational machine scheduling new orders have to be accounted for on a minute-basis. The unifying element are uncertainties in the course of time. There is no systematic, interdisciplinary approach.Several approaches are pursued in research problem-dependently: In online optimization there is no knowledge on future events and decision are made such that even in the worst case the solution is not too far away from the optimal solution that can be computed in retrospective. In stochastic programming one assumes a set of future scenarios along with probabilities and one decides in the sense of the expected outcome. In robust optimization feasibility is guaranteed for all scenarios which is why the degrees of freedom for optimization are restricted. The main deficiency of current research comprises the inconsistent handling of the factors time and uncertainty. Online optimization suffers from the worst case orientation, stochastic programming results are based on unknown stochastic assumptions, robust optimization is not specifically designed to multi-stage problems. General extensions, such as an analysis of the value of future data, is just in the beginning of its scientific evolution. Flexible implementations within planning and control tools in supply chain management do not exist.Therefore, our goal consists in the consolidation of the different approaches dealing with uncertainty in a unified framework facilitating a context-dependent selection of a suitable solution methodology (algorithm from online optimization, stochastic programming, orrobust optimization). This comprises distributional methods of analysis which allow to assess and compare the quality of algorithms and the value of data. Sensitivity analysis is used then in order to check the behavior of different methods under varying circumstances, i.e., under different types of uncertainty. Based on exemplary Problems from production and logistics, we check the applicability of the methods in practice. Furthermore, we intend to lead planning and control tools towards an adaptive functional logic. The increasing amounts of data available in practice, e.g., from GPS or RFID chips, indicate that a comprehensive methological understanding is necessary in order to be able to decide on the value of information and to apply suitable optimization methods. This fact is supported by on-going industrial initiatives such as Industry 4.0 in Germany or the Industrial Internet in the US.

在数学优化中，通常假设一个问题的数据是完全已知的。然而，在实践中，这个假设通常不满足，因为数据是在不确定的情况下需要迭代决策的过程中已知的。时间动态优化问题的应用出现在不同的层次上：例如，在战略供应链规划中，每季度提供一次数据，而在操作机器调度中，新订单必须以分钟为基础进行计算。统一的因素是时间进程中的不确定性。没有系统的、跨学科的方法。在研究中，有几种方法是与问题相关的：在在线优化中，没有关于未来事件的知识，并且做出决策，即使在最坏的情况下，解决方案也不会离可以在回顾中计算的最优解决方案太远。在随机规划中，人们假设一系列未来情景和概率，并根据预期结果做出决定。在鲁棒优化中，保证了所有情况下的可行性，这就是优化自由度受到限制的原因。目前研究的主要不足在于对时间和不确定性因素的处理不一致。在线优化受最坏情况导向的影响，随机规划结果基于未知的随机假设，鲁棒优化不是专门针对多阶段问题设计的。一般的扩展，例如对未来数据价值的分析，只是其科学演变的开始。在供应链管理的计划和控制工具中不存在灵活的实现。因此，我们的目标是在一个统一的框架中整合处理不确定性的不同方法，促进上下文相关的合适解决方法的选择（来自在线优化、随机规划或鲁棒优化的算法）。这包括分布分析方法，允许评估和比较算法的质量和数据的价值。然后使用灵敏度分析来检查不同方法在不同情况下的行为，即在不同类型的不确定度下。以生产和物流中的典型问题为例，验证了方法在实践中的适用性。此外，我们打算将计划和控制工具引向自适应功能逻辑。实践中可用的数据量不断增加，例如，来自GPS或RFID芯片的数据表明，为了能够确定信息的价值并应用合适的优化方法，需要全面的方法理解。这一事实得到了德国工业4.0或美国工业互联网等正在进行的工业倡议的支持。