Nonclassical Discrete Optimization Problems

在本研究计划中，我们将研究在复杂制造和服务系统的规划操作中出现的几类离散优化模型。这些课程包括网络建设问题，涉及建设新交通网络或修复受损网络的规划建设活动；处理不确定决策的鲁棒优化模型在线供应链调度问题，在未来需求信息有限的情况下，帮助协调供应链的调度、批处理和交付决策；在新产品开发过程中模拟企业竞争的竞争性项目进度问题选择可能受到随机故障影响的服务设施的最佳位置的模型，或为面临随机需求的给定零售商提供供应的制造商和配送中心的位置和补充参数的模型。这些模型是“非经典”的，因为它们是新的或最近在文献中出现的，目前还没有足够有效的计算方法来处理它们。本研究计划的主要目标是发展一套理论结果和计算方法，以便在实践中使用这些模型，并了解它们的可能性和局限性。这将为规划复杂操作的从业者提供新的有力工具，带来对该领域的新认识，并开辟新的重要研究方向。

In this research program, we will study several classes of discrete optimization models that arise in planning operations in complex manufacturing and service systems. These classes include network construction problems that deal with planning construction activities for building new transportation networks or restoring damaged networks; robust optimization models that deal with decision-making under uncertainty; online supply chain scheduling problems that help coordinate scheduling, batching, and delivery decisions in supply chains where little information about future demand is available; competitive project scheduling problems that model competition between firms in development of new products; models for choosing optimally locations of service facilities that may be subject to random failures, or locations and replenishment parameters of manufacturers and distribution centers that supply a given set of retailers facing random demand. The models are "non-classical" in the sense that they are new or appeared in the literature recently, and at present there are no sufficiently effective computational approaches to handle them. The main goal of this research program is to develop a set of theoretical results and computational methods that will allow to use these models in practice and to understand their possibilities and limitations. This will provide new powerful tools to practitioners who deal with planning complex operations, bring new understanding of the area, and open new important research directions.