Nonclassical Discrete Optimization Problems

在这个研究项目中，我们将研究在复杂的制造和服务系统中的计划操作中出现的几类离散优化模型。这些类别包括：网络建设问题，涉及建设新的运输网络或修复受损网络的计划建设活动；稳健优化模型，处理不确定情况下的决策；在线供应链调度问题，帮助协调未来需求信息较少的供应链中的调度、分批和交付决策；竞争性项目调度问题，模拟公司之间在开发新产品时的竞争；服务设施的最优位置选择模型，可能受到随机故障的影响；制造商和配送中心的位置和补给参数。这些模型是“非经典”的，因为它们是新的或最近出现在文献中的，目前还没有足够有效的计算方法来处理它们。该研究计划的主要目标是开发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。这将为处理复杂行动计划的从业者提供新的强大工具，带来对该领域的新理解，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.