Stochastic Capacity Expansion with Applications in Logistics and Telecommunications Networks

有关能力扩展的决策，即确定能力获取和分配的最佳时机和水平，往往是有效战略规划的关键要素。在不准确的长期预测的不确定性下，往往需要投入大量的金融资本。在运输和电信这两个部门，网络容量决策是业务的核心。******作为一种通用工具，随机规划/机会约束规划可能为不确定条件下的产能扩张建模提供重要的灵活性。尽管这种灵活性使得解决实际规模数据的最优性问题变得困难，但随机规划/机会约束规划的最新进展使我们能够解决更大的实例。因此，我们正在进行的研究项目的目的是双重的。首先，从长远来看，PI旨在为生产和库存管理系统开发新的数学规划方法，并将其应用于提高业务运营的效率和效果。第二，发展和研究不确定条件下产能扩张的随机规划/机会约束规划模型。在此过程中，HQP将接受业务分析，特别是优化方面的培训。这些新模型将通过对通常可用的多种产能来源（包括现货市场产能和合同产能）进行建模，更准确地反映商业现实。此外，将为这些模型开发创新的解决方案技术。因此，我们的研究计划将产生一个更丰富和现实的产能扩张框架，并将推进随机规划/机会约束规划方法。******提出的模型和解决方法将随后应用于铁路和电信网络。具体来说，铁路网络的阻塞问题是一个自然的应用，因为涉及的资源包括轨道的数量，它们的容量和堆场空间。我们的第二个应用是电信内容交付网络（cdn，例如Akamai），涉及视频、软件或数据在互联网上的最佳分发。具体来说，资源的获取和分配——包括与边缘服务器相关的存储空间和带宽——对cdn来说是至关重要的战略决策。因此，这些类型的确定代表了应用所建议框架的另一种理想环境，因为存在多种资源和涉及的大量不确定性。******最后，在我们的研究项目过程中，高素质的人才（包括博士和硕士学生）将接受商业分析方面的培训，特别是大规模的优化，这将为他们在学术界和工业界的就业做好准备

Decisions concerning capacity expansion, i.e., determining the optimal timing and level of capacity acquisition and allocation, are often crucial elements of effective strategic planning. The commitment of substantial financial capital is often required under the uncertainties of inaccurate long-range forecasts. Transportation and telecommunications are two sectors in which network capacity decisions are central to the business.******As a general purpose tool, stochastic programming / chance-constrained programming potentially offer important flexibility in the modeling of capacity expansion under uncertainty. Although this flexibility makes it difficult to solve problems to optimality for real-size data, recent progress in stochastic programming / chance-constrained programming allows us to solve larger instances. Accordingly, the aim of our on-going research program is twofold. First, long-term, the PI aims to develop new mathematical programming methodologies for production and inventory management systems, and apply them to improve the efficiency and effectiveness of business operations. Second, the short-term goal is to develop and study new stochastic programming / chance-constrained programming models for capacity expansion under uncertainty. In the process, HQP will be trained in business analytics, especially optimization. These new models will more accurately reflect the realities of business, by modeling the multiple sources of capacity that are typically available, including the spot market capacity and contract capacity. Moreover, innovative solution techniques for these models will be developed. As such, our research program of will yield a much richer and realistic framework for capacity expansion and will advance stochastic programming / chance-constrained programming methodologies.******The proposed models and solution methodologies will then be applied to railway and telecommunications networks. Specifically, the blocking problem of railway networks is a natural application as the resources involved include the number of tracks, their capacity and yard space. Our second application, to telecommunications Content Delivery Networks (CDNs, e.g., Akamai), concerns the optimal distribution of video, software, or data across the Internet. Specifically, the acquisition and allocation of resources - including the storage space and bandwidth associated with edge servers - are crucial strategic decisions for CDNs. As such, these types of determinations represent another ideal context to apply the proposed framework given the multiple resources and the substantial uncertainties involved.******Finally, in the course of our research program, High Quality Personnel (both PhD and MSc students) will be trained in business analytics, especially large-scale optimization, that will prepare them for employment in academics and industry.**