Stochastic Capacity Expansion with Applications in Logistics and Telecommunications Networks

关于能力扩展的决定，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。在长期预测不准确的不确定情况下，往往需要投入大量资金。运输和电信是网络容量决策对业务至关重要的两个部门。**作为一种通用工具，随机规划/机会约束规划可能提供重要的灵活性，在不确定性下的容量扩张建模。虽然这种灵活性使得它很难解决问题的最优性的真实大小的数据，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情况。因此，我们正在进行的研究计划的目的是双重的。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益。第二，短期目标是开发和研究新的随机规划/机会约束规划模型，用于不确定情况下的产能扩张。在此过程中，HQP将接受业务分析培训，特别是优化。这些新模型将通过对通常可用的多种容量来源（包括现货市场容量和合同容量）进行建模，更准确地反映业务现实。此外，还将开发这些模型的创新解决方案。因此，我们的研究计划将为容量扩展提供更丰富和现实的框架，并将推进随机规划/机会约束规划方法。然后，将所提出的模型和解决方法应用于铁路和电信网络。具体而言，铁路网络的阻塞问题是一个自然的应用，因为所涉及的资源包括轨道的数量，它们的容量和车场空间。我们的第二个应用是电信内容分发网络（CDN，例如，Akamai），关注的是视频、软件或数据在互联网上的最佳分发。具体而言，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）是CDN的关键战略决策。因此，鉴于涉及多种资源和大量不确定性，这些类型的确定是适用拟议框架的另一个理想背景。最后，在我们的研究计划中，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.**