Stochastic Capacity Expansion with Applications in Logistics and Telecommunications Networks

关于扩大能力的决定，即确定获得和分配能力的最佳时机和水平，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性下，往往需要大量金融资本的承诺。运输和电信是网络容量决策对业务至关重要的两个行业。 作为一种通用工具，随机规划/机会约束规划在不确定条件下的产能扩张建模中具有重要的灵活性。虽然这种灵活性使得解决实际大小数据的问题变得困难，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计划的目的是双重的。首先，从长远来看，PI的目标是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有效性。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，用于不确定条件下的产能扩张。在此过程中，HQP将接受业务分析方面的培训，特别是优化。这些新模型将通过对通常可用的多种能力来源进行建模，包括现货市场能力和合同能力，从而更准确地反映业务现实。此外，还将为这些模型开发创新的解决方案技术。因此，我们的研究计划将为产能扩展提供一个更加丰富和现实的框架，并将推动随机规划/机会约束规划方法的发展。 然后，建议的模型和解决方法将应用于铁路和电信网络。具体地说，铁路网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数量、轨道容量和站场空间。我们的第二个应用是电信内容分发网络(CDN，例如Akamai)，涉及跨互联网的视频、软件或数据的最佳分发。具体地说，获取和分配资源--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，鉴于所涉及的多种资源和相当大的不确定性，这些类型的确定是适用拟议框架的另一种理想情况。 最后，在我们的研究计划过程中，高素质的人员(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行业就业做好准备。

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.