Stochastic Capacity Expansion with Applications in Logistics and Telecommunications Networks

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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.**