Planning and protecting critical infrastructure: Three applications of optimization under uncertainty or variability
Musselman, Amelia E.
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This dissertation presents the study of three strategic planning problems in the area of critical infrastructure planning and protection. Each of these problems involves real-world data that is uncertain or stochastic, and we use a range of methods to accommodate such data. First, we consider a network interdiction problem in which an adversary seeks to maximize the damage of transporting illicit nuclear material to a selected target while the defender seeks to minimize this damage. We model the problem as a bi-level program where the adversary's goal is to maximize damage to the system while the defender seeks to minimize damage under a limited budget. Furthermore, since effectiveness of mitigation options is often difficult to assess, we take a robust optimization approach to allow for parametric uncertainty. In order to account for the combined impact of mitigation options, we consider multiple attributes: situational awareness, detection, and interdiction. We test our method on a synthetic example of the U.S. supply chain network that includes rail, air, and maritime transportation between both domestic and international locations. For this test example, we are able to achieve a large decrease in damage with a mitigation budget that is only a small percent of the cost to implement all mitigation options. This approach allows consideration of joint strengths of complementary mitigation options and can be applied to any situation in which a defender has multiple options for defending a network. Second, we consider the problem of electrification in sub-Saharan Africa. Many people across Africa are without sufficient access to electricity. The unavailability and unreliability of electricity resources in Africa contribute to developmental challenges in many areas including business, education, and healthcare. In this research, we develop a multi-period optimization model for power generation and transmission system expansion planning in sub-Saharan Africa. Although optimization models have been developed to address power generation expansion planning in Africa they largely neglect the restricted budget for electricity development, assuming 100% of demand will be met in the near future. In order to advise development decisions under budgetary restrictions we consider a variety of electrification policies and analyze the impact of varying the fraction of demand met on the cost of power system expansion. We test our model on a case study of Rwanda and find that the electrification goals affect the cost, transmission system, and timing of construction decisions. This comprehensive approach provides richer insight into electrification choices and their consequences than existing electricity production planning models for developing countries by considering both strategic and operational planning decisions under a variety of electrification policy options. Finally, we present a multi-objective optimization model to strategically locate wind farms to reduce the negative impact of wind variability on the rest of the power system. In order to model the impact of wind variability without explicitly modeling the highly complex structure of the full electricity generation and transmission system, we develop a metric, which we call demand deficit, that measures the load that the remainder of the system would need to account for under wind fluctuations. We aim to select a complementary set of wind sites to minimize both demand deficit and the variability in this deficit. To approach this problem we first develop two heuristics to find an approximate solution using the complete dataset and then solve the exact optimization problem for a well-selected subset of the data. We solve our model using demand data and potential wind sites for the Southwest Power Pool. We find that though demand deficit decreases monotonically as more sites are added, the variability across time initially increases then decreases. For a fixed number of sites, demand deficit and variability in this deficit are competing objectives. Unlike previous work, this framework allows us to compare demand deficit and variability trade-offs when an integer number of sites is selected.