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This dissertation consists of three essays focusing on the use of mobile power sources to restore power distribution systems and on the timely response to medical emergencies, such as out-of-hospital cardiac arrests.
The first chapter of the dissertation investigates the effective utilization of mobile power source technologies for resilience delivery in power distribution systems during extreme disasters. We introduce the concept of mobility-as-a-service for resilience delivery in power distribution systems. The proposed models aid system operators in making informed decisions regarding the coordinated operations of mobile power sources and repair crews, enhancing resilience in the power distribution system and taking into account constraints in both the energy and transportation networks. The proposed joint optimization framework coordinates the existing resources for effective service restoration. Relaxing the need for multiple and iterative exchanges of data and decisions between the two networks, the suggested approach minimizes the risks of communication failures/latencies and cyber-attacks during service restoration, which otherwise would impede timely and reliable decision-making for resilience. An extensive numerical and scenario-based analysis of the proposed mobility-as-a-service models sheds insights on how to coordinate the available resources for effective response and recovery decisions against high-impact, low-probability events.
The dissertation's second chapter focuses on the endogenous uncertainty in routing and scheduling decision-making for mobile power sources. This type of uncertainty refers to the uncertain availability of a mobile power source, which depends on its workload—determined by its location and assigned tasks. The proposed restoration model is formulated as a mixed-integer nonlinear programming problem with nonconvex continuous relaxation. The study presents computationally tractable linearization procedures that reformulate the mixed-integer nonlinear programming model into an equivalent mixed-integer linear programming problem. Case studies across different power systems illustrate the significance of incorporating endogenous uncertainties in the decision-making process and demonstrate the effectiveness of the proposed restoration scheme in enhancing the resilience of the power distribution system.
The third chapter of the dissertation focuses on the leading cause of death among adults in the United States – out-of-hospital cardiac arrests (OHCAs). This study introduces a novel class of survival optimization models that aim to maximize the probability of survival following an OHCA incident by optimizing emergency medical services vehicle routing and scheduling decisions. A key novelty of the proposed model lies in the integration of a survival function—formulated as a decreasing monotone function of the total response time—as the objective function, encompassing both travel and waiting times, and in the explicit modeling of endogenous (decision-dependent) uncertainty in waiting time. The survival optimization model takes the form of a nonconvex mixed-integer nonlinear programming problem. We apply linearization techniques for polynomial terms and the idempotent property to reformulate the mixed-integer nonlinear programming problem as an equivalent mixed-integer linear programming problem. Furthermore, we introduce symmetry-breaking constraints and optimality-based cuts to tighten the formulation and to improve computational efficiency. Using real-world data from Virginia Beach, Virginia, we demonstrate the practical relevance and performance of our approach in improving survival outcomes for OHCA incidents.
