Short-notice disasters such as hurricanes involve uncertainties in many facets, from the time of its occurrence to its impacts’ magnitude. Failure to incorporate these uncertainties can affect the effectiveness of the emergency responses. In the case of a hurricane event, uncertainties and corresponding impacts during a storm event can quickly cascade. Over the past decades, various storm forecast models have been developed to predict the storm uncertainties; however, access to the usage of these models is limited. Hence, as the first part of this research, a data-driven simulation model is developed with aim to generate spatial-temporal storm predicted hazards for each possible hurricane track modeled. The simulation model identifies a means to represent uncertainty in storm’s movement and its associated potential hazards in the form of probabilistic scenarios tree where each branch is associated with scenario-level storm track and weather profile. Storm hazards, such as strong winds, torrential rain, and storm surges, can inflict significant damage on the road network and affect the population’s ability to move during the storm event. A cascading network failure algorithm is introduced in the second part of the research. The algorithm takes the scenario-level storm hazards to predict uncertainties in mobility states over the storm event. In the third part of the research, a methodology is proposed to generate a sequence of actions that simultaneously solve the evacuation flow scheduling and suggested routes which minimize the total flow time, or the makespan, for the evacuation process from origins to destinations in the resulting stochastic time-dependent network. The methodology is implemented for the 2017 Hurricane Irma case study to recommend an evacuation policy for Manatee County, FL. The results are compared with evacuation plans for assumed scenarios; the research suggests that evacuation recommendations that are based on single scenarios reduce the effectiveness of the evacuation procedure. The overall contributions of the research presented here are new methodologies to: (1) predict and visualize the spatial-temporal impacts of an oncoming storm event, (2) predict uncertainties in the impacts to transportation infrastructure and mobility, and (3) determine the quickest evacuation schedule and routes under the uncertainties within the resulting stochastic transportation networks.

This dissertation focuses on three large-scale optimization problems and devising algorithms to solve them. In addition to the societal impact of each problem’s solution, this dissertation contributes to the optimization literature a set of decomposition algorithms for problems whose optimal solution is sparse. These algorithms exploit problem-specific properties and use tailored strategies based on iterative refinement (outer-approximations). The proposed algorithms are not rooted in duality theory, providing an alternative to existing methods based on linear programming relaxations. However, it is possible to embed existing decomposition methods into the proposed framework. These general decomposition principles extend to other combinatorial optimization problems.

The first problem is a route assignment and scheduling problem in which a set of vehicles need to traverse a directed network while maintaining a minimum inter-vehicle distance at any time. This problem is inspired by applications in hazmat logistics and the coordination of autonomous agents. The proposed approach includes realistic features such as continuous-time vehicle scheduling, heterogeneous speeds, minimum and maximum waiting times at any node, among others.

The second problem is a fixed-charge network design, which aims to find a minimum-cost plan to transport a target amount of a commodity between known origins and destinations. In addition to the typical flow decisions, the model chooses the capacity of each arc and selects sources and sinks. The proposed algorithms admit any nondecreasing piecewise linear cost structure. This model is applied to the Carbon Capture and Storage (CCS) problem, which is to design a minimum-cost pipeline network to transport CO2 between industrial sources and geologic reservoirs for long-term storage.

The third problem extends the proposed decomposition framework to a special case of joint chance constraint programming with independent random variables. This model is applied to the probabilistic transportation problem, where demands are assumed stochastic and independent. Using an empirical probability distribution, this problem is formulated as an integer program with the goal of finding a minimum-cost distribution plan that satisfies all the demands with a minimum given probability. The proposed scalable algorithm is based on a concave envelop approximation of the empirical probability function, which is iteratively refined as needed.

Modern manufacturing systems are part of a complex supply chain where customer preferences are constantly evolving. The rapidly evolving market demands manufacturing organizations to be increasingly agile and flexible. Medium term capacity planning for manufacturing systems employ queueing network models based on stationary demand assumptions. However, these stationary demand assumptions are not very practical for rapidly evolving supply chains. Nonstationary demand processes provide a reasonable framework to capture the time-varying nature of modern markets. The analysis of queues and queueing networks with time-varying parameters is mathematically intractable. In this dissertation, heuristics which draw upon existing steady state queueing results are proposed to provide computationally efficient approximations for dynamic multi-product manufacturing systems modeled as time-varying queueing networks with multiple customer classes (product types). This dissertation addresses the problem of performance evaluation of such manufacturing systems.

This dissertation considers the two key aspects of dynamic multi-product manufacturing systems - namely, performance evaluation and optimal server resource allocation. First, the performance evaluation of systems with infinite queueing room and a first-come first-serve service paradigm is considered. Second, systems with finite queueing room and priorities between product types are considered. Finally, the optimal server allocation problem is addressed in the context of dynamic multi-product manufacturing systems. The performance estimates developed in the earlier part of the dissertation are leveraged in a simulated annealing algorithm framework to obtain server resource allocations.

Model-based clustering is a sub-field of statistical modeling and machine learning. The mixture models use the probability to describe the degree of the data point belonging to the cluster, and the probability is updated iteratively during the clustering. While mixture models have demonstrated the superior performance in handling noisy data in many fields, there exist some challenges for high dimensional dataset. It is noted that among a large number of features, some may not indeed contribute to delineate the cluster profiles. The inclusion of these “noisy” features will confuse the model to identify the real structure of the clusters and cost more computational time. Recognizing the issue, in this dissertation, I propose a new feature selection algorithm for continuous dataset first and then extend to mixed datatype. Finally, I conduct uncertainty quantification for the feature selection results as the third topic.

The first topic is an embedded feature selection algorithm termed Expectation-Selection-Maximization (ESM) model that can automatically select features while optimizing the parameters for Gaussian Mixture Model. I introduce a relevancy index (RI) revealing the contribution of the feature in the clustering process to assist feature selection. I demonstrate the efficacy of the ESM by studying two synthetic datasets, four benchmark datasets, and an Alzheimer’s Disease dataset.

The second topic focuses on extending the application of ESM algorithm to handle mixed datatypes. The Gaussian mixture model is generalized to Generalized Model of Mixture (GMoM), which can not only handle continuous features, but also binary and nominal features.

The last topic is about Uncertainty Quantification (UQ) of the feature selection. A new algorithm termed ESOM is proposed, which takes the variance information into consideration while conducting feature selection. Also, a set of outliers are generated in the feature selection process to infer the uncertainty in the input data. Finally, the selected features and detected outlier instances are evaluated by visualization comparison.

This dissertation investigates congestion mitigation during the ingress of a planned special event (PSE). PSEs would impact the regular operation of the transportation system within certain time periods due to increased travel demand or reduced capacities on certain road segments. For individual attendees, cruising for parking during a PSE could be a struggle given the severe congestion and scarcity of parking spaces in the network. With the development of smartphones-based ridesharing services such as Uber/Lyft, more and more attendees are turning to ridesharing rather than driving by themselves. This study explores congestion mitigation during a planned special event considering parking, ridesharing and network configuration from both attendees and planner’s perspectives.

Parking availability (occupancy of parking facility) information is the fundamental building block for both travelers and planners to make parking-related decisions. It is highly valued by travelers and is one of the most important inputs to many parking models. This dissertation proposes a model-based practical framework to predict future occupancy from historical occupancy data alone. The framework consists of two modules: estimation of model parameters, and occupancy prediction. At the core of the predictive framework, a queuing model is employed to describe the stochastic occupancy change of a parking facility.

From an attendee’s perspective, the probability of finding parking at a particular parking facility is more treasured than occupancy information for parking search. However, it is hard to estimate parking probabilities even with accurate occupancy data in a dynamic environment. In the second part of this dissertation, taking one step further, the idea of introducing learning algorithms into parking guidance and information systems that employ a central server is investigated, in order to provide estimated optimal parking searching strategies to travelers. With the help of the Markov Decision Process (MDP), the parking searching process on a network with uncertain parking availabilities can be modeled and analyzed.

Finally, from a planner’s perspective, a bi-level model is proposed to generate a comprehensive PSE traffic management plan considering parking, ridesharing and route recommendations at the same time. The upper level is an optimization model aiming to minimize total travel time experienced by travelers. In the lower level, a link transmission model incorporating parking and ridesharing is used to evaluate decisions from and provide feedback to the upper level. A congestion relief algorithm is proposed and tested on a real-world network.

I study the problem of locating Relay nodes (RN) to improve the connectivity of a set

of already deployed sensor nodes (SN) in a Wireless Sensor Network (WSN). This is

known as the Relay Node Placement Problem (RNPP). In this problem, one or more

nodes called Base Stations (BS) serve as the collection point of all the information

captured by SNs. SNs have limited transmission range and hence signals are transmitted

from the SNs to the BS through multi-hop routing. As a result, the WSN

is said to be connected if there exists a path for from each SN to the BS through

which signals can be hopped. The communication range of each node is modeled

with a disk of known radius such that two nodes are said to communicate if their

communication disks overlap. The goal is to locate a given number of RNs anywhere

in the continuous space of the WSN to maximize the number of SNs connected (i.e.,

maximize the network connectivity). To solve this problem, I propose an integer

programming based approach that iteratively approximates the Euclidean distance

needed to enforce sensor communication. This is achieved through a cutting-plane

approach with a polynomial-time separation algorithm that identies distance violations.

I illustrate the use of my algorithm on large-scale instances of up to 75 nodes

which can be solved in less than 60 minutes. The proposed method shows solutions

times many times faster than an alternative nonlinear formulation.

The energy consumption by public drinking water and wastewater utilities represent up to 30%-40% of a municipality energy bill. The largest energy consumption is used to operate motors for pumping. As a result, the engineering and control community develop the Variable Speed Pumps (VSPs) which allow for regulating valves in the network instead of the traditional binary ON/OFF pumps. Potentially, VSPs save up to 90% of annual energy cost compared to the binary pump. The control problem has been tackled in the literature as “Pump Scheduling Optimization” (PSO) with a main focus on the cost minimization. Nonetheless, engineering literature is mostly concerned with the problem of understanding “healthy working conditions” (e.g., leakages, breakages) for a water infrastructure rather than the costs. This is very critical because if we operate a network under stress, it may satisfy the demand at present but will likely hinder network functionality in the future.

This research addresses the problem of analyzing working conditions of large water systems by means of a detailed hydraulic simulation model (e.g., EPANet) to gain insights into feasibility with respect to pressure, tank level, etc. This work presents a new framework called Feasible Set Approximation – Probabilistic Branch and Bound (FSA-PBnB) for the definition and determination of feasible solutions in terms of pumps regulation. We propose the concept of feasibility distance, which is measured as the distance of the current solution from the feasibility frontier to estimate the distribution of the feasibility values across the solution space. Based on this estimate, pruning the infeasible regions and maintaining the feasible regions are proposed to identify the desired feasible solutions. We test the proposed algorithm with both theoretical and real water networks. The results demonstrate that FSA-PBnB has the capability to identify the feasibility profile in an efficient way. Additionally, with the feasibility distance, we can understand the quality of sub-region in terms of feasibility.

The present work provides a basic feasibility determination framework on the low dimension problems. When FSA-PBnB extends to large scale constraint optimization problems, a more intelligent sampling method may be developed to further reduce the computational effort.

Healthcare operations have enjoyed reduced costs, improved patient safety, and

innovation in healthcare policy over a huge variety of applications by tackling prob-

lems via the creation and optimization of descriptive mathematical models to guide

decision-making. Despite these accomplishments, models are stylized representations

of real-world applications, reliant on accurate estimations from historical data to jus-

tify their underlying assumptions. To protect against unreliable estimations which

can adversely affect the decisions generated from applications dependent on fully-

realized models, techniques that are robust against misspecications are utilized while

still making use of incoming data for learning. Hence, new robust techniques are ap-

plied that (1) allow for the decision-maker to express a spectrum of pessimism against

model uncertainties while (2) still utilizing incoming data for learning. Two main ap-

plications are investigated with respect to these goals, the first being a percentile

optimization technique with respect to a multi-class queueing system for application

in hospital Emergency Departments. The second studies the use of robust forecasting

techniques in improving developing countries’ vaccine supply chains via (1) an inno-

vative outside of cold chain policy and (2) a district-managed approach to inventory

control. Both of these research application areas utilize data-driven approaches that

feature learning and pessimism-controlled robustness.

Recently, automation, shared use, and electrification are proposed and viewed as the “three revolutions” in the future transportation sector to significantly relieve traffic congestion, reduce pollutant emissions, and increase transportation system sustainability. Motivated by the three revolutions, this research targets on the passenger-focused scheduled transportation systems, where (1) the public transit systems provide high-quality ridesharing schedules/services and (2) the upcoming optimal activity planning systems offer the best vehicle routing and assignment for household daily scheduled activities.

The high quality of system observability is the fundamental guarantee for accurately predicting and controlling the system. The rich information from the emerging heterogeneous data sources is making it possible. This research proposes a modeling framework to systemically account for the multi-source sensor information in urban transit systems to quantify the estimated state uncertainty. A system of linear equations and inequalities is proposed to generate the information space. Also, the observation errors are further considered by a least square model. Then, a number of projection functions are introduced to match the relation between the unique information space and different system states, and its corresponding state estimate uncertainties are further quantified by calculating its maximum state range.

In addition to optimizing daily operations, the continuing advances in information technology provide precious individual travel behavior data and trip information for operational planning in transit systems. This research also proposes a new alternative modeling framework to systemically account for boundedly rational decision rules of travelers in a dynamic transit service network with tight capacity constraints. An agent-based single-level integer linear formulation is proposed and can be effectively by the Lagrangian decomposition.

The recently emerging trend of self-driving vehicles and information sharing technologies starts creating a revolutionary paradigm shift for traveler mobility applications. By considering a deterministic traveler decision making framework, this research addresses the challenges of how to optimally schedule household members’ daily scheduled activities under the complex household-level activity constraints by proposing a set of integer linear programming models. Meanwhile, in the microscopic car-following level, the trajectory optimization of autonomous vehicles is also studied by proposing a binary integer programming model.