The use of Red Blood Cells (RBCs) is a pillar of modern health care. Annually, the lives of hundreds of thousands of patients are saved through ready access to safe, fresh, blood-type compatible RBCs. Worldwide, hospitals have the common goal to better utilize available blood units by maximizing patients served and reducing blood wastage. Managing blood is challenging because blood is perishable, its supply is stochastic and its demand pattern is highly uncertain. Additionally, RBCs are typed and patient compatibility is required.

This research focuses on improving blood inventory management at the hospital level. It explores the importance of hospital characteristics, such as demand rate and blood-type distribution in supply and demand, for improving RBC inventory management. Available inventory models make simplifying assumptions; they tend to be general and do not utilize available data that could improve blood delivery. This dissertation develops useful and realistic models that incorporate data characterizing the hospital inventory position, distribution of blood types of donors and the population being served.

The dissertation contributions can be grouped into three areas. First, simulations are used to characterize the benefits of demand forecasting. In addition to forecast accuracy, it shows that characteristics such as forecast horizon, the age of replenishment units, and the percentage of demand that is forecastable influence the benefits resulting from demand variability reduction.

Second, it develops Markov decision models for improved allocation policies under emergency conditions, where only the units on the shelf are available for dispensing. In this situation the RBC perishability has no impact due to the short timeline for decision making. Improved location-specific policies are demonstrated via simulation models for two emergency event types: mass casualty events and pandemic influenza.

Third, improved allocation policies under normal conditions are found using Markov decision models that incorporate temporal dynamics. In this case, hospitals receive replenishment and units age and outdate. The models are solved using Approximate Dynamic Programming with model-free approximate policy iteration, using machine learning algorithms to approximate value or policy functions. These are the first stock- and age-dependent allocation policies that engage substitution between blood type groups to improve inventory performance.

Due to environmental and geopolitical reasons, many countries are embracing electric vehicles (EVs) as an alternative to gasoline powered automobiles. Other alternative-fuel vehicles (AFVs) powered by compressed gas, hydrogen or biodiesel have also been tested for replacing gasoline powered vehicles. However, since the associated refueling infrastructure of AFVs is sparse and is gradually being built, the distance between recharging points (RPs) becomes a crucial prohibitive attribute in attracting drivers to use such vehicles. Optimally locating RPs will both increase demand and help in developing the refueling infrastructure.

The major emphasis in this dissertation is the development of theories and associated algorithms for a new set of location problems defined on continuous network space related to siting multiple RPs for range limited vehicles.

This dissertation covers three optimization problems: locating multiple RPs on a line network, locating multiple RPs on a comb tree network, and locating multiple RPs on a general tree network. For each of the three problems, finding the minimum number of RPs needed to refuel all Origin-Destination (O-D) flows is considered as the first objective. For this minimum number, the location objective is to locate this number of RPs to minimize weighted sum of the travelling distance for all O-D flows. Different exact algorithms are proposed to solve each of the three algorithms.

In the first part of this dissertation, the simplest case of locating RPs on a line network is addressed. Scenarios include single one-way O-D pair, multiple one-way O-D pairs, round trips, etc. A mixed integer program with linear constraints and quartic objective function is formulated. A finite dominating set (FDS) is identified, and based on the existence of FDS, the problem is formulated as a shortest path problem. In the second part, the problem is extended to comb tree networks. Finally, the problem is extended to general tree networks. The extension to a probabilistic version of the location problem is also addressed.

Optimization of on-demand transportation systems and ride-sharing services involves solving a class of complex vehicle routing problems with pickup and delivery with time windows (VRPPDTW). Previous research has made a number of important contributions to the challenging pickup and delivery problem along different formulation or solution approaches. However, there are a number of modeling and algorithmic challenges for a large-scale deployment of a vehicle routing and scheduling algorithm, especially for regional networks with various road capacity and traffic delay constraints on freeway bottlenecks and signal timing on urban streets. The main thrust of this research is constructing hyper-networks to implicitly impose complicated constraints of a vehicle routing problem (VRP) into the model within the network construction. This research introduces a new methodology based on hyper-networks to solve the very important vehicle routing problem for the case of generic ride-sharing problem. Then, the idea of hyper-networks is applied for (1) solving the pickup and delivery problem with synchronized transfers, (2) computing resource hyper-prisms for sustainable transportation planning in the field of time-geography, and (3) providing an integrated framework that fully captures the interactions between supply and demand dimensions of travel to model the implications of advanced technologies and mobility services on traveler behavior.

This research develops heuristics to manage both mandatory and optional network capacity reductions to better serve the network flows. The main application discussed relates to transportation networks, and flow cost relates to travel cost of users of the network. Temporary mandatory capacity reductions are required by maintenance activities. The objective of managing maintenance activities and the attendant temporary network capacity reductions is to schedule the required segment closures so that all maintenance work can be completed on time, and the total flow cost over the maintenance period is minimized for different types of flows. The goal of optional network capacity reduction is to selectively reduce the capacity of some links to improve the overall efficiency of user-optimized flows, where each traveler takes the route that minimizes the traveler’s trip cost. In this dissertation, both managing mandatory and optional network capacity reductions are addressed with the consideration of network-wide flow diversions due to changed link capacities.

This research first investigates the maintenance scheduling in transportation networks with service vehicles (e.g., truck fleets and passenger transport fleets), where these vehicles are assumed to take the system-optimized routes that minimize the total travel cost of the fleet. This problem is solved with the randomized fixed-and-optimize heuristic developed. This research also investigates the maintenance scheduling in networks with multi-modal traffic that consists of (1) regular human-driven cars with user-optimized routing and (2) self-driving vehicles with system-optimized routing. An iterative mixed flow assignment algorithm is developed to obtain the multi-modal traffic assignment resulting from a maintenance schedule. The genetic algorithm with multi-point crossover is applied to obtain a good schedule.

Based on the Braess’ paradox that removing some links may alleviate the congestion of user-optimized flows, this research generalizes the Braess’ paradox to reduce the capacity of selected links to improve the efficiency of the resultant user-optimized flows. A heuristic is developed to identify links to reduce capacity, and the corresponding capacity reduction amounts, to get more efficient total flows. Experiments on real networks demonstrate the generalized Braess’ paradox exists in reality, and the heuristic developed solves real-world test cases even when commercial solvers fail.

This dissertation carries out an inter-disciplinary research of operations research, statistics, power system engineering, and economics. Specifically, this dissertation focuses on a special power system scheduling problem, a unit commitment problem with uncertainty. This scheduling problem is a two-stage decision problem. In the first stage, system operator determines the binary commitment status (on or off) of generators in advance. In the second stage, after the realization of uncertainty, the system operator determines generation levels of the generators. The goal of this dissertation is to develop computationally-tractable methodologies and algorithms to solve large-scale unit commitment problems with uncertainty.

In the first part of this dissertation, two-stage models are studied to solve the problem. Two solution methods are studied and improved: stochastic programming and robust optimization. A scenario-based progressive hedging decomposition algorithm is applied. Several new hedging mechanisms and parameter selections rules are proposed and tested. A data-driven uncertainty set is proposed to improve the performance of robust optimization.

In the second part of this dissertation, a framework to reduce the two-stage stochastic program to a single-stage deterministic formulation is proposed. Most computation of the proposed approach can be done by offline studies. With the assistance of offline analysis, simulation, and data mining, the unit commitment problems with uncertainty can be solved efficiently.

Finally, the impacts of uncertainty on energy market prices are studied. A new component of locational marginal price, a marginal security component, which is the weighted shadow prices of the proposed security constraints, is proposed to better represent energy prices.

Vehicles powered by electricity and alternative-fuels are becoming a more popular form of transportation since they have less of an environmental impact than standard gasoline vehicles. Unfortunately, their success is currently inhibited by the sparseness of locations where the vehicles can refuel as well as the fact that many of the vehicles have a range that is less than those powered by gasoline. These factors together create a "range anxiety" in drivers, which causes the drivers to worry about the utility of alternative-fuel and electric vehicles and makes them less likely to purchase these vehicles. For the new vehicle technologies to thrive it is critical that range anxiety is minimized and performance is increased as much as possible through proper routing and scheduling. In the case of long distance trips taken by individual vehicles, the routes must be chosen such that the vehicles take the shortest routes while not running out of fuel on the trip. When many vehicles are to be routed during the day, if the refueling stations have limited capacity then care must be taken to avoid having too many vehicles arrive at the stations at any time. If the vehicles that will need to be routed in the future are unknown then this problem is stochastic. For fleets of vehicles serving scheduled operations, switching to alternative-fuels requires ensuring the schedules do not cause the vehicles to run out of fuel. This is especially problematic since the locations where the vehicles may refuel are limited due to the technology being new. This dissertation covers three related optimization problems: routing a single electric or alternative-fuel vehicle on a long distance trip, routing many electric vehicles in a network where the stations have limited capacity and the arrivals into the system are stochastic, and scheduling fleets of electric or alternative-fuel vehicles with limited locations to refuel. Different algorithms are proposed to solve each of the three problems, of which some are exact and some are heuristic. The algorithms are tested on both random data and data relating to the State of Arizona.

Facility location models are usually employed to assist decision processes in urban and regional planning. The focus of this research is extensions of a classic location problem, the Weber problem, to address continuously distributed demand as well as multiple facilities. Addressing continuous demand and multi-facilities represents major challenges. Given advances in geographic information systems (GIS), computational science and associated technologies, spatial optimization provides a possibility for improved problem solution. Essential here is how to represent facilities and demand in geographic space. In one respect, spatial abstraction as discrete points is generally assumed as it simplifies model formulation and reduces computational complexity. However, errors in derived solutions are likely not negligible, especially when demand varies continuously across a region. In another respect, although mathematical functions describing continuous distributions can be employed, such theoretical surfaces are generally approximated in practice using finite spatial samples due to a lack of complete information. To this end, the dissertation first investigates the implications of continuous surface approximation and explicitly shows errors in solutions obtained from fitted demand surfaces through empirical applications. The dissertation then presents a method to improve spatial representation of continuous demand. This is based on infill asymptotic theory, which indicates that errors in fitted surfaces tend to zero as the number of sample points increases to infinity. The implication for facility location modeling is that a solution to the discrete problem with greater demand point density will approach the theoretical optimum for the continuous counterpart. Therefore, in this research discrete points are used to represent continuous demand to explore this theoretical convergence, which is less restrictive and less problem altering compared to existing alternatives. The proposed continuous representation method is further extended to develop heuristics to solve the continuous Weber and multi-Weber problems, where one or more facilities can be sited anywhere in continuous space to best serve continuously distributed demand. Two spatial optimization approaches are proposed for the two extensions of the Weber problem, respectively. The special characteristics of those approaches are that they integrate optimization techniques and GIS functionality. Empirical results highlight the advantages of the developed approaches and the importance of solution integration within GIS.