Electric cars are projected to become the vehicles of the future. A major barrier for their expansion is range anxiety stemming from the limited range a typical EV can travel. EV batteries' performance and capacity are affected by many factors. In particular, the decrease in ambient temperature below a certain threshold will adversely affect the battery's efficiency. This research develops deterministic and two-stage stochastic program model for charging stations' optimal location to facilitate the routing decisions of delivery services that use EVs while considering the variability inherent in climate and customer demand. To evaluate the proposed formulation and solution approach's performance, Fargo city in North Dakota is selected as a tested. For the first chapter, we formulated this problem as a mixed-integer linear programming model that captures the realistic charging behavior of the DCFC's in association with the ambient temperature and their subsequent impact on the EV charging station location and routing decisions. Two innovative heuristics are proposed to solve this challenging model in a realistic test setting, namely, the two-phase Tabu Search-modified Clarke and Wright algorithm and the Sweep-based Iterative Greedy Adaptive Large Neighborhood algorithm. The results clearly indicate that the EV DCFC charging station location decisions are highly sensitive to the ambient temperature, the charging time, and the initial state-of-charge. The results provide numerous managerial insights for decision-makers to efficiently design and manage the DCFC EV logistic network for cities that suffer from high-temperature fluctuations. For the second chapter, a novel solution approach based on the progressive hedging algorithm is presented to solve the resulting mathematical model and to provide high-quality solutions within reasonable running times for problems with many scenarios. We observe that the location-routing decisions are susceptible to the EV logistic's underlying climate, signifying that decision-makers of the DCFC EV logistic network for cities that suffer from high-temperature fluctuations would not overlook the effect of climate to design and manage the respective logistic network efficiently.

Integer partitions have been studied by many mathematicians over hundreds of years. Many identities exist between integer partitions, such as Euler’s discovery that every number has the same amount of partitions into distinct parts as into odd parts. These identities can be proven using methods such as conjugation or generating functions. Over the years, mathematicians have worked to expand partition identities to vectors. In 1963, M. S. Cheema proved that every vector has the same number of partitions into distinct vectors as into vectors with at least one component odd. This parallels Euler’s result for integer partitions. The primary purpose of this paper is to use generating functions to prove other vector partition identities that parallel results of integer partitions.

A Positive Engagement, Continuously Variable Transmission (PECVT) allows for a continuously variable transmission ratio over a given range using positively engaged members, such as gear teeth, to transmit torque. This research is an investigation of PECVTs to establish a classification system and governing principles that must be satisfied for an embodiment to overcome the non-integer tooth problem. Results of an external patent search are given as examples of different concepts and PECVT embodiments that have been employed to negate the effects of the non-integer tooth problem. To classify all published and unpublished PECVT embodiments, a classification system is developed, based on how particular PECVT embodiments overcome the non-integer tooth problem. Two classes of PECVTs are defined: 1) the problem correction class and 2) the alternate device class. General principles that must be satisfied for a promising PECVT embodiment to exist in each class of PECVTs are also developed. These principles, along with the classification system, are the major contribution of this research. The principles describe what an embodiment in each of the PECVT classes must accomplish to negate the effects of the non-integer tooth problem. A product development phase integrated with TRIZ methodology is implemented to generate several concepts that satisfy the newly developed general principles and the product specifications that were also created. A screening and scoring process is used to eliminate less promising concepts and to find the most viable PECVT embodiment. An embodiment that only operates at preferred transmission ratios, where no meshing problems exist, proves to be the most promising concept based on the results of this methodology. The embodiment also utilizes cams and a differential device to provide the needed correction to the orientation of the driving members when misalignment occurs. This misalignment only occurs while transitioning between preferred operating ratios. A case study of the final embodiment developed by Vernier Moon Technologies and Brigham Young University is presented and analyzed to show how the final concepts ensure proper engagement without the effects of the non-integer tooth problem. The final embodiment is not the optimal solution but represents a conceptual design of an embodiment that satisfies the governing principles. The classification system and the governing principles that have been established are valid for all PECVT embodiments and will be valuable in future research. Future work yet to be conducted for this research, including an involutometry analysis, is discussed as well as other recommendations.

A new architecture for a frequency synthesizer with adjustable output frequency range and channel spacing is introduced. It is intended for the generation of closely spaced frequency channels in the GHz range while producing minimal spurious phase noise components. The architecture employs two independent phase-locked loops that are driven in cascade by a single reference oscillator. The approach provides fine resolution and wide bandwidth as well as low phase noise and should find application in many contemporary communication systems. The synthesizer can be operated in either of two different modes: nonfractional and mini-denominator fractional modes. The architecture produces no fractional spurs in the first mode and relatively small phase spurs when operated in the second mode. For example, in an application to a P-GSM 900 system, it is capable of tuning from 890 – 915 MHz with a channel spacing of 200 kHz and shows worst case phase spurs of -100 dBc at an offset frequency of 833 kHz. Because of the low magnitude and location of the worst case spurs, the phase-locked loop filters can be designed with a wide bandwidth which in turn results in a fast settling time. A linear frequency-switching settling time (to 0.01% of frequency increments) of 128 μs is typical in the P-GSM 900 application.

The goal of this thesis is to create an optimization model to optimize the routing of trains within railway stations. This problem is known as the train platforming problem, and the model we present is an integer programming model. By this model we aim to optimize factors such as walking distance, switch usage or platform usage. We validate the model by implementing the model for Linköping station, which is a typical mid size station in the Swedish railway network. This implementation is done for different time horizons, ranging from 2 hours to one day, which corresponds to train sets ranging from 27 to 265 trains. In the conclusion we see that the model is efficient for optimizing the train platforming problem for the implemented station and timetables, and that the model has a possibility to optimize the four objectives tested. Furthermore we see that optimizing certain objectives gives solutions that are also good with regards to other objective functions. / Målet med den här uppsatsen är att skapa en optimeringsmodell för att optimera valet av vägar för tåg genom tågstationer. Modellen vi presenterar är en heltalsmodell, där syftet är att minimera bland annat gångavstånd, användningen av tågväxlar eller användningen av perronger. För att testa modellen presenterar vi en implementation av modellen för stationen i Linköping, vilken är en typisk mellanstor station i det svenska tågnätet. Impplementeringen är gjord för olika tidslängder, från 2 timmar till ett dygn vilket motsvarar dataset från 27 till 265 tåg. Vi drar slutsatsen att modellen på ett effektivt sätt kan lösa valet av tågvägar genom stationen, för de fyra tidtabeller och den station vi har implementerat. Vidare ser vi att modellen har potential att optimera de fyra målfunktioner vi testat och att optimering av några av målfunktionerna ger lösningar som är bra även med hänsyn till de andra målfunktionerna.

PLAS is a cloud-based software used for planning and scheduling fleets of vehicles for material transport. PLAS consists of two components; the Logistic Flow Solver (LFS) and the Material Transport Scheduler (MTS). Based on transportation requests, the LFS generates a set of logistic flows. The MTS then transforms the logistic flows into tasks that are assigned to the vehicles. The LFS is implemented with Mixed Integer Linear Programming (MILP). Currently, the LFS and the MTS are decoupled from each other and there is information that is not considered in the LFS. Thus, the choice of logistic flows generated with the current formulation may negatively impact the final transport plan. The objective of this thesis is to investigate how the generation of logistic flows can be improved. Two alternative mathematical models for the LFS were developed using MILP formulation. Compared to the current model, more information is taken into account in the two new models. Three different objective functions were considered. Scheduling of the vehicles were modelled as pickup and delivery problems, where pickup and delivery pairs correspond to the generated logistic flows. The models were implemented using Google OR-Tools, an open-source software suite for optimization. The different mathematical formulations were evaluated based on their performance for test problems with different fleet compositions. The results show that problem characteristics influence the performance of the models and that there is no model that gives the best result for every type of problem. Therefore, it is necessary to analyse problem characteristics in order to choose a suitable model for generation of logistic flows. / PLAS är en molnbaserad mjukvara som används för planering och schemaläggning av fordonsflottor för materialtransport. PLAS består av två komponenter; Logistic Flow Solver (LFS) and Material Transport Scheduler (MTS). Baserat på transportbehov genererar LFS ett antal logistikflöden. MTS omvandlar sedan logistikflödena till uppdrag som är tilldelade till fordonen. LFS är implementerad med blandad heltalsprogrammering. För närvarande är LFS och MTS frikopplade från varandra och det finns information som inte tas hänsyn till i LFS. Därför kan valet av logistikflöden genererade med den nuvarande formuleringen negativt påverka den slutliga transportplanen. Målet med detta examensarbete är att undersöka hur genereringen av logistikflöden kan förbättras. Två alternativa matematiska modeller utvecklades med MILP-formulering. Jämfört med den nuvarande modellen, tar de två nya modellerna hänsyn till mer information. Tre olika målfunktioner beaktades. Modellerna implementerades med Google OR-Tools, en öppen programvara för optimering. De matematiska formuleringarna utvärderades baserat på deras prestation på testproblem med olika kompositioner av fordonsflottor. Resultaten visar att problemegenskaper påverkar modellernas prestationer och att det inte finns någon modell som ger bäst resultat för varje problemtyp. Därför är det nödvändigt att analysera problemegenskaper för att kunna välja en lämplig modell för generering av logistikflöden.

Throughout United States and world history, disasters have caused not only significant loss of life, property but also enormous financial loss. The tsunami that occurred on December 26, 2004 is a telling example of the devastation that can occur unexpectedly. This unexpected natural event never happened before in this area. In addition, there was a lack of an emergency response plan for events of that magnitude. Therefore, this event resulted not only in a natural catastrophe for the people of South and Southeast Asia, but it is also considered one of the greatest natural disasters in world history. After the giant wave dissipated, there were more than 230,000 people dead and more than US$10 billion in property damage and loss. Another significant event was the terrorist incident on September 11, 2001 (commonly referred to as 9/11) in United States. This event was unexpected and an unnatural, i.e., man-made event. It resulted in approximately 3,000 lives lost and about US$21 billion in property damage. These and other unexpected (or unanticipated) events give emergency management officials short- or no-notice to prevent or respond to the situation. These and other facts motivate the need for better emergency evacuation route planning (EERP) approaches in order to minimize the loss of human lives and property in short- or no-notice emergency situations. This research considers aspects of evacuation routing that have received little attention in research and, more importantly, in practice. Previous EERP models only either consider unidirectional evacuee flow from the source of a hazard to destinations of safety or unidirectional emergency first responder flow to the hazard source. However, in real-life emergency situations, these heterogeneous, incompatible flows occur simultaneously over a bi-directional capacitated lane-based travel network, especially in short- and no-notice emergencies. After presenting a review of the work related to the multiple flow EERP problem, mathematical formulations are presented for the EERP problem where the objective for each problem is to identify an evacuation routing plan (i.e., a traffic flow schedule) that maximizes evacuee and responder flow and minimizes network clearance time of both types of flow. In addition, we integrate the general human response behavior flow pattern, where the cumulative flow behavior follows different degrees of an S-shaped curve depending upon the level of the evacuation order. We extend the analysis to consider potential traffic flow conflicts between the two types of flow under these conditions. A conflict occurs when flow of different types occupy a roadway segment at the same time. Further, with different degrees of flow movement flow for both evacuee and responder flow, the identification of points of flow congestion on the roadway segments that occur within the transportation network is investigated.

Downstream vehicles detect an emergency response vehicle (ERV) through sirens and/or strobe lights. These traditional warning systems do not give any recommendation about how to react, leaving the drivers confused and often adopting unsafe behavior while trying to open a passage for the ERV. In this research, an advanced intra-link emergency assistance system, that leverages the emerging technologies of the connected vehicle environment, is proposed. The proposed system assumes the presence of a centralized system that gathers/disseminates information from/to connected vehicles via vehicle-to-infrastructure (V2I) communications. The major contribution of this dissertation is the intra-link level support provided to ERV as well as non-ERVs. The proposed system provides network-wide assistance as it also considers the routing of ERVs. The core of the system is a mathematical program - a set of equations and inequalities - that generates, based on location and speed data from connected vehicles that are downstream of the ERV, the fastest intra-link ERV movement. It specifies for each connected non-ERV a final assigned position that the vehicle can reach comfortably along the link. The system accommodates partial market penetration levels and is applicable on large transportation link segments with signalized intersections. The system consists of three modules (1) an ERV route generation module, (2) a criticality analysis module and (2) the sequential optimization module. The first module determines the ERV's route (set of links) from the ERV's origin to the desired destination in the network. Based on this selected route, the criticality analysis module scans/filters the connected vehicles of interest and determines whether any of them should be provided with a warning/instruction message. As the ERV is moving towards its destination, new non-ERVs should be notified. When a group of non-ERVs is identified by the criticality analysis module, a sequential optimization module is activated. The proposed system is evaluated using simulation under different combinations of market penetration and congestion levels. Benefits in terms of ERV travel time with an average reduction of 9.09% and in terms of vehicular interactions with an average reduction of 35.46% and 81.38% for ERV/non-ERV and non-ERV/non-ERV interactions respectively are observed at 100% market penetration, when compared to the current practice where vehicles moving to the nearest edge. / Doctor of Philosophy / Downstream vehicles detect an emergency response vehicle (ERV) through sirens and/or strobe lights. These traditional warning systems do not give any recommendations about how to react, leaving the drivers confused and often adopting unsafe behavior while trying to open a passage for the ERV. In this research, an advanced intra-link emergency assistance system, that leverages the emerging technologies of the connected vehicle environment, is proposed. The proposed system assumes the presence of a centralized system that gathers/disseminates information from/to connected vehicles via vehicle-to-infrastructure (V2I) communications. The major contribution of this dissertation is the intra-link level support provided to ERV as well as non-ERVs. The proposed system provides network-wide assistance as it also considers the routing of ERVs. The core of the system is a mathematical program - a set of equations and inequalities - that generates, based on location and speed data from connected vehicles that are downstream of the ERV, the fastest intra-link ERV movement. It specifies for each connected non-ERV a final assigned position that the vehicle can reach comfortably along the link. The system accommodates partial market penetration levels and is applicable on large transportation link segments with signalized intersections. The system consists of three modules (1) an ERV route generation module, (2) a criticality analysis module and (2) the sequential optimization module. The first module determines the ERV’s route (set of links) from the ERV’s origin to the desired destination in the network. Based on this selected route, the criticality analysis module scans/filters the connected vehicles of interest and determines whether any of them should be provided with a warning/instruction message. As the ERV is moving towards its destination, new non-ERVs should be notified. When a group of non-ERVs is identified by the criticality analysis module, a sequential optimization module is activated. The proposed system is evaluated using simulation under different combinations of market penetration and congestion levels. Benefits in terms of ERV travel time with an average reduction of 9.09% and in terms of vehicular interactions with an average reduction of 35.46% and 81.38% for ERV/non-ERV and non-ERV/non-ERV interactions respectively are observed at 100% market penetration, when compared to the current practice where vehicles moving to the nearest edge.

In countries like the US, public school systems function through school districts, which are geographical areas where schools share the same administrative structure and are often coterminous with the boundary of a city or a county. School districts play an important role in the functioning of society. In a well-run school district with safe and well-functioning schools, graduating enough students can enhance the quality of life in its area. Conversely, a poorly run district may cause growth in the area to be far less than surrounding areas, or even a decline in population over time. To promote the efficient functioning of the school district, the boundaries of public schools are redrawn from time to time by the school board/planning officials. In the majority of the cases, this process of redrawing the school boundaries, also called school redistricting or school boundary formation, is done manually by the planners and involves hand-drawn maps. Given the rapid advancements in GIS made in the last decade and the availability of high-quality geospatial data, we opine that an objective treatment of the school redistricting problem by a data-driven model can assist the school board/ decision-makers by providing them with automated plans. These automated plans may serve as possible suggestions to the planners, who can adapt them to prepare their own plans in the way they see fit based on their subjective knowledge and expertise. In this dissertation, we propose algorithmic techniques for solving the problem of (school) redistricting, which is an NP-hard problem. We primarily investigate optimization-based algorithms for solving the problem. Our approaches include (i) clustering, (ii) local search, and (iii) memetic algorithms. We also propose ways of solving the problem using exact methods and fair redistricting techniques based on ethical considerations. The techniques developed here are generic enough to be applied to other redistricting problems with some degree of modification in the objective function and constraint-handling techniques. The source code and corresponding datasets are available at https://github.com/subhodipbiswas/schoolredistricting. / Doctor of Philosophy / In many countries, public school systems function through school districts, which are geographical areas where schools share the same administrative structure and are often coterminous with the boundary of a city or a county. To promote efficient functioning of the school district, the boundaries of public schools are redrawn from time to time by the school board/planning officials. In the majority of the cases, this process of redrawing the school boundaries, also called school redistricting, is done manually by the planners and involves hand-drawn maps. Given the rapid advancements in GIS made in the last decade and the availability of high-quality geospatial data, we opine that an objective treatment of the school redistricting problem by a data-driven model can assist the school board/ decision-makers by providing them with automated plans. In this presentation, we propose algorithmic techniques for solving the school redistricting problem. Our approaches include (i) clustering, (ii) local search, and (iii) memetic algorithms. We also show that MCMC-based techniques can aid in enabling exact methods to operate on this problem. Lastly, we briefly highlight ethical considerations involved in the process of school redistricting and throw light on some ways to devise more ethically-aware strategies for doing school redistricting. The results indicate that the proposed methods could be a valuable decision-making tool for school officials.

Some observations concerning the lattices of integer partitions are presented. We determine the size of the standard contexts, discuss a recursive construction and show that the lattices have unbounded breadth.