## Project Details

### Description

At the center of my interests in transportation is the analysis of complex transportation networks. The properties of transportation networks, whether they are road networks, flight networks, or shipping routes, change our lives in meaningful ways. Only in the past few decades has research into the mathematical structure of the network become so practical. My research in mathematics with industrial applications as an undergraduate, my masters degree in applied mathematics with a focus in discrete mathematics, and my industry experience at the Boeing Company make me well suited for research in this field. As a student in Industrial Engineering at Arizona State University working with Professor Pitu Mirchandani, I have been doing research on new operations research problems in public transportation networks. Specifically I have been studying the networks generated by replacing gasoline vehicles with vehicles that use alternative fuels. One of the exciting advances in the field of automotive transportation is the concept of an electric car. By using cars that require battery power instead of gasoline, consumers can help create a more sustainable country that uses less foreign oil. However, electric cars have a serious drawback: the limited range that they can travel before they recharge. One solution to this problem is to create locations where a nearly empty car battery could be immediately swapped for a fresh one. This nearly instantaneous transaction would allow consumers to continue driving beyond the original range of their cars. Until electric cars are ubiquitous, it is likely that there will only be a few places where battery swaps could occur. Thus, the locations of the swapping stations are immensely important. In the realm of public transportation, electric powered buses could be serviced by specific government owned battery swapping locations. The placement of these swapping venues is crucial since they will require the government to purchase and maintain the land, and should be centrally located to the trips the public buses are serving. These bus networks create a unique opportunity for using optimization techniques from the field of industrial engineering. The specific transportation research problem we have been working on is as follows: given a set of bus trips between locations, as well as the time the trips must be served, what is the best way to assign alternative fuel buses to the trips? Since the buses have a limited amount of battery power, they must periodically have their batteries swapped out with fresh ones at specific refueling stations. This optimization problem can be formulated as a mathematical model using a set of vertices and edges to represent the trips. A mathematical formulation will allow us to use standard operations research techniques to find solutions to the problem. While the problem of assigning buses to routes has been solved assuming unlimited fuel, by adding the constraint of a finite amount of battery and limited battery swapping locations, the problem becomes NP-hard. Even assuming that finding the optimal bus assignment, given a set of refueling locations, could be done quickly, the problem of choosing which locations would be best for the limited number of refueling stations is still difficult. We have several goals to we hope to accomplish with this research. First, we are interested in finding good heuristic algorithms to assign alternative fuel buses to trips, given a set of refueling locations. Second, given a set of trips to serve and a fixed number of refueling stations, we would like to find a heuristic algorithm to find the best locations to place the stations. Third, given a set of alternative fuel buses that have been assigned to trips and a set of refueling locations, we plan on modeling the number of batteries required at the stations so that the buses can swap batteries as necessary. This can be modeled as a stochastic process; unexpected delays in the bus schedule could cause the number of batteries required to fluctuate. At the center of my interests in transportation is the analysis of complex transportation networks. The properties of transportation networks, whether they are road networks, flight networks, or shipping routes, change our lives in meaningful ways. Only in the past few decades has research into the mathematical structure of these networks become so practical. My research in mathematics with industrial applications as an undergraduate, my masters degree in applied mathematics with a focus in discrete mathematics, and my industry experience at the Boeing Company make me well suited for research in this field. As a PhD student in industrial engineering at Arizona State University working with Professor Pitu Mirchandani, I have been doing research on new operations research problems in automotive transportation networks. Specifically I have been studying the networks generated by replacing gasoline vehicles with battery powered electric vehicles. One of the exciting advances in the field of automotive transportation is the concept of an electric automobile. By using vehicles that require battery power instead of gasoline, consumers can help create a more sustainable country that uses less foreign oil. However, electric vehicles have a serious drawback: there is a limited range that they can travel before they need to recharge. One solution to this problem is to create locations where a nearly empty vehicle battery could be immediately swapped for a fresh one. This nearly instantaneous transaction would allow consumers to continue driving beyond the original range of their automobiles. Until electric vehicles are ubiquitous, it is likely that there will only be a few places where battery swaps could occur. Thus, the locations of the swapping stations are immensely important, since if they are poorly placed then people will not purchase electric cars and the technology will not take off. In the realm of public transportation, electric powered buses could be serviced by specific government owned battery swapping locations. The placement of these swapping venues is crucial since they will require the government to purchase the land and maintain the facility, and should be centrally located to the trips the public buses are serving. These electric vehicle networks create a unique opportunity for using optimization techniques from the field of industrial engineering. The specific transportation research problem we have begun to study is as follows: for a given set of electric vehicles each with an origin, a destination, and a trip start time, what is the best way to route them through a road network? Assume that the network has several battery swapping stations placed in it. Since the number of batteries at each swapping station is limited, care must be taken to avoid sending vehicles to stations which are out of batteries. Properly managing the vehicle load across the stations will allow station operators to need fewer batteries on hand which will drive down the overall costs of the system. This will also allow for the vehicles to take shorter routes. This model can be further generalized by allowing the number of vehicles needing to move through the system to be a random variable, and for allowing the location of the swapping stations to be decision variables. We have several goals to we hope to accomplish with this research. First, we are interested in finding algorithms to route vehicles through the road network, given a set of battery swapping stations. This problem is difficult with routes of deterministic length, and becomes even more complex when the routes are allowed to have random lengths. The random route lengths represent delays in the system due to occurrences like traffic jams. Second, given knowledge of origin and destination demand for a road network, we are interested in how to decide where to place the battery swapping stations. Models exist to do this already, however they are fairly limited in the allowing of detours and random demand. We are also interested in finding the relationship between the locations of the battery swapping stations and how many Jonathan Adler Proposed Plan of Graduate Study Dwight David Eisenhower Transportation Fellowship Program batteries they should have on hand. This will allow us to minimize the overall number of batteries in the system and the overall number of stations needed. Between 2010 and 2011 and during the summer of 2012 I was a full time employee with the Boeing Company. There I was a part of the commercial market analysis team lead by Michael Warner. In this group, I used my mathematical background to try and forecast demand for air travel over the next five to twenty years. This job required me to use advanced mathematics to make intelligent predictions of the use of transportation networks in the future. Specifically, I investigated how the hub and spoke network model of airlines would change as new entrants arrived to the market, as well as how many aircraft would be needed to serve the routes. While I enjoyed my job immensely, I thought that it would be best if I went back to school to further hone my analytical skills. Thus, I took an educational leave of absence from the company so that I could attend Arizona State University and pursue a doctorate degree. At Arizona State University I have engaged in activities to prepare myself to be a researcher in the transportation field. I have submitted papers on the topic of electric vehicles to two journals, and have presented at conferences including the Transportation Research Board Annual Meeting. I have ensured I have the necessary background by taking courses relevant to transportation network analysis, and while doing so I have achieved a 4.00 GPA. I also have been heavily involved with my academic department and have taken on the leadership role of president of the student chapter of Informs, the operations research professional society. My long term goal is to remain in the transportation field as a researcher. My hope is to get a faculty position where I can continue to work on transportation problems that a relevant to todays society. I also hope to be able to work with companies doing transportation projects to provide guidance on solutions provided through academia. My experience so far with the Boeing Company and in academia has moved me in the right direction towards this goal. I believe that an advance degree from Arizona State University, especially one funded by the Dwight David Eisenhower Transportation Fellowship Program, would help me further the field of transportation.

Status | Finished |
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Effective start/end date | 9/1/13 → 9/1/14 |

### Funding

- DOT: Federal Highway Administration (FHWA): $11,500.00

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