# 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.

Status | Finished |
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Effective start/end date | 9/1/12 → 9/1/13 |

### Funding

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