### Abstract

In the early stages of development, alternative-fuel vehicles will tend to have shorter driving ranges than conventional vehicles, and the availability of stations will be limited. Given these conditions, it is important to consider the willingness of drivers to deviate to some extent from their shortest paths in order to refuel their vehicles and complete their trips. Previously, we proposed the deviation-flow refueling location model (DFRLM) for locating a given number of refueling facilities to maximize the total alternative-fuel vehicle flows that can be refueled by drivers traveling on or deviating from their shortest paths. On a real-world problem, however, the large number of possible deviations from each path and of combinations of facilities that can cover each path would make it extremely difficult to generate and solve the mixed-integer formulation. This paper develops heuristic algorithms for the DFRLM that overcome this difficulty through network transformation. Specifically, a greedy heuristic constructs and edits an artificial feasible network in which each node represents a station, origin, or destination, and each arc represents a feasible path between two nodes given the assumed driving range of vehicles. At each step of the greedy and greedy-substitution algorithms, the feasible network is edited and a shortest path algorithm is run, which determines whether each origin-destination round trip can be completed. This method allows any possible detour to be taken (up to some user-defined maximum) while also ensuring that drivers take the smallest possible detour. Computational experiments on a simple network and a real-world network for Florida show the heuristics to be efficient in solving the problems. Comparisons between the results of the DFRLM and the FRLM indicate that taking driver deviations into account in the model can have a significant effect on the locations chosen and demand covered.

Original language | English (US) |
---|---|

Pages (from-to) | 1122-1131 |

Number of pages | 10 |

Journal | Computers and Operations Research |

Volume | 40 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2013 |

### Fingerprint

### Keywords

- Detour
- Energy
- Heuristics
- Location
- Network design
- Path deviation
- Refueling station

### ASJC Scopus subject areas

- Computer Science(all)
- Management Science and Operations Research
- Modeling and Simulation

### Cite this

**A network transformation heuristic approach for the deviation flow refueling location model.** / Kim, Jong Geun; Kuby, Michael.

Research output: Contribution to journal › Article

*Computers and Operations Research*, vol. 40, no. 4, pp. 1122-1131. https://doi.org/10.1016/j.cor.2012.10.021

}

TY - JOUR

T1 - A network transformation heuristic approach for the deviation flow refueling location model

AU - Kim, Jong Geun

AU - Kuby, Michael

PY - 2013/4

Y1 - 2013/4

N2 - In the early stages of development, alternative-fuel vehicles will tend to have shorter driving ranges than conventional vehicles, and the availability of stations will be limited. Given these conditions, it is important to consider the willingness of drivers to deviate to some extent from their shortest paths in order to refuel their vehicles and complete their trips. Previously, we proposed the deviation-flow refueling location model (DFRLM) for locating a given number of refueling facilities to maximize the total alternative-fuel vehicle flows that can be refueled by drivers traveling on or deviating from their shortest paths. On a real-world problem, however, the large number of possible deviations from each path and of combinations of facilities that can cover each path would make it extremely difficult to generate and solve the mixed-integer formulation. This paper develops heuristic algorithms for the DFRLM that overcome this difficulty through network transformation. Specifically, a greedy heuristic constructs and edits an artificial feasible network in which each node represents a station, origin, or destination, and each arc represents a feasible path between two nodes given the assumed driving range of vehicles. At each step of the greedy and greedy-substitution algorithms, the feasible network is edited and a shortest path algorithm is run, which determines whether each origin-destination round trip can be completed. This method allows any possible detour to be taken (up to some user-defined maximum) while also ensuring that drivers take the smallest possible detour. Computational experiments on a simple network and a real-world network for Florida show the heuristics to be efficient in solving the problems. Comparisons between the results of the DFRLM and the FRLM indicate that taking driver deviations into account in the model can have a significant effect on the locations chosen and demand covered.

AB - In the early stages of development, alternative-fuel vehicles will tend to have shorter driving ranges than conventional vehicles, and the availability of stations will be limited. Given these conditions, it is important to consider the willingness of drivers to deviate to some extent from their shortest paths in order to refuel their vehicles and complete their trips. Previously, we proposed the deviation-flow refueling location model (DFRLM) for locating a given number of refueling facilities to maximize the total alternative-fuel vehicle flows that can be refueled by drivers traveling on or deviating from their shortest paths. On a real-world problem, however, the large number of possible deviations from each path and of combinations of facilities that can cover each path would make it extremely difficult to generate and solve the mixed-integer formulation. This paper develops heuristic algorithms for the DFRLM that overcome this difficulty through network transformation. Specifically, a greedy heuristic constructs and edits an artificial feasible network in which each node represents a station, origin, or destination, and each arc represents a feasible path between two nodes given the assumed driving range of vehicles. At each step of the greedy and greedy-substitution algorithms, the feasible network is edited and a shortest path algorithm is run, which determines whether each origin-destination round trip can be completed. This method allows any possible detour to be taken (up to some user-defined maximum) while also ensuring that drivers take the smallest possible detour. Computational experiments on a simple network and a real-world network for Florida show the heuristics to be efficient in solving the problems. Comparisons between the results of the DFRLM and the FRLM indicate that taking driver deviations into account in the model can have a significant effect on the locations chosen and demand covered.

KW - Detour

KW - Energy

KW - Heuristics

KW - Location

KW - Network design

KW - Path deviation

KW - Refueling station

UR - http://www.scopus.com/inward/record.url?scp=84871769156&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871769156&partnerID=8YFLogxK

U2 - 10.1016/j.cor.2012.10.021

DO - 10.1016/j.cor.2012.10.021

M3 - Article

VL - 40

SP - 1122

EP - 1131

JO - Surveys in Operations Research and Management Science

JF - Surveys in Operations Research and Management Science

SN - 0305-0548

IS - 4

ER -