### Abstract

A dynamic network introduced by Ford and Fulkerson is a directed graph with capacities and transit times on its arcs. The quickest transshipment problem is one of the most fundamental problems in dynamic networks. In this problem, we are given sources and sinks. Then, the goal of this problem is to find a minimum time limit such that we can send exactly the right amount of flow from sources to sinks. In this paper, we introduce a variant of this problem called the mixed evacuation problem. This problem models an emergent situation in which people can evacuate on foot or by car. The goal is to organize such a mixed evacuation so that an efficient evacuation can be achieved. In this paper, we study this problem from the theoretical and practical viewpoints. In the first part, we prove the polynomial-time solvability of this problem in the case where the number of sources and sinks is not large, and also prove the polynomial-time solvability and computational hardness of its variants with integer constraints. In the second part, we apply our model to the case study of Minabe town in Wakayama prefecture, Japan.

Original language | English |
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Title of host publication | Combinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings |

Editors | Minming Li, Lusheng Wang, T-H. Hubert Chan |

Publisher | Springer Verlag |

Pages | 18-52 |

Number of pages | 35 |

ISBN (Print) | 9783319487489 |

DOIs | |

Publication status | Published - Jan 1 2016 |

Event | 10th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2016 - Hong Kong, China Duration: Dec 16 2016 → Dec 18 2016 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10043 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 10th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2016 |
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Country | China |

City | Hong Kong |

Period | 12/16/16 → 12/18/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings*(pp. 18-52). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10043 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-48749-6_2

**The mixed evacuation problem.** / Hanawa, Yosuke; Higashikawa, Yuya; Kamiyama, Naoyuki; Katoh, Naoki; Takizawa, Atsushi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Combinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10043 LNCS, Springer Verlag, pp. 18-52, 10th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2016, Hong Kong, China, 12/16/16. https://doi.org/10.1007/978-3-319-48749-6_2

}

TY - GEN

T1 - The mixed evacuation problem

AU - Hanawa, Yosuke

AU - Higashikawa, Yuya

AU - Kamiyama, Naoyuki

AU - Katoh, Naoki

AU - Takizawa, Atsushi

PY - 2016/1/1

Y1 - 2016/1/1

N2 - A dynamic network introduced by Ford and Fulkerson is a directed graph with capacities and transit times on its arcs. The quickest transshipment problem is one of the most fundamental problems in dynamic networks. In this problem, we are given sources and sinks. Then, the goal of this problem is to find a minimum time limit such that we can send exactly the right amount of flow from sources to sinks. In this paper, we introduce a variant of this problem called the mixed evacuation problem. This problem models an emergent situation in which people can evacuate on foot or by car. The goal is to organize such a mixed evacuation so that an efficient evacuation can be achieved. In this paper, we study this problem from the theoretical and practical viewpoints. In the first part, we prove the polynomial-time solvability of this problem in the case where the number of sources and sinks is not large, and also prove the polynomial-time solvability and computational hardness of its variants with integer constraints. In the second part, we apply our model to the case study of Minabe town in Wakayama prefecture, Japan.

AB - A dynamic network introduced by Ford and Fulkerson is a directed graph with capacities and transit times on its arcs. The quickest transshipment problem is one of the most fundamental problems in dynamic networks. In this problem, we are given sources and sinks. Then, the goal of this problem is to find a minimum time limit such that we can send exactly the right amount of flow from sources to sinks. In this paper, we introduce a variant of this problem called the mixed evacuation problem. This problem models an emergent situation in which people can evacuate on foot or by car. The goal is to organize such a mixed evacuation so that an efficient evacuation can be achieved. In this paper, we study this problem from the theoretical and practical viewpoints. In the first part, we prove the polynomial-time solvability of this problem in the case where the number of sources and sinks is not large, and also prove the polynomial-time solvability and computational hardness of its variants with integer constraints. In the second part, we apply our model to the case study of Minabe town in Wakayama prefecture, Japan.

UR - http://www.scopus.com/inward/record.url?scp=85007210070&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007210070&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-48749-6_2

DO - 10.1007/978-3-319-48749-6_2

M3 - Conference contribution

SN - 9783319487489

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 18

EP - 52

BT - Combinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings

A2 - Li, Minming

A2 - Wang, Lusheng

A2 - Chan, T-H. Hubert

PB - Springer Verlag

ER -