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Partial contraflow with path reversals for evacuation planning

  • S.I.: Applications of OR in Disaster Relief Operations
  • Published:
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Abstract

The challenges in evacuation planning have been vital because of rapid disasters and limited road capacity. Contraflow strategy is very effective and widely accepted approach for the optimal use of available road network in evacuation management that increases the outward road capacities from the disastrous areas towards the safe destinations. Modeling the contraflow problem mathematically, there are available a number of efficient solution algorithms in literature, however, in general, the problem is still computationally quite hard. In this paper, we introduce the partial contraflow approach, in the abstract network setting with flow on paths and adapt the previous contraflow solution techniques to save unused capacities of road segments (elements) which can be used for supplying other facilities during emergency. We present efficient algorithms to solve the maximum static, lex-maximum static, maximum dynamic and earliest arrival partial contraflow problems on an abstract network. We also present an approximation algorithm to solve 2-value approximate earliest arrival transshipment partial contraflow problem for multi-terminal abstract network. Implementation of the partial contraflow reconfiguration leads to a significant improvement in increasing the flow values, decreasing the evacuation time, and utilizing the unused capacities of paths for humanitarian logistics and vehicle movements.

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Acknowledgements

The authors acknowledge the supports of DAAD Partnership Program and AvH Research Group Linkage Program in Graph Theory and Optimization at Central Department of Mathematics, Tribhuvan University. Additionally, the first author thanks AvH Foundation for supporting the postdoctoral research at TU Bergakademie Freiberg, Germany and the second author thanks UGC Nepal for PhD research fellowship. The authors would also like to thank the anonymous referees and the editor for their valuable suggestions to improve the quality of this paper.

Author information

Authors and Affiliations

  1. Central Department of Mathematics, Tribhuvan University, P.O.Box 13143, Kathmandu, Nepal

    Urmila Pyakurel & Tanka Nath Dhamala

  2. Department of Mathematics, Bhaktapur Multiple Campus, Tribhuvan University, Bhaktapur, Nepal

    Hari Nandan Nath

Authors
  1. Urmila Pyakurel
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  2. Hari Nandan Nath
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  3. Tanka Nath Dhamala
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Corresponding author

Correspondence to Urmila Pyakurel.

Appendix A: Kathmandu road network used in Sect. 5 (cf. Fig. 4)

Appendix A: Kathmandu road network used in Sect. 5 (cf. Fig. 4)

Road segment

Capacity (per second)

Travel time (min)

Forward

Backward

s-1

2

2

6

s-12

2

2

10

s-18

2

2

3

s-27

2

2

4

1-2

2

2

3

1-27

2

2

5

2-3

3

3

5

2-38

3

3

12

3-4

3

3

5

3-27

2

2

6

4-5

3

3

1

4-32

2

2

1

5-6

3

3

1

5-42

2

2

7

6-7

3

3

5

6-23

2

2

2

7-8

3

3

8

7-17

2

2

10

7-d

2

2

5

8-9

2

2

16

8-d

3

3

7

9-10

2

2

3

9-17

2

2

3

10-11

2

2

5

11-12

2

2

17

11-37

2

2

7

12-13

2

2

4

13-14

2

2

6

13-33

2

2

9

14-15

2

2

1

14-33

2

2

3

15-16

2

2

1

15-35

2

2

1

16-17

2

2

1

16-36

2

2

3

16-37

4

0

1

18-19

2

2

2

18-28

2

2

2

19-20

2

2

2

19-29

2

2

2

20-21

2

2

2

20-30

2

2

2

20 – 33

2

2

1

21 – 26

0

4

1

21 – 34

2

2

1

22 – 23

4

0

1

22 – 32

2

2

1

23 – 24

4

0

1

24 – 25

4

0

2

25 – 26

4

0

1

26 – 35

2

2

2

27 – 28

2

2

3

28 – 29

4

0

2

29 – 30

4

0

1

30 – 31

2

2

2

31 – 32

2

2

2

33 – 34

2

2

2

34 – 35

2

2

1

35 – 36

2

2

2

38 – 39

3

3

7

38 – 42

2

2

8

39 – 40

3

3

1

39 – 41

2

2

1

40 – 41

2

2

2

40 – d

3

3

8

41 – 42

2

2

2

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Pyakurel, U., Nath, H.N. & Dhamala, T.N. Partial contraflow with path reversals for evacuation planning. Ann Oper Res 283, 591–612 (2019). https://doi.org/10.1007/s10479-018-3031-8

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  • DOI: https://doi.org/10.1007/s10479-018-3031-8

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