Bi-level Problem with Facility Allocation for Evacuation Planning

Authors

  • Durga Prasad Khanal Saraswati Multiple Campus, Tribhuvan University, Kathmandu, Nepal
  • Urmila Pyakurel Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal.
  • Tanka Nath Dhamalab Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal.
  • Stephan Dempec Faculty of Mathematics and Computer Science, TU Bergakademie Freiberg, Germany.

DOI:

https://doi.org/10.3329/ganit.v44i2.78528

Keywords:

Evacuation planning; Maximum flow; Facility allocation; Bi-level optimization

Abstract

At the time of evacuation, placement of the facilities for the support of evacuees is an important task. The proper allocation of the facilities in such a way that the reduction in the flow value due to the placement of facilities on the arcs is minimal, is another important aspect of the problem. In this paper, we introduce an evacuation planning problem with facility allocation by using bi-level formulation. The upper level problem identifies the best possible location and lower level problem finds the optimal solution in the network with facility allocation. We solve the problem with a naive approach of combinatorial optimization and the Karush-Kuhn-Tucker (KKT) transformation.

J. Bangladesh Math. Soc. 44.2 (2024) 017–027

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Published

2024-12-29

How to Cite

Khanal, D. P., Pyakurel, U., Dhamalab, T. N., & Dempec, S. (2024). Bi-level Problem with Facility Allocation for Evacuation Planning. GANIT: Journal of Bangladesh Mathematical Society, 44(2), 17–27. https://doi.org/10.3329/ganit.v44i2.78528

Issue

Vol. 44 No. 2 (2024)

Section

Articles

License

The copyright of GANIT: Journal of Bangladesh Mathematical Society is reserved by Bangladesh Mathematical Society (web: https://bdmathsociety.org/)