A bi-level optimization model for aid distribution after the occurrence of a disaster

José Fernando Camacho-Vallejo*, Edna González-Rodríguez, F. Javier Almaguer, Rosa G. González-Ramírez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


In this paper the authors propose a bi-level mathematical programming model for humanitarian logistics to optimize decisions related to the distribution of international aid after a catastrophic disaster. In this situation, non-profit international organizations and foreign countries will offer to help by shipping certain necessary products, such as bottled water, food and medicine, but will want to minimize the shipping costs. At the same time, the affected country seeks to distribute the received aid to the affected areas as efficiently and quickly as possible. To deal with the considered problem, we reformulate the bi-level model and reduce it into a nonlinear single-level mathematical model; then we linearize it to obtain a mixed integer programming problem. To validate the proposed mathematical model, we consider as a case study the earthquake in Chile in 2010. We solve the reformulated model by using real data simulating the aid distribution scenario, and we interpret the obtained numerical results, giving some recommendations for aid distribution following future disasters.

Original languageEnglish
Pages (from-to)134-145
Number of pages12
JournalJournal of Cleaner Production
StatePublished - 15 Oct 2015
Externally publishedYes

Bibliographical note

Funding Information:
This research received partial support from the Secretariat of Public Education (SEP by its acronym in Spanish) within the Academic Groups research project PROMEP/103.5/12/4953 and the Autonomous University of Nuevo León (UANL) within the Support Program for Scientific Research and Technology (PAICYT) with the Project CE960-11 . The authors would like to thank Mr. Randy Smith for his editing review for improve the readability of this paper.

Publisher Copyright:
© 2014 Elsevier Ltd. All rights reserved.


  • Bi-level programming
  • Disasters
  • Distribution problem
  • Humanitarian logistics


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