Multi-objective optimization of two-echelon vehicle routing problem: Vaccines distribution as a case study

Nader Al Theeb, Mohammed Abu-Aleqa, Ali Diabat

Research output: Contribution to journalArticlepeer-review


During pandemics, the efficiency of the vaccine supply chain may be compromised, especially the last-mile distribution, due to poor infrastructure that is unable to support the urgent need for vaccination. In developing countries, this becomes even more challenging due to limited vehicles, road conditions, and inadequate cold storage. Since it is impractical to construct permanent warehouses when pandemics occur, vaccine distribution would be extravagant both environmentally and financially. In this study, a new multi-objective MILP model combining two-echelon vehicle routing problem (2E-VRP) and vaccine supply chain (VSC) is presented to minimize the number of unsatisfied doses undelivered to customers. A heuristic solution based on the greedy random search is proposed to solve the model, as it is classified as NP-hard model. The model is solved using the commercial solver CPLEX for different datasets. Then the heuristic is used to solve the same datasets, and the results are compared based on the solution's quality and computation efforts. Moreover, Pareto fronts were constructed to demonstrate the trade-offs between the conflicting objective functions. Finally, a real case study is solved using the proposed model to demonstrate its effectiveness compared to the original VRP, and the results showed an improvement of average 11.97% in the number of doses delivered.

Original languageEnglish (US)
Article number109590
JournalComputers and Industrial Engineering
StatePublished - Jan 2024


  • Multiple objective programming
  • Two-echelon vehicle routing problem
  • Vaccine distribution

ASJC Scopus subject areas

  • General Computer Science
  • General Engineering


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