Multi-objective mathematical model of location-routing for the distribution of the Last Mile Delivery of post parcels with Co‌2‌ emissions consideration

Articles in Press

Document Type : Research Note

Authors

1 Faculty of Management, Islamic Azad University, Firouzkooh branch, Iran

2 Department of Industrial Engineering, College of Management and Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran

3 Department of Industrial Engineering, Islamic Azad University, Firuzkooh Branch, Iran

4 Department of Management, Islamic Azad University, Firuzkooh Branch, Iran

10.24200/sci.2025.61997.7590

Abstract

In this article, a bi-objective location-routing mathematical model has been developed for the distribution of the Last Mile Delivery post parcels. The objectives of the model include minimization cost and tardiness penalty entered into the system due to the waiting of customers.  In order to solving the purposed mathematical model, a multi-objective Whale Optimization Algorithm (WOA) based on the Pareto archive and a Non-Dominated Sorting Genetic Algorithm (NSGA-II) have been used. The mathematical model solved for a sample problem by each of the algorithms, and the results have been compared according to the multi-objective evaluation criteria such as Quality Metric (QM), Diversity Metric (DM), Spacing Metric (SM), Number of Solutions (NOS), Mean Ideal Distance (MID), and computational time. The reviews of results indicate that the proposed multi-objective WOA has a higher capability in achieving accurate, diverse, and high-quality solutions rather than NSGA-II. In other words, the proposed multi-objective WOA act more efficiently to explore the feasible solution area of the problem by spending more computational time to achieve optimal solutions.

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Scientia Iranica

Articles in Press, Accepted Manuscript
Available Online from 12 May 2025

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History

  • Receive Date: 01 March 2023
  • Revise Date: 16 August 2024
  • Accept Date: 20 April 2025

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