Solving the inventory routing problem with the Archimedes optimization algorithm

Kevin Neuschwander; Thomas Hanne; Kevin Neuschwander; Thomas Hanne

doi:10.3934/era.2026394

Electronic Research Archive

2026, Volume 34, Issue 12: 9386-9405. doi: 10.3934/era.2026394

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Solving the inventory routing problem with the Archimedes optimization algorithm

Kevin Neuschwander ,
Thomas Hanne ^,

School of Business, University of Applied Sciences and Arts Northwestern Switzerland, Riggenbachstrasse 16, Olten 4600, Switzerland

Received: 24 February 2026 Revised: 30 April 2026 Accepted: 03 July 2026 Published: 10 November 2026

The inventory routing problem is a frequently occurring optimization problem in logistics processes, which considers scenarios where a vendor must find optimal solutions to distribute goods to multiple customers while having some flexibility regarding shipping times (i.e., on which days which quantities are delivered to a customer) due to warehousing possibilities. Due to the complexity of the problem, various optimization algorithms have been applied to the problem. As there is still potential for further improvements, we investigate whether the Archimedes optimization algorithm, a rather novel metaheuristic approach, can perform better compared to established algorithms such as genetic algorithms or ant colony optimization. The results show that the Archimedes optimization algorithm can be adapted and successfully applied to both basic cases of the inventory routing problem and more complex cases in small and large scenarios. In the multi-depot IRP, the algorithm finds better solutions than a genetic algorithm, which can be attributed to the fact that the genetic algorithm makes smaller changes, and more solutions must be generated to explore the solution space. However, these smaller changes are faster and allow the genetic algorithm to fine-tune solutions that are close to a local or global optimum. In the multi-product inventory routing problem, the Archimedes optimization algorithm is compared with ant colony optimization. The more complex route determination logic makes ant colony optimization slower than the Archimedes optimization algorithm but allows ant colony optimization to achieve better routes. However, ant colony optimization cannot define the delivery quantities very well, which is better achieved by the Archimedes optimization algorithm. Using the advantages of all three algorithms and generating a combined algorithm may help find even better solutions to inventory routing problems.
- inventory routing problem,
- metaheuristics,
- Archimedes optimization algorithm,
- ant colony optimization,
- genetic algorithm,
- logistics
Citation: Kevin Neuschwander, Thomas Hanne. Solving the inventory routing problem with the Archimedes optimization algorithm[J]. Electronic Research Archive, 2026, 34(12): 9386-9405. doi: 10.3934/era.2026394

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Abstract

The inventory routing problem is a frequently occurring optimization problem in logistics processes, which considers scenarios where a vendor must find optimal solutions to distribute goods to multiple customers while having some flexibility regarding shipping times (i.e., on which days which quantities are delivered to a customer) due to warehousing possibilities. Due to the complexity of the problem, various optimization algorithms have been applied to the problem. As there is still potential for further improvements, we investigate whether the Archimedes optimization algorithm, a rather novel metaheuristic approach, can perform better compared to established algorithms such as genetic algorithms or ant colony optimization. The results show that the Archimedes optimization algorithm can be adapted and successfully applied to both basic cases of the inventory routing problem and more complex cases in small and large scenarios. In the multi-depot IRP, the algorithm finds better solutions than a genetic algorithm, which can be attributed to the fact that the genetic algorithm makes smaller changes, and more solutions must be generated to explore the solution space. However, these smaller changes are faster and allow the genetic algorithm to fine-tune solutions that are close to a local or global optimum. In the multi-product inventory routing problem, the Archimedes optimization algorithm is compared with ant colony optimization. The more complex route determination logic makes ant colony optimization slower than the Archimedes optimization algorithm but allows ant colony optimization to achieve better routes. However, ant colony optimization cannot define the delivery quantities very well, which is better achieved by the Archimedes optimization algorithm. Using the advantages of all three algorithms and generating a combined algorithm may help find even better solutions to inventory routing problems.

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