The inventory routing problem (IRP) is an optimization problem many companies and organizations are confronted with in logistics processes. This optimization problem is about scenarios where a vendor must find an optimal solution to distribute goods to multiple customers. Finding a solution considering all costs and constraints is a difficult task. For this reason, many optimization algorithms have been applied to the problem.

Metaheuristic optimization methods, such as the genetic algorithm (GEA), which tries to find a solution by imitating the biologic processes of reproduction natural selection to find a solution, or the ant colony optimization algorithm (ACO), which imitates the behaviour of ants, perform well on the problem. However, there is still potential for improvement. For this reason, this thesis investigates if the Archimedes optimization algorithm (AOA), another metaheuristic approach, can perform better compared to existing algorithms. The AOA is inspired by the interactions in between objects in a liquid. Each object represents a solution to the optimization problem. Using parameters, such as density, volume and acceleration, the AOA updates the object parameters and, therefore, the solution to the inventory routing problem.

The results show that the AOA can be applied to a basic case of the inventory routing problem and to a more complex case with constraints. In both cases, the algorithm manages to improve on the initial solution in small and big scenarios. In the Multi-Depot Inventory Routing Problem, the algorithm manages to find better solutions than the GEA. The reason for this can be attributed to the fact that the GEA makes smaller changes and needs to generate more solutions to explore the solution space. These smaller changes, however, are faster and allow the GEA to fine tune solutions to find a solution very close to the local or optimum. In the Multi-Product Inventory Routing Problem, the AOA is compared to the ACO. The more complex route determination logic makes the ACO slower compared to the AOA. This additional computation time has an advantage. The ACO generates well optimized routes. However, the ACO cannot define the delivery quantities very well. The AOA on the other hand, is better at determining the quantities, but the routes could be improved. Using the advantages of all the three algorithm and generating a combined algorithm could help finding even better solutions to the inventory routing problem.