Hybrid models for the continuous facility location selection and vehicle routing problem

The logistics sector is increasingly challenged by intensified competition, fluctuating customer demands, and complex operational processes, which necessitate the development of more efficient and flexible solutions. Among the core components of supply chain management, facility location and vehicle routing decisions play a decisive role in shaping total logistics costs. These two decision types are deeply interconnected and cannot be considered independently, as their interaction directly influences overall logistics performance. In real-world scenarios, the spatial and quantitative variability of customer demands further complicates the decision-making process. Addressing facility location and distribution planning on a continuous plane offers more realistic and applicable solutions, especially in cases where conventional methods fall short. This approach, which remains limited in the existing literature, enables the integrated modeling of both strategic and operational decisions. In this study, two different hybrid models have been developed for the continuous facility location and vehicle routing problem. In both models, facility location is addressed through a nonlinear programming approach. The main distinction between the models lies in the methods used for vehicle routing. The first model utilizes mixed-integer programming, particularly suitable for small-scale data sets, while the second model employs a simulated annealing algorithm, which is more effective for large-scale data sets. Both models were tested on standard benchmark instances commonly used in the literature, and their performances were compared against two existing studies using the same data sets as well as against the best-known results in the discrete domain. Out of 104 total comparisons, the proposed models outperformed existing approaches in 94.23% of the cases. The first model achieved a 95% success rate, while the second model achieved 93.75%.