Farklı mesafe normlarına sahip birden fazla bölgede tesis yerleşimi

This study focuses on the facility location problems in multiple regions having different norms on a continuous plane. While this problem has been previously studied in the literature for two regions, this study aims to take a further step by generating the gate point formulations for three regions. It is observed that even finding a geodesic path requires significant effort, and the optimal gate-point formulations do not always have closed-form solutions. In this study, the single facility locations with multiple regions with different norms is primarily and extensively studied. Alternative mathematical models are developed for special cases of this problem where borderlines are vertical. In addition, Big Square Small Square algorithm is developed to address each case of this problem. Moreover, to handle this problem for large-scale data sets, Simulated Annealing and Tabu Search algorithm are developed for handling this problem. Furthermore, Beam Search algorithm based on Big Square Small Square algorithm is suggested. According to our results, Beam Search algorithm performs as the best heuristic method, while Big Square Small Square algorithm performs as the best exact solution approach. Lastly, the location routing problem in two regions with different norms is addressed and formulated as a Mixed-Integer Nonlinear Programming problem for multiple cases. To this end, alternative models discretizing gate-points and facility locations are also proposed.