A heuristic algorithm to solve the single-facility location routing problem on Riemannian surfaces

Location routing problem (LRP) in supply chain management is integration of the vehicle routing (VRP) and facility location problems (FLP). To the best of our knowledge, the known solutions obtained for the LRP in the literature are only obtained for the Euclidean space. Solving LRP on Riemannian manifold surface (RMS) is a more realistic approach than using Euclidean surfaces because of the curved structure of the pathways on Earth with changing local RMS curvatures. The shortest path distances on Earth’s surface can be determined by calculating geodesic distances in local neighborhoods. The special case of the LRP on RMS is the traditional LRP in the Euclidean space when the curvature of the RMS is zero. In this work, we introduce a new LRP to be solved on (RMS) and find a heuristic algorithmic solution to this LRP. In particular, we formulate the LRP for a single facility on RMS; a generalization of the surface and distance assumptions for the traditional single facility LRP. In addition, a heuristic algorithm is formulated to solve the proposed LRP on RMS with the corresponding computational results displayed for a particular scenario. The numerical results corresponding to the theoretical results introduced in this work are incomparable with the ones known in the literature for the traditional LRP because of the change in the surface and distance assumptions.