A Single-Facility Manifold Location Routing Problem with an Application to Supply Chain Management and Robotics

摘要

The location routing problem (LRP), a problem formulated for determining locations of facilities and the vehicle routes operating between these facilities, is the combination of the vehicle routing (VRP) and the facility location problems (FLP) in Euclidean space. The manifold location routing problem (MLRP) is an LRP in a Riemannian manifold setting as introduced in [14]. In seeking further advancements in the solution of LRP, MLRP improves the accuracy of the distance calculations by using geodesic distances. The shortest path distances on Earth's surface can be determined by calculating geodesic distances in local neighborhoods by using Riemannian geometry. In this work, we advance the theoretical results obtained for MLRP in [14] by incorporating support vector machines (SVM), dynamic programming, parallel programming, data mining, and Geographic Information Systems (GIS). The theory will be explained on a supply chain problem with a robotics paradigm.