Abstract
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.
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References
Aly, A., Kay, D., Litwhiler, J.: Location dominance on spherical surfaces. Oper. Res. 27, 972–981 (1979)
Do Carmo, M.P.: Differential geometry of curves and surfaces. Prentice Hall Inc., Englewood Cliffs (1976)
Aras, N., Yumusak, S.: Altınel, IK: solving the capacitated multi-facility Weber problem by simulated annealing, threshold accepting and genetic algorithms. In: Doerner, K.F., Gendreau, M., Greistorfer, P., Gutjahr, W.J., Hartl, R.F., Reimann, M. (eds.) Metaheuristics: Progress in Complex Systems Optimization, pp. 91–112. Springer, USA (2007)
Cheeger, J., Ebin, D.G.: Comparison Theorems in Riemannian Geometry. North Holland Publishing Company, American Elsevier Publishing Company Inc., Amsterdam, New York (1975)
Daskin, M.S.: What you should know about location modeling. Naval Res. Logis. 55, 283–294 (2008)
Drezner, Z., Wesolowsky, G.O.: Facility location on a sphere. J. Oper. Res. Soc. 29, 997–1004 (1978)
Gamal, M.D.H., Salhi, S.: Constructive heuristics for the uncapacitated continuous location-allocation problem. J. Oper. Res. Soc. 52, 821–829 (2001)
Jost, J.: Riemannian Geometry and Geometric Analysis, 6th edn. Springer, New York (2011)
Laporte, G.: What you should know about the vehicle routing problem. Naval Res. Logis. 54, 811–819 (2007)
Prodhon, C., Prins, C.: A survey of recent research on location-routing problems. Euro. J. Oper. Res. 238(1), 1–17 (2014)
Riemann, B: Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse. Inauguraldissertation, Göttingen (1851)
Salhi, S., Nagy, G.: Local improvement in planar facility location using vehicle routing. Ann. Oper. Res. 167, 287–296 (2009)
Sherali, H.D., Noradi, F.L.: NP-hard, capacitated, balanced p-median problems on a chain graph with a continuum of link demands. Math. Oper. Res. 13, 32–49 (1988)
Tokgöz, E., Alwazzi, S., Theodore, T.B.: A heuristic algorithm to solve the single-facility location routing problem on Riemannian surfaces. Comput. Manage. Sci. 12, 397–415 (2014). doi:10.1007/s10287-014-0226-6. Springer
Yang, X., Song, Q., Wang, Y.: A weighted support vector machine for data classification. Int. J. Pattern. Recog. Artif. Intell. WSPC 21(5), 961–976 (2007)
Acknowledgement
Dr. Theodore Trafalis was supported by RSF grant 14-41-00039 and he conducted research at National Research University Higher School of Economics.
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Tokgöz, E., Awudu, I., Trafalis, T.B. (2015). A Single-Facility Manifold Location Routing Problem with an Application to Supply Chain Management and Robotics. In: Pardalos, P., Pavone, M., Farinella, G., Cutello, V. (eds) Machine Learning, Optimization, and Big Data. MOD 2015. Lecture Notes in Computer Science(), vol 9432. Springer, Cham. https://doi.org/10.1007/978-3-319-27926-8_12
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