Supply Chain Engineering pp 213-269 | Cite as

# Single Vehicle Round-trip Routing

## Abstract

In the single vehicle routing problem a single vehicle is used to serve a set of customers. The vehicle travels on an underlying network consisting of a number of nodes and a number of arcs and edges. If the customers are located in the nodes, the problem is said to be a node routing problem. If the customers are located nearly uniformly along an arc or edge then the problem is said to be an arc routing problem. Node routing is more coabstrammon in supply chain planning, where the customer correspond to individual customers or facilities in the supply chain. Arc routing is common in public service applications such as mail delivery, garbage collection, and snow removal. The single vehicle Roundtrip node routing problem is more commonly known as the Traveling Salesman Problem (TSP) . The single vehicle arc routing problem in which the vehicle has to visit a subset of the arcs and edges is also known as the Rural Postman Problem (RPP) . If all the edges and arcs have to be visited then the problem is known as the Chinese Postman Problem (CPP) . The remainder of this chapter will be focused on the TSP.

## Keywords

Travel Salesman Problem Travel Salesman Problem Node Degree Order Picking Tour Length## References

## Publications

- Akl, S. G., & Toussaint, G. T. (1978). “A fast convex hull algorithm”.
*Information Processing Letters,**7*(5), 219–222.CrossRefGoogle Scholar - Allison, D. C., & Noga, M. T. (1984). “The L
_{1}traveling salesman problem”.*Information Processing Letters, 18*(4), 195–199.CrossRefGoogle Scholar - Applegate, D. L. (2005). “The traveling salesman problem,” Chapter 58. In A. Schrijver (Ed.),
*Combinatorial Optimization: Polyhedra and Efficiency*. Berlin: Springer.Google Scholar - Applegate, D. L., Bixby, R. E., Chvatal, V., & Cook, W. J. (2006).
*The traveling salesman problem: A computational study*. Princeton: Princeton University Press.Google Scholar - Ball, M. O., Magnanti, T. L., Monma, C. L., & Nemhauser, G. L. (Eds.). (1995).
*Network routing*. Amsterdam: Elsevier.Google Scholar - Bazaraa, M. S., Jarvis, J. J., & Sherali, H. D. (2005).
*Linear programming and network flows*(3rd ed.). Hoboken: Wiley.Google Scholar - Bellmore, M., & Nemhauser, G. L. (1968). “The traveling salesman problem: A survey”.
*Operations Research, 16*(3), 538–558.CrossRefGoogle Scholar - Boyd, S. C., Pulleyblank, W. R., & Cornuejols, G. (1987). “TRAVEL—An interactive traveling salesman problem package for the IBM personal computer”.
*Operations Research Letters, 6*(3), 141–143.CrossRefGoogle Scholar - Christofides, N., & Eilon, S. (1972). “Algorithms for large-scale traveling salesman problems”.
*Operations Research Quarterly, 23,*511–518.CrossRefGoogle Scholar - Christofides, N. (1975).
*Graph theory: An algorithmic approach*. New York: Academic Press.Google Scholar - Cook, W. (2004). “Traveling salesman tour illustrations”. www.isye.gatech.edu/faculty-staff.Google Scholar
- Clarke, G., & Wright, J. (1964). “Scheduling of vehicles from a Central Depot to a Number of Delivery Points”.
*Operations Research, 12,*568–581.CrossRefGoogle Scholar - Dantzig, G. B., Fulkerson, D. R., & Johnson, S. M. (1954). “Solution of a large-scale traveling salesman problem”.
*Operations Research, 2,*393–410.CrossRefGoogle Scholar - Gillett, B., & Miller, L. (1974) “A heuristic algorithm for the vehicle dispatch problem”.
*Operations Research, 22,*340–349.CrossRefGoogle Scholar - Golden, B. L., Bodin, L., Doyle, T., & Stewart, W. Jr. (1980). “Approximate traveling salesman algorithms”.
*Operations Research, 28*(3), 694–711.CrossRefGoogle Scholar - Glover, F. (1989). “Tabu search—Part I”.
*ORSA Journal on Computing, 1*(3) 190–206.Google Scholar - Glover, F. (1990). “Tabu search—Part II”.
*ORSA Journal on Computing, 2*(1), 4–32.Google Scholar - Helbig Hansen, K., & Krarup, J. (1974). “Improvements on the Held-Karp algorithm for the symmetric traveling salesman problem”.
*Mathematical Programming, 7,*87–96.CrossRefGoogle Scholar - Held, M., & Karp, R. M. (1970). “The traveling-salesman problem and minimum spanning trees”.
*Operations Research, 18*(6), 1138–1162.CrossRefGoogle Scholar - Held, M., & Karp, R. M. (1971). “The traveling-salesman problem and minimum spanning trees: Part II”.
*Mathematical Programming, 1,*6–25.CrossRefGoogle Scholar - Kirkpatrick, S., Gelat, C., & Vechi, M. (1983).
*Science, 220,*671–680.Google Scholar - Kruskal, J. B. (1956). “On the shortest spanning subtree of a graph and the traveling salesman problem”.
*Proceedings of the American Mathematical Society, 7*(1), 48–50.Google Scholar - Laporte, G. (1992). “The traveling salesman problem: An overview of exact and approximate algorithms”.
*European Journal of Operational Research, 59,*231–247.CrossRefGoogle Scholar - Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., & Schmoys, D. B. (1985).
*The traveling salesman problem*. Chichester: Wiley.Google Scholar - Lin, S., & Kernighan, B. (1973) “An effective heuristic algorithm for the traveling salesman problem”.
*Operations Research, 21,*498–516.CrossRefGoogle Scholar - Lin, S. (1965). “Computer solutions of the traveling salesman problem”.
*Bell System Technical Journal, 44,*2245–2269.Google Scholar - Little, J. D., Murty, K. G., Sweeney, D. W., & Karel, C. (1963). “An algorithm for the traveling salesman problem”.
*Operations Research, 11*(6), 972–989.CrossRefGoogle Scholar - Miller, C. E., Tucker, A. W., & Zemlin, R. A. (1960) “Integer programming formulations and traveling salesman problems”.
*Journal of the Association of Computing Machinery, 7,*326–329.Google Scholar - Or, I. (1976). “Traveling salesman-type combinatorial problems and their relation to the logistics of regional blood banking”. Unpublished Ph.D. Dissertation, Northwestern University, Evanston.Google Scholar
- Parker, R. G., & Rardin, R. L. (1983). “The traveling salesman problem: An update of research”.
*Naval Research Logistics Quarterly, 30,*69–99.CrossRefGoogle Scholar - Platzman, L. K., & Bartholdi, III, J. J. (1984). “Space-filling curves and the planar traveling salesman problem”. PDRC Report Series 83-02, School of Industrial and Systems Engineering, Georgia Institute of Technology.Google Scholar
- Prim, R. C. (1957). “Shortest connection networks and some generalizations”.
*Bell System Technical Journal, 36,*1389–1401.Google Scholar - Rooney, B. (2007). “UPS figures out the ‘Right Way’ to save money, Time and Gas”. abcnews.com. Accessed 4 April 2007.Google Scholar
- Rosenkrantz, D. J., Stearns, R. E., & Lewis, P. M. (1977). “An analysis of several heuristics for the traveling salesman problem”.
*SIAM Journal of Computing, 6,*563–581.CrossRefGoogle Scholar - Smith T. H., & Thompson, G. L. (1977). “A LIFO implicit enumeration search algorithm for the symmetric traveling salesman problem using Held and Karp’s 1-tree relaxation”.
*Annals of Discrete Mathematics, 1,*479–493.CrossRefGoogle Scholar - Thomasson, D. (2001). http://www.borderschess.org. Accessed 10 Jun 2011.
- Vechi, M., & Kirkpatrick, S. (1983).
*IEEE Transactions on Computer Aided Design*(Vol. CAD-2, p. 215).Google Scholar - Volgenant, T., & Jonker, R. (1982). “A branch and bound algorithm for the symmetric traveling salesman problem based on the 1-tree relaxation”.
*European Journal of Operations Research, 9,*83–89.CrossRefGoogle Scholar

## Programs

- Concorde. (2005). William Cook. http://www.tsp.gatech.edu/concorde.html. Accessed 10 Jun 2011.
- Tours. (1993). Marc Goetschalckx. http://www.isye.gatech.edu/people/faculty/Marc_Goetschalckx.Google Scholar