Abstract
The two-campus transport problem (TCTP) is a dial-a-ride problem with only two destinations. The problem is motivated by a transport problem between two campuses of an academic college. The two campuses are located in two different cities. Lecturers living in one city are sometimes asked to teach at the other city’s campus. The problem is that of transporting the lecturers from one campus to the other, using a known set of vehicles, so as to minimize the time the lecturers wait for their transport. We mathematically model the general TCTP, and provide an algorithm that solves it, which is polynomial in the number of lecturers. The algorithm is based on a reduction to a shortest path problem.
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References
Bellman, R. E. (1958). On a routing problem. Quarterly of Applied Mathematics, 16, 87–90.
Bräysy, O., & Gendreau, M. (2005). Vehicle routing problem with time windows. Parts I and II Transportation Science, 39, 104–139.
Bülbül, K., Ulusoy, G., & Sen, A. (2008). Classic transportation problems. In D. G. Taylor (Ed.), Logistics engineering handbook. Boca Raton: CRC Press.
Chakravarty, A. K., Orlin, J. B., & Rothblum, U. G. (1982). A partitioning problem with additive objective with an application to optimal inventory grouping for joint replenishment. Operating Research, 30, 1018–1022.
Chang, H., Hwang, F. K., & Rothblum, U. G. (2012). A new approach to solve open-partition problems. Journal of Combinatorial Optimization, 23(1), 61–78.
Cherkassky, B. V., Goldberg, A. V., & Radzik, T. (1996). Shortest paths algorithms: Theory and experimental evaluation. Mathematical Programming, 73, 129–174.
Cordeau, J. F., & Laporte, G. (2007). The dial-a-ride problem: Models and algorithms. Annals of Operations Research, 153, 2946.
Dijkstra, E. W. (1959). A note on two problems in connection with graphs. Numerische Mathematik, 1, 269–271.
Golden, B., Raghavan, S., & Wasil, E. (2008). The vehicle routing problem: Latest advances and new challenges. Boston: Springer.
de Paepe, W. E., Lenstra, J. K., Sgall, J., Sitters, R. A., & Stougie, L. (2004). Computer-aided complexity classification of dial-a-ride problems. Informs Journal on Computing, 16(2), 120–132.
Parragh, S. N., Doerner, K. F., & Hartl, R. F. (2008). A survey on pickup and delivery problems. Part I Journal für Betriebswirtschaft, 58(1), 21–51.
Parragh, S. N., Doerner, K. F., & Hartl, R. F. (2008). A survey on pickup and delivery problems. Part II Journal für Betriebswirtschaft, 58(2), 81–117.
Musatova, E., & Lazarev, A. (2012). Algorithm for solving two-stations railway scheduling problem, 25th European Conference on Operational Research.
Shufan, E., Ilani, H. & Grinshpoun, T. (2011). A Two-Campus Transport Problem. Proceedings of the 5th Multidisciplinary International Conference on Scheduling: Theory and Applications (MISTA 2011), (pp. 173–184).
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We wish to thank Profs. Asaf Levin and Uriel G. Rothblum for their helpful suggestions.
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Ilani, H., Shufan, E., Grinshpoun, T. et al. A reduction approach to the two-campus transport problem. J Sched 17, 587–599 (2014). https://doi.org/10.1007/s10951-013-0348-7
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DOI: https://doi.org/10.1007/s10951-013-0348-7