Optimal path of a moving service vehicle on network with probabilistic demands
Keywords:
Facility location, Moving Service Vehicle, Random demand.
Abstract
In this paper, I examine twofold problem. The first one is concerned with finding the optimal location of a single facility in a network with demands randomly distributed over the edges. The second problem is about determining the optimal path between two specified nodes of the network of a moving vehicle that continuously interacts with randomly distributed requests for service over the edges. The problems are investigated using different performance measures and probability distributions of the demands.
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References
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[11] J. C. Karkazis, C. Papadimitriou, “A Branch-and-Bound Algorithm for the Location of Facilities Causing Atmospheric Pollution,” European Journal of Operational Research 58(1992)265-281.
[12] S. Kim, H. D. Sherali, H. Park, "Minisum and minimax path of a moving facility on a network," Computers and Operations Research 19(1992)123-131.
[13] M. Labbe, “Location of an Obnoxious Facility on a Network: a Voting Approach m,”, Networks 20(1990)197-207.
[14] V.L Rehbock, C. Caccetta, C.L. Hallam and R. O’Dowd, "Optimal Submarine Transit Paths Through Sonar Fields," Research Report, Department of Mathematics and Statistics, Curtin University of Technology, 2000.
[15] K. Seong-In, In-Chan Choi, " A simple variational problem for a moving Vehicle," Operations Research Letters 16(1994)231-239.
[16] K. Seong-In , In-Chan Choi, "An optimal path of a moving vehicle on a sphere,"IIE Transactions 29(1997)383-389.
[17] H. D. Sherali, Seong-in Kim, "Variational Problems for Determining Optimal Paths of a Moving Facility," Transportation Science 26(1992)330-345.
[2] B. Ben-Moshe, M. J. Katz, M. Segal, “Obnoxious Facility Location: Complete Service with Minimal Harm,” International Journal of Computational Geometry 10(2000)581- 592.
[3] Berman and G. Y. Handler, "Optimal path of a single service unit on a network to a nonservice destination," Transptn Sci. 21(1987)115-122.
[4] Berman and M. R. Rahnama, "Optimal path of a single service unit on a network to a nonemergency destination," Transptn Sci.17(1983)218-232.
[5] P. Cappanera P., “Discrete Facility Location and Routing of Obnoxious Activities,” Discrete Applied Mathematics 133(2004)3-28.
[6] L. Chabini, “Discrete Dynamic Shortest Path Problems," in Transportation Applications: complexity and algorithms with optimal run time, 2010.
[7] E. Erkut, S. Neuman, “Analytical Models for Locating Undesirable Facilities,” European Journal of Operational Research 40(1989)275–291.
[8] A. Foul, "Determining optimal straight line route of a moving facility on the plane with random demand points," Journal of King Saud University 24(2012)19-23.
[9] I. Giannikos I., “A Multi-Objective Programming Model for Locating Treatment Sites and Routing Hazardous Waste,” European Journal of Operational Research 104(1998)333-342.
[10] G. Y. Handler and P. B. Mirchandani, Location on Networks: Theory and Algorithms. MIT Press, Cambridge, Mass, 1979.
[11] J. C. Karkazis, C. Papadimitriou, “A Branch-and-Bound Algorithm for the Location of Facilities Causing Atmospheric Pollution,” European Journal of Operational Research 58(1992)265-281.
[12] S. Kim, H. D. Sherali, H. Park, "Minisum and minimax path of a moving facility on a network," Computers and Operations Research 19(1992)123-131.
[13] M. Labbe, “Location of an Obnoxious Facility on a Network: a Voting Approach m,”, Networks 20(1990)197-207.
[14] V.L Rehbock, C. Caccetta, C.L. Hallam and R. O’Dowd, "Optimal Submarine Transit Paths Through Sonar Fields," Research Report, Department of Mathematics and Statistics, Curtin University of Technology, 2000.
[15] K. Seong-In, In-Chan Choi, " A simple variational problem for a moving Vehicle," Operations Research Letters 16(1994)231-239.
[16] K. Seong-In , In-Chan Choi, "An optimal path of a moving vehicle on a sphere,"IIE Transactions 29(1997)383-389.
[17] H. D. Sherali, Seong-in Kim, "Variational Problems for Determining Optimal Paths of a Moving Facility," Transportation Science 26(1992)330-345.
Published
2020-07-22
How to Cite
Foul, A. (2020). Optimal path of a moving service vehicle on network with probabilistic demands. Journal of Progressive Research in Mathematics, 16(3), 3020-3055. Retrieved from https://scitecresearch.com/journals/index.php/jprm/article/view/1881
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