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.
Downloads
Download data is not yet available.
References
[1] R. Batta and S. S. Chiu, "Optimal obnoxious paths on a network: transportation of hazardous materials," Ops Res 36(1988)84-92.
[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.
[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 http://scitecresearch.com/journals/index.php/jprm/article/view/1881
Issue
Section
Articles
Copyright (c) 2020 Journal of Progressive Research in Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
