Optimal route of a moving service vehicle on the plane with stochastic demands
Keywords:
Facility location; Moving Service Vehicle; Random demand; planar Location
Abstract
In this paper, I examine the problem of finding the optimal route that minimizes the sum of the weighted expected distances between the moving service vehicle and the stochastic demand points. The problem is investigated using a quadratic function for the route. Different distance measures and probability distributions of the stochastic demand points are considered.
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References
References :
[1] A.B. Arabani, R.Z. Farahani, R., " Facility location dynamics: An overview of classifications and applications, " Computers & Industrial Engineering,
62(1)(2012) 408–420.
[2] R.G. Bartle, "The Elements of Real Analysis," John Wiley & Sons (1976), New York.
[3] L. Caccetta, I. Loosen, and V. Rehbock, "Modeling Transit Paths for Military Vehicles," Proceedings of the 16th Congress of the Modelling and Simulation Society of Australia and New Zealand, MODSIM05, Melbourne, Australia, 2005.
[4] L. Caccetta, I. Loosen, and V. Rehbock, "Optimal transit path problem for submarines," In proceedings of the 4th International Conference on Engineering Applications and Computational Algorithms, DCDIS, Guelph, Canada, 2005 .
[5] W. Domschke, Drexl W.A., '' Location and Layout Planning: An International Bibliography," Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, 1985, Berlin.
[6] Z. Drezner, "Facility Location: A Survey of Applications and Methods." Springer Series in Operations Research and Financial Engineering. Editors: Drezner, Zvi (Eds) 1995.
[7] A. Foul, "Determining optimal straight line route of a moving facility on the plane with random demand points," Journal of King Saud University, 24(1)(2012) 19-23.
[8] C.L. Hallam,"Hierarchical Path Generation: An Application to Submarine Transit
Paths," Honours Dissertation, Murdoch University, Western Australia.(1997).
[9] P. Howlett, P. Pudney, and B. Benjamin, "Determination of optimal driving strategies for the control of a train," (in B.J. Noye, B.R Benjamin and L.H. Colgan (Eds)), Proc. Computational Techniques and applications, CTAC 91(1992)241-248,
[10] H.D. Sherali, Seong-in Kim, 1992. Variational Problems for Determining Optimal
Paths of a Moving Facility , Transportation Science 26(4)(1992)330-345.
[11] 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.
[12] Seong-In Kim, In-Chan Choi, "A simple variational problem for a moving vehicle,"
Operations Research Letters 16(1994)231-239.
[13] Seong-In Kim, In-Chan Choi, "An optimal path of a moving vehicle on a sphere,"
IIE Transactions 29(1997)383-389.
[14] Z. Ulukan, E. Demircioğl, "A Survey of Discrete Facility Location Problems,"
International Scholarly and Scientific Research & Innovation 9(7)(2015)2487-2492
[1] A.B. Arabani, R.Z. Farahani, R., " Facility location dynamics: An overview of classifications and applications, " Computers & Industrial Engineering,
62(1)(2012) 408–420.
[2] R.G. Bartle, "The Elements of Real Analysis," John Wiley & Sons (1976), New York.
[3] L. Caccetta, I. Loosen, and V. Rehbock, "Modeling Transit Paths for Military Vehicles," Proceedings of the 16th Congress of the Modelling and Simulation Society of Australia and New Zealand, MODSIM05, Melbourne, Australia, 2005.
[4] L. Caccetta, I. Loosen, and V. Rehbock, "Optimal transit path problem for submarines," In proceedings of the 4th International Conference on Engineering Applications and Computational Algorithms, DCDIS, Guelph, Canada, 2005 .
[5] W. Domschke, Drexl W.A., '' Location and Layout Planning: An International Bibliography," Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, 1985, Berlin.
[6] Z. Drezner, "Facility Location: A Survey of Applications and Methods." Springer Series in Operations Research and Financial Engineering. Editors: Drezner, Zvi (Eds) 1995.
[7] A. Foul, "Determining optimal straight line route of a moving facility on the plane with random demand points," Journal of King Saud University, 24(1)(2012) 19-23.
[8] C.L. Hallam,"Hierarchical Path Generation: An Application to Submarine Transit
Paths," Honours Dissertation, Murdoch University, Western Australia.(1997).
[9] P. Howlett, P. Pudney, and B. Benjamin, "Determination of optimal driving strategies for the control of a train," (in B.J. Noye, B.R Benjamin and L.H. Colgan (Eds)), Proc. Computational Techniques and applications, CTAC 91(1992)241-248,
[10] H.D. Sherali, Seong-in Kim, 1992. Variational Problems for Determining Optimal
Paths of a Moving Facility , Transportation Science 26(4)(1992)330-345.
[11] 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.
[12] Seong-In Kim, In-Chan Choi, "A simple variational problem for a moving vehicle,"
Operations Research Letters 16(1994)231-239.
[13] Seong-In Kim, In-Chan Choi, "An optimal path of a moving vehicle on a sphere,"
IIE Transactions 29(1997)383-389.
[14] Z. Ulukan, E. Demircioğl, "A Survey of Discrete Facility Location Problems,"
International Scholarly and Scientific Research & Innovation 9(7)(2015)2487-2492
Published
2019-12-20
How to Cite
Foul, A. (2019). Optimal route of a moving service vehicle on the plane with stochastic demands. Journal of Progressive Research in Mathematics, 15(4), 2793-2802. Retrieved from https://scitecresearch.com/journals/index.php/jprm/article/view/1815
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