Mathematical Model and a Case Study for Multi-Commodity Transportation Problem

Niluka Rodrigo; Lashika Rjapaksha

doi:doi:10.11648/j.ijtam.20180401.11

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Mathematical Model and a Case Study for Multi-Commodity Transportation Problem

Niluka Rodrigo, Lashika Rjapaksha

Published in International Journal of Theoretical and Applied Mathematics (Volume 4, Issue 1)

Received: 31 October 2017 Accepted: 18 December 2017 Published: 15 January 2018

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Abstract

The problem of locating distribution centers is one of the most important issues in design of supply chain. The design of the distribution system is an important issue for almost every company. Wide range of problems arising in practical applications can be formulated as Mixed-integer nonlinear Models. Multi-commodity distribution system design is a generalization of a facility location problem where we have several commodities, and shipment from a plant to customer occurs through a distribution center. This report presents a real life distribution problem. The problem is to determine which distribution centers to use so that all customer demands are satisfied, production capacities are not exceeded, and the total distribution cost that is the fixed cost of operating the distribution center and the transportation cost is minimized. A computer program (Software R) is developed to obtain the optimal solution.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 4, Issue 1)
DOI	10.11648/j.ijtam.20180401.11
Page(s)	1-7
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Transportation Problem, Multi-Commodity Distribution, Mixed-Integer Nonlinear Programs, Software R

References

[1]	A. M. Geoffrion, G. W. Graves "Multi-commodity Distribution System Design by Benders Decomposition", Management Science, Vol. 20, No. 5, Theory Series, Mathematical Programming (Jan., 1974), 822-844.
[2]	Diogo R. M. Fernandes, Caroline Rocha, Daniel Aloise, Glaydston M. Ribeiro, Enilson M. Santos, Allyson SilvaA "Simple and effective genetic algorithm for the two-stage capacitated facility location problem", Computers & Industrial Engineering 75 (2014) 200–208, www.elsevier.com/ locate/caie
[3]	Zoltan Lelkes, Endre Rev, Tivadar Farkas, Zsolt Fonyo, Tibor Kovacs and Ian Jones "Multi-commodity transportation and supply problem with stepwise constant cost function", European Symposium on Computer Arded Process Engineering – 15 L. Puigjaner and A. Espuña (Editors) © 2005 Elsevier Science.
[4]	H. Afshari, M. Amin-Nayeri, A. A. Jaafari "A Multi-objective Approach for Multi-commodity Location within Distribution Network Design Problem", Proceeding of the International Multiconference of Engineers and Computer Scientists 2010 Vol III, IMECS 2010.
[5]	Gopal Agarwal and Lokesh Vijayvargy "Designing of Multi-Commodity, Multi Location Integrated Model for Effective Logistics Management", Proceeding of the International Multi conference of Engineers and Computer Scientists 2011 Vol II, IMECS 2011.
[6]	Engr. Dr. Uzorh, A. C1and Nanna Innocent "Supply Chain Management Optimization Problem " The International Journal Of Engineering And Science (IJES) \|\| Volume \|\| 3 \|\| Issue \|\| 6 \|\| Pages \|\| 01-09 \|\| 2014 \|\| ISSN (e): 2319 – 1813 ISSN (p): 2319–1805.
[7]	Joe Lindstrom "Multi-commodity Network Flow - Methods and Applications", joeli289@student.liu.se.
[8]	P. Ji1, K. J. Chen, and Q. P. Yan "A Mathematical Model for a Multi-Commodity, Two-Stage Transportation and Inventory Problem" International Journal of Industrial Engineering, 15(3), 278-285, 2008.
[9]	Behrouz Behmardi and Shiwoo Lee "Dynamic Multi-commodity Capacitated Facility Location Problem in Supply Chain", Proceedings of the 2008 Industrial Engineering Research Conference J. Fowler and S. Mason, eds.
[10]	H. Afshari, A. A. Jaafari “A Multi-objective Approach for Multi-commodity Location within Distribution Network Design Problem”, Proceedings of the international multi-conference of Engineers and Computer Scientist 2010, vol. 3.

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APA Style

Niluka Rodrigo, Lashika Rjapaksha. (2018). Mathematical Model and a Case Study for Multi-Commodity Transportation Problem. International Journal of Theoretical and Applied Mathematics, 4(1), 1-7. https://doi.org/10.11648/j.ijtam.20180401.11

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ACS Style

Niluka Rodrigo; Lashika Rjapaksha. Mathematical Model and a Case Study for Multi-Commodity Transportation Problem. Int. J. Theor. Appl. Math. 2018, 4(1), 1-7. doi: 10.11648/j.ijtam.20180401.11

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AMA Style

Niluka Rodrigo, Lashika Rjapaksha. Mathematical Model and a Case Study for Multi-Commodity Transportation Problem. Int J Theor Appl Math. 2018;4(1):1-7. doi: 10.11648/j.ijtam.20180401.11

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@article{10.11648/j.ijtam.20180401.11,
  author = {Niluka Rodrigo and Lashika Rjapaksha},
  title = {Mathematical Model and a Case Study for Multi-Commodity Transportation Problem},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {4},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.ijtam.20180401.11},
  url = {https://doi.org/10.11648/j.ijtam.20180401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20180401.11},
  abstract = {The problem of locating distribution centers is one of the most important issues in design of supply chain. The design of the distribution system is an important issue for almost every company. Wide range of problems arising in practical applications can be formulated as Mixed-integer nonlinear Models. Multi-commodity distribution system design is a generalization of a facility location problem where we have several commodities, and shipment from a plant to customer occurs through a distribution center. This report presents a real life distribution problem. The problem is to determine which distribution centers to use so that all customer demands are satisfied, production capacities are not exceeded, and the total distribution cost that is the fixed cost of operating the distribution center and the transportation cost is minimized. A computer program (Software R) is developed to obtain the optimal solution.},
 year = {2018}
}

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TY  - JOUR
T1  - Mathematical Model and a Case Study for Multi-Commodity Transportation Problem
AU  - Niluka Rodrigo
AU  - Lashika Rjapaksha
Y1  - 2018/01/15
PY  - 2018
N1  - https://doi.org/10.11648/j.ijtam.20180401.11
DO  - 10.11648/j.ijtam.20180401.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
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EP  - 7
PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.ijtam.20180401.11
AB  - The problem of locating distribution centers is one of the most important issues in design of supply chain. The design of the distribution system is an important issue for almost every company. Wide range of problems arising in practical applications can be formulated as Mixed-integer nonlinear Models. Multi-commodity distribution system design is a generalization of a facility location problem where we have several commodities, and shipment from a plant to customer occurs through a distribution center. This report presents a real life distribution problem. The problem is to determine which distribution centers to use so that all customer demands are satisfied, production capacities are not exceeded, and the total distribution cost that is the fixed cost of operating the distribution center and the transportation cost is minimized. A computer program (Software R) is developed to obtain the optimal solution.
VL  - 4
IS  - 1
ER  -

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Author Information

Niluka Rodrigo

Department of Mathematics, University of Peradeniya, Peradeniya, Sri Lanka
Lashika Rjapaksha

Department of Mathematics, University of Peradeniya, Peradeniya, Sri Lanka

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APA Style

Niluka Rodrigo, Lashika Rjapaksha. (2018). Mathematical Model and a Case Study for Multi-Commodity Transportation Problem. International Journal of Theoretical and Applied Mathematics, 4(1), 1-7. https://doi.org/10.11648/j.ijtam.20180401.11

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ACS Style

Niluka Rodrigo; Lashika Rjapaksha. Mathematical Model and a Case Study for Multi-Commodity Transportation Problem. Int. J. Theor. Appl. Math. 2018, 4(1), 1-7. doi: 10.11648/j.ijtam.20180401.11

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AMA Style

Niluka Rodrigo, Lashika Rjapaksha. Mathematical Model and a Case Study for Multi-Commodity Transportation Problem. Int J Theor Appl Math. 2018;4(1):1-7. doi: 10.11648/j.ijtam.20180401.11

Copy | Download

@article{10.11648/j.ijtam.20180401.11,
  author = {Niluka Rodrigo and Lashika Rjapaksha},
  title = {Mathematical Model and a Case Study for Multi-Commodity Transportation Problem},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {4},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.ijtam.20180401.11},
  url = {https://doi.org/10.11648/j.ijtam.20180401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20180401.11},
  abstract = {The problem of locating distribution centers is one of the most important issues in design of supply chain. The design of the distribution system is an important issue for almost every company. Wide range of problems arising in practical applications can be formulated as Mixed-integer nonlinear Models. Multi-commodity distribution system design is a generalization of a facility location problem where we have several commodities, and shipment from a plant to customer occurs through a distribution center. This report presents a real life distribution problem. The problem is to determine which distribution centers to use so that all customer demands are satisfied, production capacities are not exceeded, and the total distribution cost that is the fixed cost of operating the distribution center and the transportation cost is minimized. A computer program (Software R) is developed to obtain the optimal solution.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Model and a Case Study for Multi-Commodity Transportation Problem
AU  - Niluka Rodrigo
AU  - Lashika Rjapaksha
Y1  - 2018/01/15
PY  - 2018
N1  - https://doi.org/10.11648/j.ijtam.20180401.11
DO  - 10.11648/j.ijtam.20180401.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 1
EP  - 7
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20180401.11
AB  - The problem of locating distribution centers is one of the most important issues in design of supply chain. The design of the distribution system is an important issue for almost every company. Wide range of problems arising in practical applications can be formulated as Mixed-integer nonlinear Models. Multi-commodity distribution system design is a generalization of a facility location problem where we have several commodities, and shipment from a plant to customer occurs through a distribution center. This report presents a real life distribution problem. The problem is to determine which distribution centers to use so that all customer demands are satisfied, production capacities are not exceeded, and the total distribution cost that is the fixed cost of operating the distribution center and the transportation cost is minimized. A computer program (Software R) is developed to obtain the optimal solution.
VL  - 4
IS  - 1
ER  -

Copy | Download