Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem

Jong Hyup Lee

doi:doi:10.11648/j.ijefm.20150305.17

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Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem

Jong Hyup Lee

Received: 31 August 2015 Accepted: 16 September 2015 Published: 26 September 2015

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Abstract

In this paper, we examine the problem of establishing minimum cost production and transportation plans that satisfy known demands over a finite planning horizon. Two products, product 1 and 2, can be produced in each of two regions. Each region uses its own facility to supply the demands for two products. Demands for product 2 in one region can be satisfied either by its own production or by transportation from other region, while no transportation between two regions is allowed for product 1. Moreover, the transportation in each period is constrained by a time-dependent capacity bound. Production and transportation costs are assumed to be non-decreasing and concave. Using a network flow approach, properties of extreme points are identified. Then, a dynamic programming algorithm is developed to find an optimal plan.

DOI	10.11648/j.ijefm.20150305.17
Published in	International Journal of Economics, Finance and Management Sciences (Volume 3, Issue 5, October 2015)
Page(s)	460-464
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

Production Planning, Dynamic Programming, Capacitated Transportation

References

[1]	Jong Hyup Lee, Jung Man Hong, “Two product, two region production, inventory, and transportation”, International Journal of Economics, Finance and Management Sciences, 2014; 2(6), pp.313-318, 2014.
[2]	H. M. Wagner and T. M. Whitin, “Dynamic Version of the Economic Lot Size Model”, Management Science, vol. 14, pp.429-450, 1968.
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[4]	M. Florian and M. Klein, “Deterministic Production Planning with Concave Costs and Capacity Constraints”, Management Science, vol. 18, pp.12-20, 1971.
[5]	C. S. Sung, “A Production Planning Model for Multi-Product Facilities” Journal of the Operations Research Society of Japan, vol. 28, no. 4, pp.345-358, 1985.
[6]	H. Luss, “A Capacity-Expansion Model for Two Facility Types”, Naval Research Logistics Quarterly, vol. 26, pp.291-303, 1979.
[7]	Nafee Rizk and Alain Martel, “Supply Chain Flow Planning Methods: A Review of the Lot-Sizing Literature”, Working Paper DT-2001-AM-1, Centre de recherche sur les technologies de l’organisation réseau (CENTOR), Université Laval, QC, Canada, January 2001.
[8]	B. Karimi, S. M. T. Fatemi Ghomi, and J.M. Wilson, “The capacitated lot sizing problem: a review of models and algorithms”, The International Journal of Management Science, Omega 31, pp.365-378, 2003.
[9]	Lisbeth Buschkuhl, Florian Sahling, Stefan Helber, and Horst Tempelmeier, “Dynamic capacitated lot-sizing problems: a classification and review of solution approaches”, OR Spectrum, vol. 32, pp.231-261, 2010.
[10]	A. Clark, B. Almada-Lobo, and C. Almeder, “Lot sizing and scheduling: industrial extensions and research opportunities”, International Journal of Production Research, vol. 49, pp. 2457 2461, 2011.
[11]	Endy Suwondo and Henry Yuliando, “Dynamic Lot-Sizing Problems: A Review on Model and Efficient Algorithm”, Agroindustrial Journal, vol. 1, issue 1, pp. 36-49, 2012.
[12]	Adulyasak, Yossiri, Jean-Francois Cordeau, and Raf Jans, “The Production Routing Problem: A Review of Formulations and Solution Algorithms”, Computers & Operations Research, available online 7 February 2014.
[13]	L. C. Coelho, J.-F. Cordeau, G. Laporte, “The inventory-routing problem with transshipment”, Computers and Operations Research, vol. 39, pp. 2537-2548, 2012.
[14]	D. Ozdemir, E. Yucesan, Y. T. Herer, “Multi-location transshipment problem with capacitated production”, European Journal of Operational Research, vol. 226, pp. 425-435, 2013.
[15]	A. J. Hoffman and J. B. Kruskal, “Integral Boundary Points of Convex Polyhedra”, in H. W. Tucker (eds.) Linear Inequalities and Related Systems, Annals of Mathematics Study, no. 38, Princeton Univ. Press, Princeton, New Jersey, pp.233-246, 1956.
[16]	G. B. Danzig, “Linear Programming and Extensions”, Princeton Univ. Press, Princeton, N. J., 1963.

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APA Style

Jong Hyup Lee. (2015). Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem. International Journal of Economics, Finance and Management Sciences, 3(5), 460-464. https://doi.org/10.11648/j.ijefm.20150305.17

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ACS Style

Jong Hyup Lee. Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem. Int. J. Econ. Finance Manag. Sci. 2015, 3(5), 460-464. doi: 10.11648/j.ijefm.20150305.17

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AMA Style

Jong Hyup Lee. Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem. Int J Econ Finance Manag Sci. 2015;3(5):460-464. doi: 10.11648/j.ijefm.20150305.17

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@article{10.11648/j.ijefm.20150305.17,
  author = {Jong Hyup Lee},
  title = {Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem},
  journal = {International Journal of Economics, Finance and Management Sciences},
  volume = {3},
  number = {5},
  pages = {460-464},
  doi = {10.11648/j.ijefm.20150305.17},
  url = {https://doi.org/10.11648/j.ijefm.20150305.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijefm.20150305.17},
  abstract = {In this paper, we examine the problem of establishing minimum cost production and transportation plans that satisfy known demands over a finite planning horizon. Two products, product 1 and 2, can be produced in each of two regions. Each region uses its own facility to supply the demands for two products. Demands for product 2 in one region can be satisfied either by its own production or by transportation from other region, while no transportation between two regions is allowed for product 1. Moreover, the transportation in each period is constrained by a time-dependent capacity bound. Production and transportation costs are assumed to be non-decreasing and concave. Using a network flow approach, properties of extreme points are identified. Then, a dynamic programming algorithm is developed to find an optimal plan.},
 year = {2015}
}

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TY  - JOUR
T1  - Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem
AU  - Jong Hyup Lee
Y1  - 2015/09/26
PY  - 2015
N1  - https://doi.org/10.11648/j.ijefm.20150305.17
DO  - 10.11648/j.ijefm.20150305.17
T2  - International Journal of Economics, Finance and Management Sciences
JF  - International Journal of Economics, Finance and Management Sciences
JO  - International Journal of Economics, Finance and Management Sciences
SP  - 460
EP  - 464
PB  - Science Publishing Group
SN  - 2326-9561
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AB  - In this paper, we examine the problem of establishing minimum cost production and transportation plans that satisfy known demands over a finite planning horizon. Two products, product 1 and 2, can be produced in each of two regions. Each region uses its own facility to supply the demands for two products. Demands for product 2 in one region can be satisfied either by its own production or by transportation from other region, while no transportation between two regions is allowed for product 1. Moreover, the transportation in each period is constrained by a time-dependent capacity bound. Production and transportation costs are assumed to be non-decreasing and concave. Using a network flow approach, properties of extreme points are identified. Then, a dynamic programming algorithm is developed to find an optimal plan.
VL  - 3
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Author Information

Jong Hyup Lee

Dept. of Information and Communications Engineering, Inje University, Gimhae, Republic of Korea

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APA Style

Jong Hyup Lee. (2015). Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem. International Journal of Economics, Finance and Management Sciences, 3(5), 460-464. https://doi.org/10.11648/j.ijefm.20150305.17

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ACS Style

Jong Hyup Lee. Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem. Int. J. Econ. Finance Manag. Sci. 2015, 3(5), 460-464. doi: 10.11648/j.ijefm.20150305.17

Copy | Download

AMA Style

Jong Hyup Lee. Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem. Int J Econ Finance Manag Sci. 2015;3(5):460-464. doi: 10.11648/j.ijefm.20150305.17

Copy | Download

@article{10.11648/j.ijefm.20150305.17,
  author = {Jong Hyup Lee},
  title = {Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem},
  journal = {International Journal of Economics, Finance and Management Sciences},
  volume = {3},
  number = {5},
  pages = {460-464},
  doi = {10.11648/j.ijefm.20150305.17},
  url = {https://doi.org/10.11648/j.ijefm.20150305.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijefm.20150305.17},
  abstract = {In this paper, we examine the problem of establishing minimum cost production and transportation plans that satisfy known demands over a finite planning horizon. Two products, product 1 and 2, can be produced in each of two regions. Each region uses its own facility to supply the demands for two products. Demands for product 2 in one region can be satisfied either by its own production or by transportation from other region, while no transportation between two regions is allowed for product 1. Moreover, the transportation in each period is constrained by a time-dependent capacity bound. Production and transportation costs are assumed to be non-decreasing and concave. Using a network flow approach, properties of extreme points are identified. Then, a dynamic programming algorithm is developed to find an optimal plan.},
 year = {2015}
}

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TY  - JOUR
T1  - Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem
AU  - Jong Hyup Lee
Y1  - 2015/09/26
PY  - 2015
N1  - https://doi.org/10.11648/j.ijefm.20150305.17
DO  - 10.11648/j.ijefm.20150305.17
T2  - International Journal of Economics, Finance and Management Sciences
JF  - International Journal of Economics, Finance and Management Sciences
JO  - International Journal of Economics, Finance and Management Sciences
SP  - 460
EP  - 464
PB  - Science Publishing Group
SN  - 2326-9561
UR  - https://doi.org/10.11648/j.ijefm.20150305.17
AB  - In this paper, we examine the problem of establishing minimum cost production and transportation plans that satisfy known demands over a finite planning horizon. Two products, product 1 and 2, can be produced in each of two regions. Each region uses its own facility to supply the demands for two products. Demands for product 2 in one region can be satisfied either by its own production or by transportation from other region, while no transportation between two regions is allowed for product 1. Moreover, the transportation in each period is constrained by a time-dependent capacity bound. Production and transportation costs are assumed to be non-decreasing and concave. Using a network flow approach, properties of extreme points are identified. Then, a dynamic programming algorithm is developed to find an optimal plan.
VL  - 3
IS  - 5
ER  -

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