Two Product, Two Region Production, Inventory, and Transportation Problems
International Journal of Economics, Finance and Management Sciences
Volume 2, Issue 6, December 2014, Pages: 313-318
Received: Nov. 14, 2014; Accepted: Nov. 30, 2014; Published: Dec. 2, 2014
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Authors
Jong Hyup Lee, Dept. of Information and Communications Engineering, Inje University, Gimhae, Republic of Korea
Jung Man Hong, LG CNS, Seoul, Republic of Korea (* Corresponding Author)
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Abstract
A deterministic production and transportation planning problem is considered over a finite time horizon for two products that 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. Production, inventory and transportation costs are assumed to be non-decreasing and concave. The objective is to find the schedule of production and transportation in each region by which the total cost over the horizon is minimized. Using a network flow approach, we develop a dynamic programming algorithm that can find an optimal policy.
Keywords
Production Planning, Network Flow, Dynamic Programming
To cite this article
Jong Hyup Lee, Jung Man Hong, Two Product, Two Region Production, Inventory, and Transportation Problems, International Journal of Economics, Finance and Management Sciences. Vol. 2, No. 6, 2014, pp. 313-318. doi: 10.11648/j.ijefm.20140206.13
References
[1]
H. M. Wagner and T. M. Whitin, “Dynamic Version of the Economic Lot Size Model”, Management Science, vol. 14, pp.429-450, 1968.
[2]
W. I. Zangwill, “Minimum Concave Cost Flows in Certain Network”, Management Science, vol. 14, pp.429-450, 1968.
[3]
M. Florian and M. Klein, “Deterministic Production Planning with Concave Costs and Capacity Constraints”, Management Science, vol. 18, pp.12-20, 1971.
[4]
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.
[5]
H. Luss, “A Capacity-Expansion Model for Two Facility Types”, Naval Research Logistics Quarterly, vol. 26, pp.291-303, 1979.
[6]
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.
[7]
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.
[8]
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.
[9]
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.
[10]
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.
[11]
R. K. Oliver and M. D. Webber, “Supply-Chain Management: Logistics Catches up with Strategy”, in Christopher, M. Logistics: The Strategic Issues, Chapman Hall, London, pp. 63–75, ISBN 0-412-41550-X, 1992.
[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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