Abstract
Manufacturing network flow (MNF) is a generalized network model that can model more complicated manufacturing scenarios, such as the synthesis of different materials to one product and/or the distilling of one material to many different products. Minimum distribution cost flow problem (MDCF) is a simplified version of MNF optimization problems, in which a general supplier wants to proportionally distribute certain amount of a particular product from a source node to several retailers at different destinations through a distribution network. A network simplex algorithm has been outlined in recent years for solving a special case of MDCF. In this paper, we characterize the network structure of the bases of the MDCF problem and develop a primal simplex algorithm that exploits the network structure of the problem. These results are extensions of those of the ordinary network flow problems. In conclusion, some related interesting problems are proposed for future research.
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References
Ahuja RK, Magnanti TL, Orlin JR (1993) Network flows: Theory, Algorithms, and applications. Prentice Hall, New Jersey
Ahuja RK, Orlin JB, Sechi GM, Zuddas P (1999) Algorithms for the simple equal flow problem. Management Scinece 45:1440–1455
Askin RG, Standridge CR (1993) Modeling and Analysis of Manufacturing System. John Wiley and Sons, New York
Bazaraa MS, Jarvis JJ, Sherali HD (1990) Linear Programming and Network Flows. John Wiley and Sons, New York
Brauldi RA (2002) Introductory combinatorics. Prentice Hall and China Machine Press, Beijing
Calvete HI (2003) Network simplex algorithm for the general equal flow problem. European Journal of Operational Research 150:585–600
Fang SC, Qi LQ (2003) Manufacturing network flows: A generalized network flow model for manufacturing process modeling. Optimization Methods and Software 18:143–165
Gülpinar N, Gutin G, Mitra G, Maors I (2000) Detecting embedded networks in LP using GUB structures and independent set algorithms. Computational Optimization and Applications 15:235–247
Gülpinar N, Mitra G, Maors I (2002) Creating advanced bases for large scale linear programs exploiting embedded network structure. Computational Optimization and Applications 21:71–93
Kennington JL, Helgason RV (1998) Algorithms for Network Programming. John Wiley and Sons, New York
Lawler EL (1976) Combinatorial optimization: Networks and matroids. Holt, Rinehart and Winston, New York
Leondes C. (Ed.) (2001) Computer Integrated Manufacturing. CRC Press, New York
Mathies S, Mevert P (1998) A hybrid algorithm for solving network flow problem with side constraints. Computational Optimization and Applications 25:745–756
Murty KG (1992) Network programming. Prentice Hall, New Jersey
Zhang BW (2005) Inverse optimization problems under Hamming distance and multicommodity production and distribution problems. PhD thesis, Zhejiang University
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This research is partially supported by the National Natural Science Foundation of China (No. 10371028) and a grant from Southern Yangtze University (No. 0003182).
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Lu, H., Yao, E. & Qi, L. Some further results on minimum distribution cost flow problems. J Comb Optim 11, 351–371 (2006). https://doi.org/10.1007/s10878-006-8211-9
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DOI: https://doi.org/10.1007/s10878-006-8211-9