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Production Scheduling by the Transportation Method of Linear Programming

Author

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  • Edward H. Bowman

    (School of Instustrial Management, Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

With fluctuating sales, a manufacturer must have fluctuating production, or fluctuating inventory, or both. Penalties are associated with either type of fluctuation. Several papers place this problem into a conventional linear-programming framework. This paper suggests that the same problem may be placed into a transportation-method framework and, further, that many transportation problems may be extended to include multiple time periods where this is meaningful. A generalized scheduling problem is placed here into the standard form of the transportation table.

Suggested Citation

  • Edward H. Bowman, 1956. "Production Scheduling by the Transportation Method of Linear Programming," Operations Research, INFORMS, vol. 4(1), pages 100-103, February.
    • Handle: RePEc:inm:oropre:v:4:y:1956:i:1:p:100-103
    DOI: 10.1287/opre.4.1.100
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    Cited by:

    1. Iara Ciurria-Infosino & Daniel Granot & Frieda Granot & Arthur F. Veinott, 2015. "Multicommodity Production Planning: Qualitative Analysis and Applications," Manufacturing & Service Operations Management, INFORMS, vol. 17(4), pages 589-607, October.
    2. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Harvey M. Wagner, 2002. "And Then There Were None," Operations Research, INFORMS, vol. 50(1), pages 217-226, February.
    4. Gomes da Silva, Carlos & Figueira, José & Lisboa, João & Barman, Samir, 2006. "An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming," Omega, Elsevier, vol. 34(2), pages 167-177, April.
    5. L Tang & G Liu & J Liu, 2008. "Raw material inventory solution in iron and steel industry using Lagrangian relaxation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 44-53, January.
    6. Wang, Reay-Chen & Liang, Tien-Fu, 2005. "Applying possibilistic linear programming to aggregate production planning," International Journal of Production Economics, Elsevier, vol. 98(3), pages 328-341, December.
    7. Hax, Arnoldo C. & Meal, Harlan C., 1973. "Hierarchical integration of production planning and scheduling," Working papers 656-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. Shih-Pin Chen & Wen-Lung Huang, 2014. "Solving Fuzzy Multiproduct Aggregate Production Planning Problems Based on Extension Principle," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-18, August.
    9. Krishna Kumar, C. & Sinha, Bani K., 1999. "Efficiency based production planning and control models," European Journal of Operational Research, Elsevier, vol. 117(3), pages 450-469, September.
    10. Logan, Samuel H., 1984. "An Annual Planning Model for Food Processing: An Example of the Tomato Industry," Research Reports 251942, University of California, Davis, Giannini Foundation.
    11. K S Hindi & K Fleszar & C Charalambous, 2003. "An effective heuristic for the CLSP with set-up times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(5), pages 490-498, May.
    12. Körpeoglu, Ersin & Yaman, Hande & Selim Aktürk, M., 2011. "A multi-stage stochastic programming approach in master production scheduling," European Journal of Operational Research, Elsevier, vol. 213(1), pages 166-179, August.
    13. Monique Guignard, 2007. "En hommage à Joseph-Louis Lagrange et à Pierre Huard," Annals of Operations Research, Springer, vol. 149(1), pages 103-116, February.

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