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An Overview of Input-Output Analysis Applied to Production-Inventory Systems

  • Robert Grubbstrom
  • Ou Tang
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    Input-Output Analysis, together with the Laplace transform, have been applied to multi-level, multi-period production-inventory systems in a number of papers. This article gives a historical overview of the areas involved in these studies. It is shown that the input and output matrices as well as the Leontief inverse can be generalised to include timing properties for the inputs by means of the Laplace transform. The consequent advantages are exemplified in different production models, treating, for instance, capacity requirements and safety stock problems. The main literature in this field concerns assembly systems, but the approach is easily applicable to process industries with a divergent material flow or when feedback is essential.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/095353100111254
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    Article provided by Taylor & Francis Journals in its journal Economic Systems Research.

    Volume (Year): 12 (2000)
    Issue (Month): 1 ()
    Pages: 3-25

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    Handle: RePEc:taf:ecsysr:v:12:y:2000:i:1:p:3-25
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    1. Grubbstrom, R. W., 1990. "The distribution of an additive in a chemical process: An application of input-output theory," Engineering Costs and Production Economics, Elsevier, vol. 19(1-3), pages 333-340, May.
    2. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    3. Bogataj, Marija, 1999. "Inventory allocation and customer travelling problem in spatial duopoly," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 271-279, March.
    4. Grubbstrom, Robert W. & Molinder, Anders, 1996. "Safety production plans in MRP-systems using transform methodology," International Journal of Production Economics, Elsevier, vol. 46(1), pages 297-309, December.
    5. Grubbstrom, Robert W., 1999. "A net present value approach to safety stocks in a multi-level MRP system," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 361-375, March.
    6. Grubbstrom, Robert W., 1998. "A net present value approach to safety stocks in planned production," International Journal of Production Economics, Elsevier, vol. 56(1), pages 213-229, September.
    7. Horvat, Liljana & Bogataj, Ludvik, 1999. "A market game with the characteristic function according to the MRP and input-output analysis model," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 281-288, March.
    8. Grubbstrom, Robert W., 1995. "Modelling production opportunities -- an historical overview," International Journal of Production Economics, Elsevier, vol. 41(1-3), pages 1-14, October.
    9. Robert W. Grubbström, 1967. "On The Application of the Laplace Transform to Certain Economic Problems," Management Science, INFORMS, vol. 13(7), pages 558-567, March.
    10. Grubbstrom, Robert W. & Ovrin, Peter, 1992. "Intertemporal generalization of the relationship between material requirements planning and input-output analysis," International Journal of Production Economics, Elsevier, vol. 26(1-3), pages 311-318, February.
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