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

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  • Robert Grubbstrom
  • Ou Tang

Abstract

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.

Suggested Citation

  • Robert Grubbstrom & Ou Tang, 2000. "An Overview of Input-Output Analysis Applied to Production-Inventory Systems," Economic Systems Research, Taylor & Francis Journals, vol. 12(1), pages 3-25.
    • Handle: RePEc:taf:ecsysr:v:12:y:2000:i:1:p:3-25
    DOI: 10.1080/095353100111254
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    1. 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.
    2. Arthur F. Veinott, 1969. "Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems," Operations Research, INFORMS, vol. 17(2), pages 262-291, April.
    3. Grubbstrom, Robert W. & Tang, Ou, 1999. "Further developments on safety stocks in an MRP system applying Laplace transforms and input-output analysis," International Journal of Production Economics, Elsevier, vol. 60(1), pages 381-387, April.
    4. 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.
    5. Andrew Vazsonyi, 1955. "The Use of Mathematics in Production and Inventory Control--II (Theory of Scheduling)," Management Science, INFORMS, vol. 1(3-4), pages 207-223, 04-07.
    6. Grubbstrom, Robert W & Molinder, Anders, 1994. "Further theoretical considerations on the relationship between MRP, input-output analysis and multi-echelon inventory systems," International Journal of Production Economics, Elsevier, vol. 35(1-3), pages 299-311, June.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Bogataj, Ludvik & Horvat, Liljana, 1996. "Stochastic considerations of Grubbstrom--Molinder model of MRP, input-output and multi-echelon inventory systems," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 329-336, August.
    12. 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.
    13. Grubbstrom, Robert W., 1995. "Modelling production opportunities -- an historical overview," International Journal of Production Economics, Elsevier, vol. 41(1-3), pages 1-14, October.
    14. 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.
    15. 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.
    16. Robin Roundy, 1986. "A 98%-Effective Lot-Sizing Rule for a Multi-Product, Multi-Stage Production / Inventory System," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 699-727, November.
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    5. Fraccascia, Luca, 2020. "Quantifying the direct network effect for online platforms supporting industrial symbiosis: an agent-based simulation study," Ecological Economics, Elsevier, vol. 170(C).
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