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Optimal Multi-Level Lot Sizing for Requirements Planning Systems

Author

Listed:
  • Earle Steinberg

    (University of Houston)

  • H. Albert Napier

    (University of Houston)

Abstract

The wide spread use of advanced information systems such as Material Requirements Planning (MRP) has significantly altered the practice of dependent demand inventory management. Recent research has focused on development of multi-level lot sizing heuristics for such systems. In this paper, we develop an optimal procedure for the multi-period, multi-product, multi-level lot sizing problem by modeling the system as a constrained generalized network with fixed charge arcs and side constraints. The network permits us to relax some of the more restrictive assumptions of previous models such as those designed for product structures with single sources or successors. The solution to the resulting minimum cost flow problem yields optimal lot sizing decisions for all purchases as well as manufactured goods and components in all periods over a finite planning horizon. A simple illustration, beginning with a master production schedule and bills of material, illustrates the suitablility of this approach for modeling complex requirements planning systems. Optimal solutions obtained by this method may also be useful in comparing results obtained from future heuristic approaches which may be more computationally efficient.

Suggested Citation

  • Earle Steinberg & H. Albert Napier, 1980. "Optimal Multi-Level Lot Sizing for Requirements Planning Systems," Management Science, INFORMS, vol. 26(12), pages 1258-1271, December.
    • Handle: RePEc:inm:ormnsc:v:26:y:1980:i:12:p:1258-1271
    DOI: 10.1287/mnsc.26.12.1258
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    Citations

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    Cited by:

    1. Dellaert, N. & Jeunet, J. & Jonard, N., 2000. "A genetic algorithm to solve the general multi-level lot-sizing problem with time-varying costs," International Journal of Production Economics, Elsevier, vol. 68(3), pages 241-257, December.
    2. Drexl, Andreas & Haase, Knut, 1995. "Proportional lotsizing and scheduling," International Journal of Production Economics, Elsevier, vol. 40(1), pages 73-87, June.
    3. Gencer, Cevriye & Erol, Serpil & Erol, Yalcin, 1999. "A decision network algorithm for multi-stage dynamic lot sizing problems," International Journal of Production Economics, Elsevier, vol. 62(3), pages 281-285, September.
    4. Grubbström, Robert W. & Tang, Ou, 2012. "The space of solution alternatives in the optimal lotsizing problem for general assembly systems applying MRP theory," International Journal of Production Economics, Elsevier, vol. 140(2), pages 765-777.
    5. Xiao, Yiyong & Kaku, Ikou & Zhao, Qiuhong & Zhang, Renqian, 2011. "A reduced variable neighborhood search algorithm for uncapacitated multilevel lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 214(2), pages 223-231, October.
    6. Dellaert, N. P. & Jeunet, J., 2003. "Randomized multi-level lot-sizing heuristics for general product structures," European Journal of Operational Research, Elsevier, vol. 148(1), pages 211-228, July.
    7. Drexl, Andreas & Haase, Knut, 1992. "A new type of model for multi-item capacitated dynamic lotsizing and scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 286, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    8. Kimms, Alf & Drexl, Andreas, 1996. "Multi-level lot sizing: A literature survey," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 405, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    9. Rajiv D. Banker & Robert J. Kauffman, 2004. "50th Anniversary Article: The Evolution of Research on Information Systems: A Fiftieth-Year Survey of the Literature in Management Science," Management Science, INFORMS, vol. 50(3), pages 281-298, March.
    10. Jörg Homberger, 2008. "A Parallel Genetic Algorithm for the Multilevel Unconstrained Lot-Sizing Problem," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 124-132, February.

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