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Economic Lot Size Determination in Multi-Stage Assembly Systems

Author

Listed:
  • Wallace B. Crowston

    (York University)

  • Michael Wagner

    (New York University)

  • Jack F. Williams

    (University of Wisconsin--Milwaukee)

Abstract

We consider the optimal lot size problem for multi-stage assembly systems where each facility may have many predecessors but only a single successor. Assumptions include constant continuous final product demand, instantaneous production, and an infinite planning horizon. Costs at each facility consist of a fixed charge per lot and a linear holding cost. Under the constraint that lot sizes remain time invariant, it is proven that the optimal lot size at each facility is an integer multiple of the lot size at the successor facility. This fact is used in the construction of a dynamic programming algorithm for the computation of optimal lot sizes. The algorithm exploits the concept of echelon stock [Clark, A. J., H. Scarf. 1960. Optimal policies for a multi-echelon inventory problem. Management Sci. 6 (4, July) 475-490; Clark, A. J., H. Scarf. 1962. Approximate solution to a simple multi-echelon inventory problem. Chapter 5. K. J. Arrow et al., eds. Studies in Applied Probability and Management Science. Stanford University Press, Stanford, California.].

Suggested Citation

  • Wallace B. Crowston & Michael Wagner & Jack F. Williams, 1973. "Economic Lot Size Determination in Multi-Stage Assembly Systems," Management Science, INFORMS, vol. 19(5), pages 517-527, January.
    • Handle: RePEc:inm:ormnsc:v:19:y:1973:i:5:p:517-527
    DOI: 10.1287/mnsc.19.5.517
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    1. Bouchery, Yann & Ghaffari, Asma & Jemai, Zied & Dallery, Yves, 2012. "Including sustainability criteria into inventory models," European Journal of Operational Research, Elsevier, vol. 222(2), pages 229-240.
    2. Dana Marsetiya Utama & Fakhrina Fahma Abdullah & Ikhlasul Amallynda & Teguh Baroto, 2024. "Integrated production-inventory model for multi-item raw materials with exponential quality degradation: a real case study," OPSEARCH, Springer;Operational Research Society of India, vol. 61(4), pages 1862-1887, December.
    3. Erenguc, S. Selcuk & Simpson, N. C. & Vakharia, Asoo J., 1999. "Integrated production/distribution planning in supply chains: An invited review," European Journal of Operational Research, Elsevier, vol. 115(2), pages 219-236, June.
    4. 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.
    5. Hsien-Jen Lin, 2015. "Two-echelon stochastic inventory system with returns and partial backlogging," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(6), pages 966-975, April.
    6. 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.
    7. Grubbstrom, Robert W., 1995. "Modelling production opportunities -- an historical overview," International Journal of Production Economics, Elsevier, vol. 41(1-3), pages 1-14, October.
    8. Beullens, Patrick, 2014. "Revisiting foundations in lot sizing—Connections between Harris, Crowther, Monahan, and Clark," International Journal of Production Economics, Elsevier, vol. 155(C), pages 68-81.
    9. 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.
    10. Ouenniche, Jamal & Boctor, Fayez F., 2001. "The two-group heuristic to solve the multi-product, economic lot sizing and scheduling problem in flow shops," European Journal of Operational Research, Elsevier, vol. 129(3), pages 539-554, March.
    11. Kim, DaeSoo, 1999. "Optimal two-stage lot sizing and inventory batching policies," International Journal of Production Economics, Elsevier, vol. 58(3), pages 221-234, January.
    12. Pundoor, Guruprasad & Chen, Zhi-Long, 2009. "Joint cyclic production and delivery scheduling in a two-stage supply chain," International Journal of Production Economics, Elsevier, vol. 119(1), pages 55-74, May.
    13. Abdul-Jalbar, B. & Gutierrez, J. & Puerto, J. & Sicilia, J., 2003. "Policies for inventory/distribution systems: The effect of centralization vs. decentralization," International Journal of Production Economics, Elsevier, vol. 81(1), pages 281-293, January.

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