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Dynamic Lot Size Models for Multi-Stage Assembly Systems

Author

Listed:
  • Wallace B. Crowston

    (York University, Ontario, Canada)

  • Michael H. Wagner

    (Graduate School of Business, New York University)

Abstract

A multi-stage assembly system is a special case of Veinott's general multi-facility system in that each facility may have any number of predecessors but at most a single successor. This paper presents two algorithms for computing optimal lot sizes in such systems with known time-varying demand. The first is a dynamic programming algorithm for which solution time increases exponentially with the number of time periods, but only linearly with the number of stages, irrespective of assembly structure. The second is a branch and bound algorithm intended for cases where the number of time periods is large but the structure is close to serial. Computational results are given and extensions considered.

Suggested Citation

  • Wallace B. Crowston & Michael H. Wagner, 1973. "Dynamic Lot Size Models for Multi-Stage Assembly Systems," Management Science, INFORMS, vol. 20(1), pages 14-21, September.
    • Handle: RePEc:inm:ormnsc:v:20:y:1973:i:1:p:14-21
    DOI: 10.1287/mnsc.20.1.14
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    Citations

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    Cited by:

    1. Tang, Ou, 2004. "Simulated annealing in lot sizing problems," International Journal of Production Economics, Elsevier, vol. 88(2), pages 173-181, March.
    2. 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.
    3. Dong, Yachao & Maravelias, Christos T., 2021. "Terminal inventory level constraints for online production scheduling," European Journal of Operational Research, Elsevier, vol. 295(1), pages 102-117.
    4. Chu, Chi-Leung & Leon, V. Jorge, 2009. "Scalable methodology for supply chain inventory coordination with private information," European Journal of Operational Research, Elsevier, vol. 195(1), pages 262-279, May.
    5. N.C. Simpson & S. Selcuk Erenguc, 2005. "Modeling multiple stage manufacturing systems with generalized costs and capacity issues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 560-570, September.
    6. 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.
    7. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2006. "Primal-Dual Algorithms for Deterministic Inventory Problems," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 267-284, May.
    8. Marcin Bienkowski & Martin Böhm & Jaroslaw Byrka & Marek Chrobak & Christoph Dürr & Lukáš Folwarczný & Łukasz Jeż & Jiří Sgall & Nguyen Kim Thang & Pavel Veselý, 2020. "Online Algorithms for Multilevel Aggregation," Operations Research, INFORMS, vol. 68(1), pages 214-232, January.
    9. Simpson, N. C., 1999. "Multiple level production planning in rolling horizon assembly environments," European Journal of Operational Research, Elsevier, vol. 114(1), pages 15-28, April.
    10. 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.
    11. 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.
    12. 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.
    13. Xiao, Yiyong & Zhang, Renqian & Zhao, Qiuhong & Kaku, Ikou & Xu, Yuchun, 2014. "A variable neighborhood search with an effective local search for uncapacitated multilevel lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 102-114.
    14. H-J Kim & D-H Lee & P Xirouchakis & O K Kwon, 2009. "A branch and bound algorithm for disassembly scheduling with assembly product structure," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(3), pages 419-430, March.

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