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Heuristics for Multilevel Lot-Sizing with a Bottleneck

Author

Listed:
  • Peter J. Billington

    (Graduate School of Business, Northeastern University, Boston, Massachusetts)

  • John O. McClain

    (Johnson Graduate School of Management, Cornell University, Ithaca, New York 14853)

  • L. Joseph Thomas

    (Johnson Graduate School of Management, Cornell University, Ithaca, New York 14853)

Abstract

In this paper we present a heuristic method, based on Lagrangian relaxation, for multilevel lot-sizing when there is a single bottleneck facility. A series of Lagrangian relaxations (one for each item in the product structure) is imbedded in a branch and bound procedure. The objective is to find a production schedule that fits within available capacity at minimum cost. The method has two solution phases, dual and primal. In the dual phase of the procedure, implied costs of setups and production are determined based on a tentative schedule. The primal phase is repeated with these new prices and we iterate to reach a good solution. The solution procedure is first tested on two special cases: uncapacitated multilevel lot-sizing and the capacitated, single-level multi-item lot sizing problem. The results show that the solution procedure can provide better solutions than some heuristics designed especially for those problems. Test results on the bottleneck problem indicate that good feasible solutions are found for problems too difficult to solve with exact methods.

Suggested Citation

  • Peter J. Billington & John O. McClain & L. Joseph Thomas, 1986. "Heuristics for Multilevel Lot-Sizing with a Bottleneck," Management Science, INFORMS, vol. 32(8), pages 989-1006, August.
    • Handle: RePEc:inm:ormnsc:v:32:y:1986:i:8:p:989-1006
    DOI: 10.1287/mnsc.32.8.989
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    Cited by:

    1. Doostmohammadi, Mahdi & Akartunalı, Kerem, 2018. "Valid inequalities for two-period relaxations of big-bucket lot-sizing problems: Zero setup case," European Journal of Operational Research, Elsevier, vol. 267(1), pages 86-95.
    2. Elena Katok & Holly S. Lewis & Terry P. Harrison, 1998. "Lot Sizing in General Assembly Systems with Setup Costs, Setup Times, and Multiple Constrained Resources," Management Science, INFORMS, vol. 44(6), pages 859-877, June.
    3. Drexl, Andreas & Haase, Knut, 1995. "Proportional lotsizing and scheduling," International Journal of Production Economics, Elsevier, vol. 40(1), pages 73-87, June.
    4. 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.
    5. Huang, Hai-Jun & Xu, Gang, 1998. "Aggregate scheduling and network solving of multi-stage and multi-item manufacturing systems," European Journal of Operational Research, Elsevier, vol. 105(1), pages 52-65, February.
    6. Ozdamar, Linet & Barbarosoglu, Gulay, 2000. "An integrated Lagrangean relaxation-simulated annealing approach to the multi-level multi-item capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 68(3), pages 319-331, December.
    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. Ozdamar, Linet & Birbil, Sevket Ilker, 1998. "Hybrid heuristics for the capacitated lot sizing and loading problem with setup times and overtime decisions," European Journal of Operational Research, Elsevier, vol. 110(3), pages 525-547, November.
    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. Chakravarty, Amiya K. & Balakrishnan, Nagraj, 1998. "Reacting in real-time to production contingencies in a capacitated flexible cell," European Journal of Operational Research, Elsevier, vol. 110(1), pages 1-19, October.
    11. Kerem Akartunalı & Andrew Miller, 2012. "A computational analysis of lower bounds for big bucket production planning problems," Computational Optimization and Applications, Springer, vol. 53(3), pages 729-753, December.
    12. Sahling, Florian & Hahn, Gerd J., 2019. "Dynamic lot sizing in biopharmaceutical manufacturing," International Journal of Production Economics, Elsevier, vol. 207(C), pages 96-106.
    13. dos Santos-Meza, Elisangela & Oliveira dos Santos, Maristela & Nereu Arenales, Marcos, 2002. "A lot-sizing problem in an automated foundry," European Journal of Operational Research, Elsevier, vol. 139(3), pages 490-500, June.
    14. Helber, Stefan & Sahling, Florian, 2010. "A fix-and-optimize approach for the multi-level capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 123(2), pages 247-256, February.
    15. Chatterjee A K & Mukherjee, Saral, 2006. "Unified Concept of Bottleneck," IIMA Working Papers WP2006-05-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    16. Kerem Akartunalı & Ioannis Fragkos & Andrew J. Miller & Tao Wu, 2016. "Local Cuts and Two-Period Convex Hull Closures for Big-Bucket Lot-Sizing Problems," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 766-780, November.
    17. Kolisch, R., 2000. "Integration of assembly and fabrication for make-to-order production," International Journal of Production Economics, Elsevier, vol. 68(3), pages 287-306, December.
    18. Brahimi, Nadjib & Dauzere-Peres, Stephane & Najid, Najib M. & Nordli, Atle, 2006. "Single item lot sizing problems," European Journal of Operational Research, Elsevier, vol. 168(1), pages 1-16, January.

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