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Some insights into proportional lot sizing and scheduling

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  • Kimms, Alf
  • Drexl, Andreas

Abstract

This paper deals with proportional lot sizing and scheduling (PLSP) and gives some insights into the properties of this problem. Such insights may be useful for developing heuristic and/or exact solution procedures. The emphasis of this paper is on the multi-level, multi-machine case. We provide a mixed-integer programming model, relate it to other models that can be found in the literature, and discuss characteristics which make solving instances of the PLSP-model become a hard task.

Suggested Citation

  • Kimms, Alf & Drexl, Andreas, 1996. "Some insights into proportional lot sizing and scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 406, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    • Handle: RePEc:zbw:cauman:406
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    References listed on IDEAS

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    1. Panayotis Afentakis & Bezalel Gavish, 1986. "Optimal Lot-Sizing Algorithms for Complex Product Structures," Operations Research, INFORMS, vol. 34(2), pages 237-249, April.
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    3. Drexl, Andreas & Haase, Knut, 1995. "Proportional lotsizing and scheduling," International Journal of Production Economics, Elsevier, vol. 40(1), pages 73-87, June.
    4. Gary D. Eppen & R. Kipp Martin, 1987. "Solving Multi-Item Capacitated Lot-Sizing Problems Using Variable Redefinition," Operations Research, INFORMS, vol. 35(6), pages 832-848, December.
    5. Kirca, Omer & Kokten, Melih, 1994. "A new heuristic approach for the multi-item dynamic lot sizing problem," European Journal of Operational Research, Elsevier, vol. 75(2), pages 332-341, June.
    6. Haase, Knut, 1993. "Capacitated lot-sizing with linked production quantities of adjacent periods," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 334, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    7. Haase, Knut & Kimms, Alf, 1996. "Lot sizing and scheduling with sequence dependent setup costs and times and efficient rescheduling opportunities," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 393, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    8. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    9. Horst Tempelmeier & Matthias Derstroff, 1996. "A Lagrangean-Based Heuristic for Dynamic Multilevel Multiitem Constrained Lotsizing with Setup Times," Management Science, INFORMS, vol. 42(5), pages 738-757, May.
    10. Lotfi, Vahid & Chen, Wun-Hwa, 1991. "An optimal algorithm for the multi-item capacitated production planning problem," European Journal of Operational Research, Elsevier, vol. 52(2), pages 179-193, May.
    11. Kimms, A., 1996. "Multi-level, single-machine lot sizing and scheduling (with initial inventory)," European Journal of Operational Research, Elsevier, vol. 89(1), pages 86-99, February.
    12. Moustapha Diaby & Harish C. Bahl & Mark H. Karwan & Stanley Zionts, 1992. "A Lagrangean Relaxation Approach for Very-Large-Scale Capacitated Lot-Sizing," Management Science, INFORMS, vol. 38(9), pages 1329-1340, September.
    13. Marc Salomon & Leo G. Kroon & Roelof Kuik & Luk N. Van Wassenhove, 1991. "Some Extensions of the Discrete Lotsizing and Scheduling Problem," Management Science, INFORMS, vol. 37(7), pages 801-812, July.
    14. Fleischmann, Bernhard, 1990. "The discrete lot-sizing and scheduling problem," European Journal of Operational Research, Elsevier, vol. 44(3), pages 337-348, February.
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    Cited by:

    1. Fandel, Gunter & Stammen-Hegene, Cathrin, 2006. "Simultaneous lot sizing and scheduling for multi-product multi-level production," International Journal of Production Economics, Elsevier, vol. 104(2), pages 308-316, December.
    2. Drexl, A. & Kimms, A., 1997. "Lot sizing and scheduling -- Survey and extensions," European Journal of Operational Research, Elsevier, vol. 99(2), pages 221-235, June.

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