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Multilevel Lot Sizing with Setup Times and Multiple Constrained Resources: Internally Rolling Schedules with Lot-Sizing Windows

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  • Hartmut Stadtler

    (Technische Universität Darmstadt, Institut für Betriebswirtschaftslehre, Fachgebiet Fertigungs- und Materialwirtschaft, Hochschulstra(beta)e 1, D-64289 Darmstadt, Germany)

Abstract

In this paper a new time-oriented decomposition heuristic is proposed to solve the dynamic multi-item multilevel lot-sizing problem in general product structures with single and multiple constrained resources as well as setup times. While lot-sizing decisions are made sequentially within an internally rolling planning interval (or lot-sizing window), capacities are always considered over the entire planning horizon. For each submodel a model formulation based on the “Simple Plant Location” representation is developed. These mixed-integer linear submodels are solved by standard mathematical programming software even for relatively large test instances. Extensive computational tests show that the heuristic proposed provides a better solution quality than a well-known special purpose heuristic.

Suggested Citation

  • Hartmut Stadtler, 2003. "Multilevel Lot Sizing with Setup Times and Multiple Constrained Resources: Internally Rolling Schedules with Lot-Sizing Windows," Operations Research, INFORMS, vol. 51(3), pages 487-502, June.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:3:p:487-502
    DOI: 10.1287/opre.51.3.487.14949
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    References listed on IDEAS

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    1. 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.
    2. Stadtler, Hartmut, 2000. "Improved rolling schedules for the dynamic single level lot sizing problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 14079, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    3. Peter J. Billington & John O. McClain & L. Joseph Thomas, 1983. "Mathematical Programming Approaches to Capacity-Constrained MRP Systems: Review, Formulation and Problem Reduction," Management Science, INFORMS, vol. 29(10), pages 1126-1141, October.
    4. Yves Pochet & Laurence A. Wolsey, 1991. "Solving Multi-Item Lot-Sizing Problems Using Strong Cutting Planes," Management Science, INFORMS, vol. 37(1), pages 53-67, January.
    5. 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.
    6. Maes, Johan & McClain, John O. & Van Wassenhove, Luk N., 1991. "Multilevel capacitated lotsizing complexity and LP-based heuristics," European Journal of Operational Research, Elsevier, vol. 53(2), pages 131-148, July.
    7. 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.
    8. Stadtler, Hartmut, 1997. "Reformulations of the shortest route model for dynamic multi-item multi-level capacitated lotsizing," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 7096, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    9. Dillenberger, Christof & Escudero, Laureano F. & Wollensak, Artur & Zhang, Wu, 1994. "On practical resource allocation for production planning and scheduling with period overlapping setups," European Journal of Operational Research, Elsevier, vol. 75(2), pages 275-286, June.
    10. Hartmut Stadtler, 2000. "Improved Rolling Schedules for the Dynamic Single-Level Lot-Sizing Problem," Management Science, INFORMS, vol. 46(2), pages 318-326, February.
    11. Fleischmann, Bernhard, 1990. "The discrete lot-sizing and scheduling problem," European Journal of Operational Research, Elsevier, vol. 44(3), pages 337-348, February.
    12. 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.
    13. Tempelmeier, Horst & Helber, Stefan, 1994. "A heuristic for dynamic multi-item multi-level capacitated lotsizing for general product structures," European Journal of Operational Research, Elsevier, vol. 75(2), pages 296-311, June.
    14. Terry P. Harrison & Holly S. Lewis, 1996. "Lot Sizing in Serial Assembly Systems with Multiple Constrained Resources," Management Science, INFORMS, vol. 42(1), pages 19-36, January.
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