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A new type of model for multi-item capacitated dynamic lotsizing and scheduling

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  • Drexl, Andreas
  • Haase, Knut

Abstract

Three types of multi-item capacitated dynamic lotsizing and scheduling models are well established until now: The capacitated lotsizing problem, the discrete lotsizing and scheduling problem as well as the continuous setup lotsizing problem. An analysis of the underlying fundamental assumptions provides the basis for introducing a new model type, the proportional lotsizing and scheduling problem. This model type is well suited for incorporating some of the extensions relevant with respect to practice: Setup times, sequence dependent setup costs (times), multiple machines as well as multiple stages. Last but not least we show how make-or-buy decisions may be modelled within this framework. This is relevant regarding three important aspects: First it is more general, second it is of practical relevance, third it provides the basis for overcoming difficulties associated with feasibility problems. The last fact opens up new avenues especially for the development of efficient local search procedures.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:cauman:286
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    1. Jose Juan Carreno, 1990. "Economic Lot Scheduling for Multiple Products on Parallel Identical Processors," Management Science, INFORMS, vol. 36(3), pages 348-358, March.
    2. Kuik, R. & Salomon, M., 1990. "Multi-level lot-sizing problem: Evaluation of a simulated-annealing heuristic," European Journal of Operational Research, Elsevier, vol. 45(1), pages 25-37, March.
    3. William W. Trigeiro & L. Joseph Thomas & John O. McClain, 1989. "Capacitated Lot Sizing with Setup Times," Management Science, INFORMS, vol. 35(3), pages 353-366, March.
    4. 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.
    5. Gregory Dobson, 1987. "The Economic Lot-Scheduling Problem: Achieving Feasibility Using Time-Varying Lot Sizes," Operations Research, INFORMS, vol. 35(5), pages 764-771, October.
    6. Gerard M. Campbell & Vincent A. Mabert, 1991. "Cyclical Schedules for Capacitated Lot Sizing with Dynamic Demands," Management Science, INFORMS, vol. 37(4), pages 409-427, April.
    7. Christoph Haehling von Lanzenauer, 1970. "A Production Scheduling Model by Bivalent Linear Programming," Management Science, INFORMS, vol. 17(1), pages 105-111, September.
    8. Uday S. Karmarkar & Sham Kekre & Sunder Kekre, 1987. "The Dynamic Lot-Sizing Problem with Startup and Reservation Costs," Operations Research, INFORMS, vol. 35(3), pages 389-398, June.
    9. Cattrysse, Dirk & Maes, Johan & Van Wassenhove, Luk N., 1990. "Set partitioning and column generation heuristics for capacitated dynamic lotsizing," European Journal of Operational Research, Elsevier, vol. 46(1), pages 38-47, May.
    10. 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.
    11. Panayotis Afentakis & Bezalel Gavish, 1986. "Optimal Lot-Sizing Algorithms for Complex Product Structures," Operations Research, INFORMS, vol. 34(2), pages 237-249, April.
    12. Salah E. Elmaghraby, 1978. "The Economic Lot Scheduling Problem (ELSP): Review and Extensions," Management Science, INFORMS, vol. 24(6), pages 587-598, February.
    13. André Gascon & Robert C. Leachman, 1988. "A Dynamic Programming Solution to the Dynamic, Multi-Item, Single-Machine Scheduling Problem," Operations Research, INFORMS, vol. 36(1), pages 50-56, February.
    14. 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.
    15. Uday S. Karmarkar & Linus Schrage, 1985. "The Deterministic Dynamic Product Cycling Problem," Operations Research, INFORMS, vol. 33(2), pages 326-345, April.
    16. 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.
    17. Earle Steinberg & H. Albert Napier, 1980. "Optimal Multi-Level Lot Sizing for Requirements Planning Systems," Management Science, INFORMS, vol. 26(12), pages 1258-1271, December.
    18. Harish C. Bahl & Larry P. Ritzman & Jatinder N. D. Gupta, 1987. "OR Practice—Determining Lot Sizes and Resource Requirements: A Review," Operations Research, INFORMS, vol. 35(3), pages 329-345, June.
    19. Laurence A. Wolsey, 1989. "Uncapacitated Lot-Sizing Problems with Start-Up Costs," Operations Research, INFORMS, vol. 37(5), pages 741-747, October.
    20. Albert Wagelmans & Stan van Hoesel & Antoon Kolen, 1992. "Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case," Operations Research, INFORMS, vol. 40(1-supplem), pages 145-156, February.
    21. 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.
    22. 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.
    23. T. L. Magnanti & R. Vachani, 1990. "A Strong Cutting Plane Algorithm for Production Scheduling with Changeover Costs," Operations Research, INFORMS, vol. 38(3), pages 456-473, June.
    24. L. S. Lasdon & R. C. Terjung, 1971. "An Efficient Algorithm for Multi-Item Scheduling," Operations Research, INFORMS, vol. 19(4), pages 946-969, August.
    25. Roll, Yaakov & Karni, Reuven, 1991. "Multi-item, multi-level lot sizing with an aggregate capacity constraint," European Journal of Operational Research, Elsevier, vol. 51(1), pages 73-87, March.
    26. Wen-Lian Hsu, 1983. "On the General Feasibility Test of Scheduling Lot Sizes for Several Products on One Machine," Management Science, INFORMS, vol. 29(1), pages 93-105, January.
    27. 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.
    28. HSU, Wen-Lian, 1983. "On the general feasibility test of scheduling lot sizes for several products on one machine," LIDAM Reprints CORE 515, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    29. Tony J. Van Roy & Laurence A. Wolsey, 1987. "Solving Mixed Integer Programming Problems Using Automatic Reformulation," Operations Research, INFORMS, vol. 35(1), pages 45-57, February.
    30. 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.
    31. Lozano, Sebastian & Larraneta, Juan & Onieva, Luis, 1991. "Primal-dual approach to the single level capacitated lot-sizing problem," European Journal of Operational Research, Elsevier, vol. 51(3), pages 354-366, April.
    32. Fleischmann, Bernhard, 1990. "The discrete lot-sizing and scheduling problem," European Journal of Operational Research, Elsevier, vol. 44(3), pages 337-348, February.
    33. Awi Federgruen & Michal Tzur, 1991. "A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time," Management Science, INFORMS, vol. 37(8), pages 909-925, August.
    34. Andreas Drexl, 1991. "Scheduling of Project Networks by Job Assignment," Management Science, INFORMS, vol. 37(12), pages 1590-1602, December.
    35. Sang-Bum Lee & Paul H. Zipkin, 1989. "A Dynamic Lot-Size Model with Make-or-Buy Decisions," Management Science, INFORMS, vol. 35(4), pages 447-458, April.
    36. Gabriel R. Bitran & Hirofumi Matsuo, 1986. "The Multi-Item Capacitated Lot Size Problem: Error Bounds of Manne's Formulations," Management Science, INFORMS, vol. 32(3), pages 350-359, March.
    37. M. Florian & J. K. Lenstra & A. H. G. Rinnooy Kan, 1980. "Deterministic Production Planning: Algorithms and Complexity," Management Science, INFORMS, vol. 26(7), pages 669-679, July.
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    Cited by:

    1. Drexl, Andreas & Jordan, Carsten, 1993. "Wissensbasierte Produktionsprozeßplanung bei reihenfolgeabhängigen Rüstkosten und -zeiten," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 321, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. 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.
    3. Drexl, Andreas & Fleischmann, B. & Günther, H.-O. & Stadtler, H. & Tempelmeier, H., 1993. "Konzeptionelle Grundlagen kapazitätsorientierter PPS-Systeme," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 315, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    4. Bruggemann, Wolfgang & Jahnke, Hermann, 2000. "The discrete lot-sizing and scheduling problem: Complexity and modification for batch availability," European Journal of Operational Research, Elsevier, vol. 124(3), pages 511-528, August.
    5. Drexl, Andreas & Haase, Knut, 1993. "Sequential-analysis-based randomized-regret-methods for lotsizing and scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 323, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

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