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The capacitated lot sizing problem: a review of models and algorithms

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Listed:
  • Karimi, B.
  • Fatemi Ghomi, S. M. T.
  • Wilson, J. M.

Abstract

Lot sizing is one of the most important and also one of the most difficult problems in production planning. This subject has been studied extensively in the literature. In this article, we consider single-level lot sizing problems, their variants and solution approaches. After introducing factors affecting formulation and the complexity of production planning problems, and introducing different variants of lot sizing and scheduling problems, we discuss single-level lot sizing problems, together with exact and heuristic approaches for their solution. We conclude with some suggestions for future research.

Suggested Citation

  • Karimi, B. & Fatemi Ghomi, S. M. T. & Wilson, J. M., 2003. "The capacitated lot sizing problem: a review of models and algorithms," Omega, Elsevier, vol. 31(5), pages 365-378, October.
  • Handle: RePEc:eee:jomega:v:31:y:2003:i:5:p:365-378
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    1. Wee, Hui-Ming, 1999. "Deteriorating inventory model with quantity discount, pricing and partial backordering," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 511-518, March.
    2. 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.
    3. Meyr, H., 2000. "Simultaneous Lotsizing and Scheduling by combining Local Search with Dual Reoptimization," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 39380, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    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. Selen, W. J. & Heuts, R. M., 1989. "A modified priority index for Gunther's lot-sizing heuristic under capacitated single stage production," European Journal of Operational Research, Elsevier, vol. 41(2), pages 181-185, July.
    6. Ganas, Ioannis S. & Papachristos, Sotirios, 1997. "Analytical evaluation of heuristics performance for the single-level lot-sizing problem for products with constant demand," International Journal of Production Economics, Elsevier, vol. 48(2), pages 129-139, January.
    7. Millar, Harvey H. & Yang, Minzhu, 1994. "Lagrangian heuristics for the capacitated multi-item lot-sizing problem with backordering," International Journal of Production Economics, Elsevier, vol. 34(1), pages 1-15, February.
    8. 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.
    9. 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.
    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. Gabriel R. Bitran & Horacio H. Yanasse, 1982. "Computational Complexity of the Capacitated Lot Size Problem," Management Science, INFORMS, vol. 28(10), pages 1174-1186, October.
    12. Armentano, Vinícius A. & França, Paulo M. & de Toledo, Franklina M. B., 1999. "A network flow model for the capacitated lot-sizing problem," Omega, Elsevier, vol. 27(2), pages 275-284, April.
    13. 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).
    14. Gaetan Belvaux & Laurence A. Wolsey, 2001. "Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs," Management Science, INFORMS, vol. 47(7), pages 993-1007, July.
    15. Chand, Suresh, 1982. "Lot sizing for products with finite demand horizon and periodic review inventory policy," European Journal of Operational Research, Elsevier, vol. 11(2), pages 145-148, October.
    16. Wolsey, L. A., 1995. "Progress with single-item lot-sizing," LIDAM Reprints CORE 1174, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Wolsey, Laurence A., 1995. "Progress with single-item lot-sizing," European Journal of Operational Research, Elsevier, vol. 86(3), pages 395-401, November.
    18. Alan S. Manne, 1957. "Programming of Economic Lot Sizes," Cowles Foundation Discussion Papers 23, Cowles Foundation for Research in Economics, Yale University.
    19. BARANY, Imre & VAN ROY, Tony J. & WOLSEY, Laurence A., 1984. "Strong formulations for multi-item capacitated lot sizing," LIDAM Reprints CORE 590, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Fleischmann, B. & Meyr, H., 1997. "The General Lotsizing and Scheduling Problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 36068, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    21. E. F. Peter Newson, 1975. "Multi-Item Lot Size Scheduling by Heuristic Part I: With Fixed Resources," Management Science, INFORMS, vol. 21(10), pages 1186-1193, June.
    22. Chung, Chia-Shin & Flynn, James & Lin, Chien-Hua Mike, 1994. "An effective algorithm for the capacitated single item lot size problem," European Journal of Operational Research, Elsevier, vol. 75(2), pages 427-440, June.
    23. Gelders, Ludo F. & Van Wassenhove, Luk N., 1981. "Production planning: a review," European Journal of Operational Research, Elsevier, vol. 7(2), pages 101-110, June.
    24. 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.
    25. Drexl, Andreas & Haase, Knut, 1995. "Proportional lotsizing and scheduling," International Journal of Production Economics, Elsevier, vol. 40(1), pages 73-87, June.
    26. C. P. M. van Hoesel & A. P. M. Wagelmans, 2001. "Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 339-357, May.
    27. Dong X. Shaw & Albert P. M. Wagelmans, 1998. "An Algorithm for Single-Item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs," Management Science, INFORMS, vol. 44(6), pages 831-838, June.
    28. 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.
    29. 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).
    30. 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.
    31. BELVAUX, Gaetan & WOLSEY, Laurence A., 2001. "Modelling practical lot-sizing problems as mixed-integer programs," LIDAM Reprints CORE 1516, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    32. 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.
    33. Hartmut Stadtler, 2000. "Improved Rolling Schedules for the Dynamic Single-Level Lot-Sizing Problem," Management Science, INFORMS, vol. 46(2), pages 318-326, February.
    34. 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.
    35. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    36. Imre Barany & Tony J. Van Roy & Laurence A. Wolsey, 1984. "Strong Formulations for Multi-Item Capacitated Lot Sizing," Management Science, INFORMS, vol. 30(10), pages 1255-1261, October.
    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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