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Lot Sizing in General Assembly Systems with Setup Costs, Setup Times, and Multiple Constrained Resources

  • Elena Katok

    (Division of Economics and Business, Colorado School of Mines, Golden, Colorado 80401)

  • Holly S. Lewis

    (Department of Management Science and Information Systems, The Pennsylvania State University, University Park, Pennsylvania 16802)

  • Terry P. Harrison

    (Department of Management Science and Information Systems, The Pennsylvania State University, University Park, Pennsylvania 16802)

We introduce a heuristic method for finding good, feasible solutions for multiproduct lot sizing problems with general assembly structures, multiple constrained resources, and nonzero setup costs and setup times. We evaluate the performance of this heuristic by comparing its solutions to optimal solutions of small randomly generated problems and to time-truncated Optimization Subroutine Library (OSL) solutions of medium-sized randomly generated problems. In the first case, the heuristic locates solutions averaging 4 percent worse than optimal in less than 1 percent of time required by OSL. The heuristic solutions to medium-sized problems are approximately 26 percent better than solutions OSL finds after 10,000 CPU seconds, and the heuristic finds these solutions in approximately 10 percent of OSL time.

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File URL: http://dx.doi.org/10.1287/mnsc.44.6.859
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Article provided by INFORMS in its journal Management Science.

Volume (Year): 44 (1998)
Issue (Month): 6 (June)
Pages: 859-877

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Handle: RePEc:inm:ormnsc:v:44:y:1998:i:6:p:859-877
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  1. 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.
  2. Joseph D. Blackburn & Robert A. Millen, 1982. "Improved Heuristics for Multi-Stage Requirements Planning Systems," Management Science, INFORMS, vol. 28(1), pages 44-56, January.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Kuik, Roelof & Salomon, Marc & van Wassenhove, Luk N., 1994. "Batching decisions: structure and models," European Journal of Operational Research, Elsevier, vol. 75(2), pages 243-263, June.
  12. 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.
  13. 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.
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