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Lot Sizing in Serial Assembly Systems with Multiple Constrained Resources

Author

Listed:
  • Terry P. Harrison

    (Management Science and Information Systems Department, 303 Beam Business Administration Building, Pennsylvania State University, University Park, Pennsylvania 16802)

  • Holly S. Lewis

    (Management Science and Information Systems Department, 303 Beam Business Administration Building, Pennsylvania State University, University Park, Pennsylvania 16802)

Abstract

We present a heuristic for lot sizing in serial assembly systems with multiple contrained resources. This procedure, the Coefficient Modification Heuristic (CMH), exploits a special problem structure by solving repetitively a small linear programming restriction of the original problem. The key idea is to modify the constraint coefficients of certain variables in the LP restriction to implicitly account for the capacity consumed in setups. We compare the performance of the CMH with the commercial code, Optimization System Library (OSL), on three families of test problems. The first set is a collation of small-scale random problems that are solved to optimality to provide known benchmarks. The second is a set of problems based on a real printed circuit board manufacturing situation. The third group is a set of medium-scale randomly generated problems based on the underlying structure of the printed circuit board set. Overall, the CMH found solutions that averaged 18% better than time constrained OSL runs in a small fraction of the corresponding CPU times.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:1:p:19-36
    DOI: 10.1287/mnsc.42.1.19
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    Citations

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    Cited by:

    1. Elena Katok & Dennis Ott, 2000. "Using Mixed-Integer Programming to Reduce Label Changes in the Coors Aluminum Can Plant," Interfaces, INFORMS, vol. 30(2), pages 1-12, April.
    2. 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.
    3. Sarker, Bhaba R. & Diponegoro, Ahmad, 2009. "Optimal production plans and shipment schedules in a supply-chain system with multiple suppliers and multiple buyers," European Journal of Operational Research, Elsevier, vol. 194(3), pages 753-773, May.
    4. Berretta, Regina & Rodrigues, Luiz Fernando, 2004. "A memetic algorithm for a multistage capacitated lot-sizing problem," International Journal of Production Economics, Elsevier, vol. 87(1), pages 67-81, January.
    5. Hadjinicola, George C. & Soteriou, Andreas C., 2003. "Reducing the cost of defects in multistage production systems: A budget allocation perspective," European Journal of Operational Research, Elsevier, vol. 145(3), pages 621-634, March.
    6. Pesenti, Raffaele & Ukovich, Walter, 2003. "Economic lot scheduling on multiple production lines with resource constraints," International Journal of Production Economics, Elsevier, vol. 81(1), pages 469-481, January.
    7. VAN VYVE, Mathieu & POCHET, Yves, 2001. "A general heuristic or production planning problems," LIDAM Discussion Papers CORE 2001056, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Lee, S. D. & Rung, J. M., 2000. "Production lot sizing in failure prone two-stage serial systems," European Journal of Operational Research, Elsevier, vol. 123(1), pages 42-60, May.
    9. Simpson, N. C., 1999. "Multiple level production planning in rolling horizon assembly environments," European Journal of Operational Research, Elsevier, vol. 114(1), pages 15-28, April.
    10. 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.
    11. Helber, Stefan & Sahling, Florian, 2010. "A fix-and-optimize approach for the multi-level capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 123(2), pages 247-256, February.
    12. Yves Pochet & Mathieu Van Vyve, 2004. "A General Heuristic for Production Planning Problems," INFORMS Journal on Computing, INFORMS, vol. 16(3), pages 316-327, August.
    13. Süral, Haldun & Denizel, Meltem & Van Wassenhove, Luk N., 2009. "Lagrangean relaxation based heuristics for lot sizing with setup times," European Journal of Operational Research, Elsevier, vol. 194(1), pages 51-63, April.
    14. Jans, Raf & Degraeve, Zeger, 2007. "Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1855-1875, March.

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