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Lot Sizing and Sequencing for N Products on One Facility

Author

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  • Christian M. Delporte

    (Université de Louvain, Belgium)

  • L. Joseph Thomas

    (Cornell University)

Abstract

The problem of determining both lot sizes and repeating sequences for N products on one facility is difficult due to the combinatorial and continuous nature of the problem. The work that has been done on the problem has made various assumptions ("zero-switch rule" or "equal lot size," for example) to simplify the problem. Several heuristics have been suggested that come fairly close to a computable lower bound on cost. This paper discusses a mathematical programming formulation of the entire problem, along with reasons for its (current) nonpracticality. Heuristics for reducing the problem to a manageable mathematical programming formulation are presented. Specifically, a formulation is given when the sequence is known with both (potentially unequal) lot sizes and idle time periods as variables. The formulation is a convex quadratic program. Heuristics for finding sequences (to feed to the quadratic program) are explored, and examples from previous literature demonstrate that the methods here give consistent results as good as and sometimes significantly better than previous methods. Finally, we discuss situations in which such methods might be important and situations in which easier methods should suffice.

Suggested Citation

  • Christian M. Delporte & L. Joseph Thomas, 1977. "Lot Sizing and Sequencing for N Products on One Facility," Management Science, INFORMS, vol. 23(10), pages 1070-1079, June.
  • Handle: RePEc:inm:ormnsc:v:23:y:1977:i:10:p:1070-1079
    DOI: 10.1287/mnsc.23.10.1070
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    Citations

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    Cited by:

    1. Oner, Selma & Bilgic, Taner, 2008. "Economic lot scheduling with uncontrolled co-production," European Journal of Operational Research, Elsevier, vol. 188(3), pages 793-810, August.
    2. P. C. Geng & R. G. Vickson, 1988. "Two heuristics for the economic lot scheduling problem: An experimental study," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(4), pages 605-617, August.
    3. Banerjee, Avijit, 2009. "Simultaneous determination of multiproduct batch and full truckload shipment schedules," International Journal of Production Economics, Elsevier, vol. 118(1), pages 111-117, March.
    4. Heuts, R.M.J. & Nederstigt, P. & Roebroek, W. & Selen, W.J., 1992. "Multi-product cycling with packaging in the process industry," Other publications TiSEM 533d6bbb-e61a-4e4b-a44e-1, Tilburg University, School of Economics and Management.
    5. Vidal-Carreras, Pilar I. & Garcia-Sabater, Jose P. & Coronado-Hernandez, Jairo R., 2012. "Economic lot scheduling with deliberated and controlled coproduction," European Journal of Operational Research, Elsevier, vol. 219(2), pages 396-404.
    6. Carstensen, Peter, 1997. "Das Economic Lot Scheduling Problem: Überblick und LP-basiertes Verfahren," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 465, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    7. Goncalves, JoseF. & Leachman, Robert C., 1998. "A hybrid heuristic and linear programming approach to multi-product machine scheduling," European Journal of Operational Research, Elsevier, vol. 110(3), pages 548-563, November.
    8. Sağlam, Ümit & Banerjee, Avijit, 2018. "Integrated multiproduct batch production and truck shipment scheduling under different shipping policies," Omega, Elsevier, vol. 74(C), pages 70-81.
    9. Micha Kahlen & Karsten Schroer & Wolfgang Ketter & Alok Gupta, 2024. "Smart Markets for Real-Time Allocation of Multiproduct Resources: The Case of Shared Electric Vehicles," Information Systems Research, INFORMS, vol. 35(2), pages 871-889, June.
    10. Khouja, Moutaz, 1997. "The scheduling of economic lot sizes on volume flexible production systems," International Journal of Production Economics, Elsevier, vol. 48(1), pages 73-86, January.
    11. Wagner, Bret J. & Davis, Darwin J., 2002. "A search heuristic for the sequence-dependent economic lot scheduling problem," European Journal of Operational Research, Elsevier, vol. 141(1), pages 133-146, August.
    12. Seki, Yoichi & Kogure, Keiji, 1996. "Lot scheduling problem for continuous demand," International Journal of Production Economics, Elsevier, vol. 44(1-2), pages 7-15, June.
    13. Heuts, R.M.J. & Nederstigt, P. & Roebroek, W. & Selen, W.J., 1992. "Multi-product cycling with packaging in the process industry," Research Memorandum FEW 544, Tilburg University, School of Economics and Management.
    14. Khouja, Moutaz & Michalewicz, Zgibniew & Wilmot, Michael, 1998. "The use of genetic algorithms to solve the economic lot size scheduling problem," European Journal of Operational Research, Elsevier, vol. 110(3), pages 509-524, November.
    15. Guillermo Gallego & Robin Roundy, 1992. "The economic lot scheduling problem with finite backorder costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 729-739, August.
    16. Rappold, James A. & Yoho, Keenan D., 2014. "Setting safety stocks for stable rotation cycle schedules," International Journal of Production Economics, Elsevier, vol. 156(C), pages 146-158.

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