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Lot Sizing Policies for Finite Production Rate Assembly Systems

Author

Listed:
  • Derek Atkins

    (University of British Columbia, Vancouver, Canada)

  • Maurice Queyranne

    (University of British Columbia, Vancouver, Canada)

  • Daning Sun

    (The Cariboo University College, Kamloops, B.C., Canada)

Abstract

An assembly production system with n facilities has a constant external demand occurring at the end facility. Production rates at each facility are finite and nonincreasing along any path in the assembly network. Associated with each facility are a setup cost and positive echelon holding cost rate. The formulation of the lot sizing problem is developed in terms of integer-ratio lot size policies. This formulation provides a unification of the integer-split policies formulation of L. B. Schwarz and L. Schrage and the integer-multiple policies formulation of J. P. Moily, allowing either assumption to be operative at any point in the system. A relaxed solution to this unified formulation provides a lower bound to the cost of any feasible policy. The derivation of this Lower Bound Theorem is novel and relies on the notion of path holding costs, which is a generalization of echelon holding costs. An optimal power-of-two lot size policy is found by an O ( n 5 ) algorithm and its cost is within 2% of the optimum in the worst case.

Suggested Citation

  • Derek Atkins & Maurice Queyranne & Daning Sun, 1992. "Lot Sizing Policies for Finite Production Rate Assembly Systems," Operations Research, INFORMS, vol. 40(1), pages 126-141, February.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:1:p:126-141
    DOI: 10.1287/opre.40.1.126
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    Citations

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    Cited by:

    1. Chung-Piaw Teo & Dimitris Bertsimas, 2001. "Multistage Lot Sizing Problems via Randomized Rounding," Operations Research, INFORMS, vol. 49(4), pages 599-608, August.
    2. Lee, Shine-Der & Fu, Yen-Chen, 2014. "Joint production and delivery lot sizing for a make-to-order producer–buyer supply chain with transportation cost," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 66(C), pages 23-35.
    3. Kimms, Alf & Drexl, Andreas, 1996. "Multi-level lot sizing: A literature survey," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 405, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    4. Pundoor, Guruprasad & Chen, Zhi-Long, 2009. "Joint cyclic production and delivery scheduling in a two-stage supply chain," International Journal of Production Economics, Elsevier, vol. 119(1), pages 55-74, May.
    5. 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.
    6. Daning Sun & Maurice Queyranne, 2002. "Production and Inventory Model Using Net Present Value," Operations Research, INFORMS, vol. 50(3), pages 528-537, June.
    7. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.
    8. Ian R. Webb & Bruce R. Buzby & Gerard M. Campbell, 1997. "Cyclical schedules for the joint replenishment problem with dynamic demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(6), pages 577-589, September.

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