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98%-Effective Lot Sizing for Series Inventory Systems with Backlogging

Author

Listed:
  • Derek Atkins

    (University of British Columbia, Vancouver, British Columbia, Canada)

  • Daning Sun

    (University College of the Cariboo, Kamloops, British Columbia, Canada)

Abstract

For deterministic series inventory systems with backlogging, we show that the continuous relaxation of the best integer frequency policies is a lower bound on all feasible policies. The problem with backlogging can be reduced, in O ( n ) time, to an equivalent problem without backlogging. Therefore, based on the result of R. O. Roundy (Roundy, R. O. 1983. 94%-Effective lot-sizing in multistage assembly systems. Technical Report 674, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York.), the best integer frequency policy provides a solution which is within 2% of the optimal.

Suggested Citation

  • Derek Atkins & Daning Sun, 1995. "98%-Effective Lot Sizing for Series Inventory Systems with Backlogging," Operations Research, INFORMS, vol. 43(2), pages 335-345, April.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:2:p:335-345
    DOI: 10.1287/opre.43.2.335
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    Citations

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    Cited by:

    1. Boissiere, J. & Frein, Y. & Rapine, C., 2008. "Optimal stationary policies in a 3-stage serial production-distribution logistic chain facing constant and continuous demand," European Journal of Operational Research, Elsevier, vol. 186(2), pages 608-619, April.
    2. Daning Sun, 2004. "Existence and Properties of Optimal Production and Inventory Policies," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 923-934, November.
    3. Chung-Piaw Teo & Dimitris Bertsimas, 2001. "Multistage Lot Sizing Problems via Randomized Rounding," Operations Research, INFORMS, vol. 49(4), pages 599-608, August.
    4. Wen-Tsung Ho & Shu-Fang Lai & Yun-Kuei Huang, 2014. "An Optimal Mixed Batch Shipment Policy for Multiple Items in a Single-Supplier Multiple-Retailer Integrated System," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 636-658, February.
    5. Abdul-Jalbar, Beatriz & Gutiérrez, José M. & Sicilia, Joaquín, 2009. "A two-echelon inventory/distribution system with power demand pattern and backorders," International Journal of Production Economics, Elsevier, vol. 122(2), pages 519-524, December.
    6. Julien Bramel & Shobhna Goyal & Paul Zipkin, 2000. "Coordination of Production/Distribution Networks with Unbalanced Leadtimes," Operations Research, INFORMS, vol. 48(4), pages 570-577, August.
    7. 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.
    8. Fangruo Chen, 1999. "94%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand," Management Science, INFORMS, vol. 45(12), pages 1679-1696, December.
    9. Wee, H. M. & Yang, P. C., 2004. "The optimal and heuristic solutions of a distribution network," European Journal of Operational Research, Elsevier, vol. 158(3), pages 626-632, November.
    10. Brian Q. Rieksts & José A. Ventura & Yale T. Herer & Daning Sun, 2007. "Technical note: Worst‐case performance of power‐of‐two policies for serial inventory systems with incremental quantity discounts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 583-587, August.
    11. Daning Sun & Maurice Queyranne, 2002. "Production and Inventory Model Using Net Present Value," Operations Research, INFORMS, vol. 50(3), pages 528-537, June.
    12. Boissière, J. & Frein, Y. & Rapine, C., 2008. "Lot-sizing in a serial distribution system with capacitated in-system production flow," International Journal of Production Economics, Elsevier, vol. 112(1), pages 483-494, March.
    13. Ming Hu & Yi Yang, 2014. "Modified Echelon ( r, Q ) Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory Systems," Operations Research, INFORMS, vol. 62(4), pages 812-828, August.
    14. Fangruo Chen, 2000. "Effectiveness of (R, Q) policies in one‐warehouse multiretailer systems with deterministic demand and backlogging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 422-439, August.
    15. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.

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