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A Dual Ascent Procedure for Multiproduct Dynamic Demand Coordinated Replenishment with Backlogging

Author

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  • E. Powell Robinson, Jr.

    (Department of Business Analysis, College of Business Administration, Texas A&M University, College Station, Texas 77812)

  • Li-Lian Gao

    (Department of Management, School of Business, Hofstra University, Hempstead, New York 11550)

Abstract

This paper describes a mixed-integer programming formulation and dual ascent based branch-and-bound algorithm for the multiproduct dynamic demand coordinated replenishment problem with backlogging. The single sourcing properties of the formulation and the hierarchical structure of the fixed-charge and continuous variables yield an extremely tight linear programming relaxation for the problem. A branch-and-bound algorithm based on Erlenkotter's dual ascent, dual adjustment, and primal construction concepts exploits these properties to obtain an efficient solution procedure. Computational results indicate that the new procedures find optimal solutions in less than five percent of the computational time of the most efficient previous algorithm. The heuristic performance of the procedures also demonstrate their superiority over existing approaches. We solved problems with 12 time periods and 20 products in 0.41 CPU seconds, and heuristic solutions with a worst-case three-percent optimality gap are found in 0.068 CPU seconds. The efficiency and large-scale capability of the procedures make their potential application in inventory requirements planning systems promising.

Suggested Citation

  • E. Powell Robinson, Jr. & Li-Lian Gao, 1996. "A Dual Ascent Procedure for Multiproduct Dynamic Demand Coordinated Replenishment with Backlogging," Management Science, INFORMS, vol. 42(11), pages 1556-1564, November.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:11:p:1556-1564
    DOI: 10.1287/mnsc.42.11.1556
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    Citations

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    Cited by:

    1. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Dong Liang & Wilbert E. Wilhelm, 2013. "Dual‐ascent and primal heuristics for production‐assembly‐distribution system design," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 1-18, February.
    3. E P Robinson & A Narayanan & L-L Gao, 2007. "Effective heuristics for the dynamic demand joint replenishment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 808-815, June.
    4. Robinson, Powell & Narayanan, Arunachalam & Sahin, Funda, 2009. "Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms," Omega, Elsevier, vol. 37(1), pages 3-15, February.
    5. Chia‐Shin Chung & Sin‐Hoon Hum & Omer Kirca, 2000. "An optimal procedure for the coordinated replenishment dynamic lot‐sizing problem with quantity discounts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 686-695, December.
    6. Narayanan, Arunachalam & Robinson, Powell, 2010. "Efficient and effective heuristics for the coordinated capacitated lot-size problem," European Journal of Operational Research, Elsevier, vol. 203(3), pages 583-592, June.
    7. Oğuz Solyalı & Haldun Süral, 2012. "The one-warehouse multi-retailer problem: reformulation, classification, and computational results," Annals of Operations Research, Springer, vol. 196(1), pages 517-541, July.
    8. Ertogral, Kadir, 2008. "Multi-item single source ordering problem with transportation cost: A Lagrangian decomposition approach," European Journal of Operational Research, Elsevier, vol. 191(1), pages 156-165, November.
    9. Narayanan, Arunachalam & Robinson, Powell, 2010. "Evaluation of joint replenishment lot-sizing procedures in rolling horizon planning systems," International Journal of Production Economics, Elsevier, vol. 127(1), pages 85-94, September.
    10. Kremer, Mirko & Schneeweiss, Christoph & Zimmermann, Michael, 2006. "On the validity of aggregate models in designing supply chain contracts," International Journal of Production Economics, Elsevier, vol. 103(2), pages 656-666, October.

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