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Dynamic Lot Sizing for Multi-Echelon Distribution Systems with Purchasing and Transportation Price Discounts

Author

Listed:
  • Moustapha Diaby

    (Arizona State University, Tempe, Arizona)

  • Alain Martel

    (Laval University, Quebec, Canada)

Abstract

We consider the problem of determining optimal purchasing and shipping quantities over a finite planning horizon for arborescent, multi-echelon physical distribution systems with deterministic, time-varying demands. We assume that the inventory holding cost at a given warehouse of the distribution network is a linear function of the inventory level, and that the total procurement cost (i.e., ordering, plus purchasing, plus transportation and reception costs) is a general piecewise-linear function of the quantities shipped to and from the warehouse. We formulate a mixed integer linear programming model of the problem and develop a Lagrangian relaxation-based procedure to solve it. We show computational results for problems with 12 periods, up to 15 warehouses, and 3 transportation price ranges.

Suggested Citation

  • Moustapha Diaby & Alain Martel, 1993. "Dynamic Lot Sizing for Multi-Echelon Distribution Systems with Purchasing and Transportation Price Discounts," Operations Research, INFORMS, vol. 41(1), pages 48-59, February.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:1:p:48-59
    DOI: 10.1287/opre.41.1.48
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    Citations

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    Cited by:

    1. Engebrethsen, Erna & Dauzère-Pérès, Stéphane, 2019. "Transportation mode selection in inventory models: A literature review," European Journal of Operational Research, Elsevier, vol. 279(1), pages 1-25.
    2. Akbalik, A. & Pochet, Y., 2009. "Valid inequalities for the single-item capacitated lot sizing problem with step-wise costs," European Journal of Operational Research, Elsevier, vol. 198(2), pages 412-434, October.
    3. Karla E. Bourland & Candace Arai Yano, 1996. "Lot sizing when yields increase during the production run," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(8), pages 1035-1047, December.
    4. Hark-Chin Hwang, 2009. "Inventory Replenishment and Inbound Shipment Scheduling Under a Minimum Replenishment Policy," Transportation Science, INFORMS, vol. 43(2), pages 244-264, May.
    5. 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.
    6. Yue Jin & Ana Muriel, 2009. "Single‐warehouse multi‐retailer inventory systems with full truckload shipments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(5), pages 450-464, August.
    7. Hill, James & Galbreth, Michael, 2008. "A heuristic for single-warehouse multiretailer supply chains with all-unit transportation cost discounts," European Journal of Operational Research, Elsevier, vol. 187(2), pages 473-482, June.
    8. Hadi Farhangi, 2021. "Multi-Echelon Supply Chains with Lead Times and Uncertain Demands," SN Operations Research Forum, Springer, vol. 2(3), pages 1-25, September.
    9. Sıla Çetinkaya & Halit Üster & Gopalakrishnan Easwaran & Burcu Baris Keskin, 2009. "An Integrated Outbound Logistics Model for Frito-Lay: Coordinating Aggregate-Level Production and Distribution Decisions," Interfaces, INFORMS, vol. 39(5), pages 460-475, October.
    10. Akbalik, Ayse & Penz, Bernard, 2009. "Exact methods for single-item capacitated lot sizing problem with alternative machines and piece-wise linear production costs," International Journal of Production Economics, Elsevier, vol. 119(2), pages 367-379, June.
    11. Aghezzaf, El-Houssaine, 2007. "Production planning and warehouse management in supply networks with inter-facility mold transfers," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1122-1139, November.
    12. Ugarte, Armando & Oren, Shmuel, 2000. "Coordination of internal supply chains in vertically integrated high-tech manufacturing organizations (HTMOs)," International Journal of Production Economics, Elsevier, vol. 67(3), pages 235-252, October.
    13. 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.
    14. Rizk, Nafee & Martel, Alain & Ramudhin, Amar, 2006. "A Lagrangean relaxation algorithm for multi-item lot-sizing problems with joint piecewise linear resource costs," International Journal of Production Economics, Elsevier, vol. 102(2), pages 344-357, August.
    15. Ruiz-Benítez, Rocío & Ketzenberg, Michael & van der Laan, Erwin A., 2014. "Managing consumer returns in high clockspeed industries," Omega, Elsevier, vol. 43(C), pages 54-63.
    16. Lai, Minghui & Cai, Xiaoqiang & Li, Xiang, 2017. "Mechanism design for collaborative production-distribution planning with shipment consolidation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 137-159.
    17. Chung-Lun Li & Vernon Ning Hsu & Wen-Qiang Xiao, 2004. "Dynamic Lot Sizing with Batch Ordering and Truckload Discounts," Operations Research, INFORMS, vol. 52(4), pages 639-654, August.
    18. N Rizk & A Martel & S D'Amours, 2008. "Synchronized production–distribution planning in a single-plant multi-destination network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 90-104, January.

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