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Optimal policy for an inventory system with backlogging and all-units discounts: Application to the composite lot size model

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  • San-José, Luis A.
  • García-Laguna, Juan
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    Abstract

    This paper examines an inventory model with full backlogging and all-units quantity discounts. The practical scenario of a salesperson offering compensation to a client so as not to lose the sale is considered. The cost of a backorder thus includes both a fixed cost and a further cost which is proportional to the length of time the said backorder exists. A first algorithm is developed to determine the optimal policy while some extensions to this algorithm are obtained that include additional conditions on the model. In particular, the well known composite lot size model, developed by Tersine, is solved, incorporating a new stockout cost and a new all-units discount. Numerical examples are provided to illustrate the application of the algorithms.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 192 (2009)
    Issue (Month): 3 (February)
    Pages: 808-823

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    Handle: RePEc:eee:ejores:v:192:y:2009:i:3:p:808-823

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Logistics Inventory model Backlogging Price discounts Freight rates Inspection discounts;

    References

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    1. Rubin, Paul A. & Benton, W. C., 2003. "Evaluating jointly constrained order quantity complexities for incremental discounts," European Journal of Operational Research, Elsevier, vol. 149(3), pages 557-570, September.
    2. Matsuyama, Keisuke, 2001. "The EOQ-Models modified by introducing discount of purchase price or increase of setup cost," International Journal of Production Economics, Elsevier, vol. 73(1), pages 83-99, August.
    3. Aucamp, Donald C., 1982. "Nonlinear freight costs in the EOQ problem," European Journal of Operational Research, Elsevier, vol. 9(1), pages 61-63, January.
    4. Wee, Hui-Ming, 1999. "Deteriorating inventory model with quantity discount, pricing and partial backordering," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 511-518, March.
    5. Fazel, Farzaneh & Fischer, Klaus P. & Gilbert, Erika W., 1998. "JIT purchasing vs. EOQ with a price discount: An analytical comparison of inventory costs," International Journal of Production Economics, Elsevier, vol. 54(1), pages 101-109, January.
    6. Swenseth, Scott R. & Godfrey, Michael R., 2002. "Incorporating transportation costs into inventory replenishment decisions," International Journal of Production Economics, Elsevier, vol. 77(2), pages 113-130, May.
    7. Benton, W. C. & Park, Seungwook, 1996. "A classification of literature on determining the lot size under quantity discounts," European Journal of Operational Research, Elsevier, vol. 92(2), pages 219-238, July.
    8. Ertogral, K. & Darwish, M. & Ben-Daya, M., 2007. "Production and shipment lot sizing in a vendor-buyer supply chain with transportation cost," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1592-1606, February.
    9. W. J. Baumol & H. D. Vinod, 1970. "An Inventory Theoretic Model of Freight Transport Demand," Management Science, INFORMS, vol. 16(7), pages 413-421, March.
    10. Burwell, Timothy H. & Dave, Dinesh S. & Fitzpatrick, Kathy E. & Roy, Melvin R., 1997. "Economic lot size model for price-dependent demand under quantity and freight discounts," International Journal of Production Economics, Elsevier, vol. 48(2), pages 141-155, January.
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