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An optimal replenishment policy for an EOQ model with partial backlogging

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  • Joaquín Sicilia
  • Luis San-José
  • Juan García-Laguna

Abstract

We study an inventory system where demand on the stockout period is partially backlogged. The backlogged demand ratio is a mixture of two exponential functions. The shortage cost has two significant costs: the unit backorder cost (which includes a fixed cost and a cost proportional to the length of time for which the backorder exists) and the cost of lost sales. A general procedure to determine the optimal policy and the minimum inventory cost for all the parameter values is developed. This model generalizes several inventory systems analyzed by different authors. Numerical examples are used to illustrate the theoretical results. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Joaquín Sicilia & Luis San-José & Juan García-Laguna, 2009. "An optimal replenishment policy for an EOQ model with partial backlogging," Annals of Operations Research, Springer, vol. 169(1), pages 93-115, July.
    • Handle: RePEc:spr:annopr:v:169:y:2009:i:1:p:93-115:10.1007/s10479-008-0393-3
    DOI: 10.1007/s10479-008-0393-3
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    References listed on IDEAS

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    1. San José, L.A. & Sicilia, J. & Garcia-Laguna, J., 2006. "Analysis of an inventory system with exponential partial backordering," International Journal of Production Economics, Elsevier, vol. 100(1), pages 76-86, March.
    2. Abad, P. L., 2003. "Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale," European Journal of Operational Research, Elsevier, vol. 144(3), pages 677-685, February.
    3. Chu, Peter & Yang, Kuo-Lung & Liang, Shing-Ko & Niu, Thomas, 2004. "Note on inventory model with a mixture of back orders and lost sales," European Journal of Operational Research, Elsevier, vol. 159(2), pages 470-475, December.
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    6. Chung, Kun-Jen & Goyal, Suresh Kumar & Huang, Yung-Fu, 2005. "The optimal inventory policies under permissible delay in payments depending on the ordering quantity," International Journal of Production Economics, Elsevier, vol. 95(2), pages 203-213, February.
    7. Dye, Chung-Yuan & Chang, Horng-Jinh & Teng, Jinn-Tsair, 2006. "A deteriorating inventory model with time-varying demand and shortage-dependent partial backlogging," European Journal of Operational Research, Elsevier, vol. 172(2), pages 417-429, July.
    8. M. J. M. Posner & B. Yansouni, 1972. "A class of inventory models with customer impatience," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 19(3), pages 483-492, September.
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    Cited by:

    1. K. Skouri & I. Konstantaras & S. Manna & K. Chaudhuri, 2011. "Inventory models with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages," Annals of Operations Research, Springer, vol. 191(1), pages 73-95, November.
    2. Pentico, David W. & Drake, Matthew J., 2011. "A survey of deterministic models for the EOQ and EPQ with partial backordering," European Journal of Operational Research, Elsevier, vol. 214(2), pages 179-198, October.

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