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Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate


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  • Skouri, K.
  • Konstantaras, I.
  • Papachristos, S.
  • Ganas, I.
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    In this paper, an inventory model with general ramp type demand rate, time dependent (Weibull) deterioration rate and partial backlogging of unsatisfied demand is considered. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The model is fairly general as the demand rate, up to the time point of its stabilization, is a general function of time. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The optimal replenishment policy for the model is derived for both the above mentioned policies.

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    Bibliographic Info

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

    Volume (Year): 192 (2009)
    Issue (Month): 1 (January)
    Pages: 79-92

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    Handle: RePEc:eee:ejores:v:192:y:2009:i:1:p:79-92

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    Keywords: Inventory Ramp type demand Deteriorating items Partial backlogging;


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    1. Goyal, S.K., 1987. "Economic ordering policy for deteriorating items over an infinite time horizon," European Journal of Operational Research, Elsevier, vol. 28(3), pages 298-301, March.
    2. Deng, Peter Shaohua & Lin, Robert H.-J. & Chu, Peter, 2007. "A note on the inventory models for deteriorating items with ramp type demand rate," European Journal of Operational Research, Elsevier, vol. 178(1), pages 112-120, April.
    3. L. A. San José & J. Sicilia & J. García-Laguna, 2005. "An Inventory System With Partial Backlogging Modeled According To A Linear Function," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 189-209.
    4. P. L. Abad, 1996. "Optimal Pricing and Lot-Sizing Under Conditions of Perishability and Partial Backordering," Management Science, INFORMS, vol. 42(8), pages 1093-1104, August.
    5. Goyal, S. K. & Giri, B. C., 2001. "Recent trends in modeling of deteriorating inventory," European Journal of Operational Research, Elsevier, vol. 134(1), pages 1-16, October.
    6. 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.
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    Cited by:
    1. Sarkar, Biswajit & Sarkar, Sumon, 2013. "Variable deterioration and demand—An inventory model," Economic Modelling, Elsevier, vol. 31(C), pages 548-556.
    2. Wang, Kung-Jeng & Lin, Y.S. & Yu, Jonas C.P., 2011. "Optimizing inventory policy for products with time-sensitive deteriorating rates in a multi-echelon supply chain," International Journal of Production Economics, Elsevier, vol. 130(1), pages 66-76, March.
    3. Fernández, Arturo J. & Pérez-González, Carlos J. & Aslam, Muhammad & Jun, Chi-Hyuck, 2011. "Design of progressively censored group sampling plans for Weibull distributions: An optimization problem," European Journal of Operational Research, Elsevier, vol. 211(3), pages 525-532, June.
    4. Teng, Jinn-Tsair & Min, Jie & Pan, Qinhua, 2012. "Economic order quantity model with trade credit financing for non-decreasing demand," Omega, Elsevier, vol. 40(3), pages 328-335.
    5. 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.
    6. Hung, Kuo-Chen, 2011. "An inventory model with generalized type demand, deterioration and backorder rates," European Journal of Operational Research, Elsevier, vol. 208(3), pages 239-242, February.
    7. Yang, Hui-Ling, 2012. "Two-warehouse partial backlogging inventory models with three-parameter Weibull distribution deterioration under inflation," International Journal of Production Economics, Elsevier, vol. 138(1), pages 107-116.
    8. Lin, Shih-Wei, 2011. "Inventory models with managerial policy independent of demand," European Journal of Operational Research, Elsevier, vol. 211(3), pages 520-524, June.
    9. Bakker, Monique & Riezebos, Jan & Teunter, Ruud H., 2012. "Review of inventory systems with deterioration since 2001," European Journal of Operational Research, Elsevier, vol. 221(2), pages 275-284.


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