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Limit distribution of inventory level of perishable inventory model. (English) Zbl 1235.90008
Summary: We study a perishable inventory model, which assumes that each perishable item has finite lifetime, and only one item is consumed each time. The lifetimes of perishable items are independent random variables with the general distribution and so are the consumption internal. Under this assumption, by using backward equations and limit distribution of Markov skeleton processes, this paper obtains the existence conditions and the explicit expression of the limit distribution of the inventory level of perishable inventory model.

90B05 Inventory, storage, reservoirs
Full Text: DOI
[1] T. M. Whitin, Theory of Inventory Management, Princeton University Press, Princeton, NJ, USA, 1957.
[2] P. M. Ghare and G. P. Schrader, “A model for an exponentially decaying inventory,” Journal of Industrial Engineering, vol. 14, no. 5, pp. 238-243, 1963.
[3] F. Raafat, “Survey of literature on continuously deteriorating inventory models,” Journal of the Operational Research Society, vol. 42, no. 1, pp. 27-37, 1991. · Zbl 0718.90025 · doi:10.1057/jors.1991.4
[4] S. K. Goyal and B. C. Giri, “Recent trends in modeling of deteriorating inventory,” European Journal of Operational Research, vol. 134, no. 1, pp. 1-16, 2001. · Zbl 0978.90004 · doi:10.1016/S0377-2217(00)00248-4
[5] R. X. Li, H. J. Lan, and J. R. Mawhinney, “A review on deteriorating inventory study,” Journal Service Science & Management, vol. 3, pp. 117-129, 2010.
[6] B. Karmakar and K. D. Choudhury, “A review on inventory models for deteriorating items with shortages,” Assam University Journal of Science & Technology : Physical Sciences and Technology, vol. 6, pp. 51-59, 2010.
[7] C. L. Williams and B. E. Patuwo, “A perishable inventory model with positive order lead times,” European Journal of Operational Research, vol. 116, no. 2, pp. 352-373, 1999. · Zbl 1009.90003 · doi:10.1016/S0377-2217(98)00105-2
[8] Y. Adachi, T. Nose, and S. Kuriyama, “Optimal inventory control policy subject to different selling prices of perishable commodities,” International Journal of Production Economics, vol. 60, pp. 389-394, 1999. · doi:10.1016/S0925-5273(98)00200-X
[9] P. S. Deng, R. H.-J. Lin, and P. Chu, “A note on the inventory models for deteriorating items with ramp type demand rate,” European Journal of Operational Research, vol. 178, no. 1, pp. 112-120, 2007. · Zbl 1110.90006 · doi:10.1016/j.ejor.2006.01.028
[10] G. P. Samanta and A. Roy, “A production inventory model with deteriorating items and shortages,” Yugoslav Journal of Operations Research, vol. 14, no. 2, pp. 219-230, 2004. · Zbl 1061.90005 · doi:10.2298/YJOR0402219S
[11] S. R. Singh, N. Kumar, and R. Kumari, “Two warehouse inventory model for deteriorating items with shortages under inflation and time value of money,” International Journal of Computational and Applied Mathematics, vol. 4, no. 1, pp. 83-94, 2009.
[12] N. H. Shah and K. T. Shukla, “Deteriorating inventory model for waiting time partial backlogging,” Applied Mathematical Sciences, vol. 3, no. 9-12, pp. 421-428, 2009. · Zbl 1172.90316 · www.m-hikari.com
[13] N. H. Shah and Y. K. Shah, “Literature survey on inventory model for deteriorating items,” Economic Annals, vol. 44, pp. 221-237, 2000.
[14] Y. K. Shah and M. C. Jaiswal, “An order-level inventory model for a system with constant rate of deterioration,” Opsearch, vol. 14, no. 3, pp. 174-184, 1977.
[15] S.-P. Wang, “An inventory replenishment policy for deteriorating items with shortages and partial backlogging,” Computers & Operations Research, vol. 29, no. 14, pp. 2043-2051, 2002. · Zbl 1010.90001 · doi:10.1016/S0305-0548(01)00072-7
[16] N. Ravichandran, “Stochastic analysis of a continuous review perishable inventory system with positive lead time and Poisson demand,” European Journal of Operational Research, vol. 84, no. 2, pp. 444-457, 1995. · Zbl 0927.90007 · doi:10.1016/0377-2217(93)E0254-U
[17] H. N. Chiu, “An approximation to the continuous review inventory model with perishable items and lead times,” European Journal of Operational Research, vol. 87, no. 1, pp. 93-108, 1995. · Zbl 0914.90098 · doi:10.1016/0377-2217(94)00060-P
[18] L. Liu and T. Yang, “An (s, S) random lifetime inventory model with a positive lead time,” European Journal of Operational Research, vol. 113, no. 1, pp. 52-63, 1999. · Zbl 0948.90006 · doi:10.1016/S0377-2217(97)00426-8
[19] B. Sivakumar, “A perishable inventory system with retrial demands and a finite population,” Journal of Computational and Applied Mathematics, vol. 224, no. 1, pp. 29-38, 2009. · Zbl 1152.90002 · doi:10.1016/j.cam.2008.03.041
[20] H. K. Alfares, “Inventory model with stock-level dependent demand rate and variable holding cost,” International Journal of Production Economics, vol. 108, no. 1-2, pp. 259-265, 2007. · doi:10.1016/j.ijpe.2006.12.013
[21] T. Roy and K. S. Chaudhuri, “A production-inventory model under stock-dependent demand, Weibull distribution deterioration and shortage,” International Transactions in Operational Research, vol. 16, no. 3, pp. 325-346, 2009. · Zbl 1171.90320 · doi:10.1111/j.1475-3995.2008.00676.x
[22] K. Kanchanasuntorn and A. Techanitisawad, “An approximate periodic model for fixed-life perishable products in a two-echelon inventory-distribution system,” International Journal of Production Economics, vol. 100, no. 1, pp. 101-115, 2006. · doi:10.1016/j.ijpe.2004.10.010
[23] Z. Hou, Z. Liu, and J. Zou, “QNQL processes: (H,Q)-processes and their applications,” Chinese Science Bulletin, vol. 42, no. 11, pp. 881-886, 1997. · Zbl 0883.60101 · doi:10.1007/BF02882537
[24] Z.-T. Hou, “Markov skeleton processes and applications to queueing systems,” Acta Mathematicae Applicatae Sinica. English Series, vol. 18, no. 4, pp. 537-552, 2002. · Zbl 1023.60079 · doi:10.1007/s102550200056
[25] Z. Hou, C. Yuan, J. Zou et al., “Transient distribution of the length of GI/G/N queueing systems,” Stochastic Analysis and Applications, vol. 21, no. 3, pp. 567-592, 2003. · Zbl 1054.60095 · doi:10.1081/SAP-120020427
[26] Z. T. Hou and G. X. Liu, Markov Skeleton Processes and Their Applications, Science Press and International Press, 2005.
[27] H. L. Dong, Z. T. Hou, and G. C. Jiang, “Limit distribution of Markov skeleton processes,” Acta Mathematicae Applicatae Sinica, vol. 33, no. 2, pp. 290-296, 2010 (Chinese). · Zbl 1224.60223
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