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**Order level inventory models for deteriorating seasonable/Fashionable products with time dependent demand and shortages.**
*(English)*
Zbl 1179.90022

Summary: An order level inventory model for seasonable/fashionable products subject to a period of increasing demand followed by a period of level demand and then by a period of decreasing demand rate (three branches ramp type demand rate) is considered. The unsatisfied demand is partially backlogged with a time dependent backlogging rate. In addition, the product deteriorates with a time dependent, namely, Weibull, deterioration rate. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The optimal replenishment policy for the model is derived for both the above mentioned policies.

### MSC:

90B05 | Inventory, storage, reservoirs |

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\textit{K. Skouri} and \textit{I. Konstantaras}, Math. Probl. Eng. 2009, Article ID 679736, 24 p. (2009; Zbl 1179.90022)

### References:

[1] | M. Resh, M. Friedman, and L. C. Barbosa, “On a general solution of the deterministic lot size problem with time-proportional demand,” Operations Research, vol. 24, no. 4, pp. 718-725, 1976. · Zbl 0363.90044 |

[2] | W. A. Donaldson, “Inventory replenishment policy for a linear trend in demand: an analytic solution,” Operational Research Quarterly, vol. 28, pp. 663-670, 1977. · Zbl 0372.90052 |

[3] | U. Dave and L. K. Patel, “(T,Si) policy inventory model for deteriorating items with time proportional demand,” Journal of the Operational Research Society, vol. 32, no. 2, pp. 137-142, 1981. · Zbl 0447.90020 |

[4] | S. K. Goyal, “On improving replenishment policies for linear trend in demand,” Engineering Costs and Production Economics, vol. 10, no. 1, pp. 73-76, 1986. |

[5] | M. Hariga, “An EOQ model for deteriorating items with shortages and time varying demand,” Journal of the Operational Research Society, vol. 46, pp. 398-404, 1995. · Zbl 0836.90068 |

[6] | M. A. Hariga and L. Benkherouf, “Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand,” European Journal of Operational Research, vol. 79, no. 1, pp. 123-137, 1994. · Zbl 0812.90039 |

[7] | H.-L. Yang, J.-T. Teng, and M.-S. Chern, “Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand,” Naval Research Logistics, vol. 48, no. 2, pp. 144-158, 2001. · Zbl 0981.90003 |

[8] | R. M. Hill, “Inventory models for increasing demand followed by level demand,” Journal of the Operational Research Society, vol. 46, no. 10, pp. 1250-1259, 1995. · Zbl 0843.90039 |

[9] | B. Mandal and A. K. Pal, “Order level inventory system with ramp type demand rate for deteriorating items,” Journal of Interdisciplinary Mathematics, vol. 1, no. 1, pp. 49-66, 1998. · Zbl 0911.90142 |

[10] | J.-W. Wu, C. Lin, B. Tan, and W.-C. Lee, “An EOQ inventory model with ramp type demand rate for items with Weibull deterioration,” International Journal of Information and Management Sciences, vol. 10, no. 3, pp. 41-51, 1999. · Zbl 0963.90009 |

[11] | K.-S. Wu and L.-Y. Ouyang, “A replenishment policy for deteriorating items with ramp type demand rate,” Proceedings of the National Science Council, Republic of China A, vol. 24, no. 4, pp. 279-286, 2000. |

[12] | K.-S. Wu, “An EOQ inventory model for items with Weibull distribution deterioration, ramp type demand rate and partial backlogging,” Production Planning and Control, vol. 12, no. 8, pp. 787-793, 2001. |

[13] | B. C. Giri, A. K. Jalan, and K. S. Chaudhuri, “Economic order quantity model with Weibull deterioration distribution, shortage and ramp-type demand,” International Journal of Systems Science, vol. 34, no. 4, pp. 237-243, 2003. · Zbl 1074.90505 |

[14] | S. K. Manna and K. S. Chaudhuri, “An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages,” European Journal of Operational Research, vol. 171, no. 2, pp. 557-566, 2006. · Zbl 1090.90068 |

[15] | 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 |

[16] | K. Skouri, I. Konstantaras, S. Papachristos, and I. Ganas, “Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate,” European Journal of Operational Research, vol. 192, no. 1, pp. 79-92, 2009. · Zbl 1171.90326 |

[17] | P. M. Ghare and G. F. Schrader, “A model for exponentially decaying inventories,” Journal of Industrial Engineering, vol. 14, pp. 238-243, 1963. |

[18] | R. P. Covert and G. C. Philip, “An EOQ model for items with Weibull distribution deterioration,” AIIE Transaction, vol. 5, no. 4, pp. 323-326, 1973. |

[19] | P. R. Tadikamalla, “An EOQ inventory model for items with gamma distribution,” AIIE Transaction, vol. 10, no. 1, pp. 100-103, 1978. |

[20] | 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 |

[21] | 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 |

[22] | P. L. Abad, “Optimal pricing and lot-sizing under conditions of perishability and partial backordering,” Management Science, vol. 42, no. 8, pp. 1093-1104, 1996. · Zbl 0879.90069 |

[23] | H.-J. Chang and C.-Y. Dye, “An EOQ model for deteriorating items with time varying demand and partial backlogging,” Journal of the Operational Research Society, vol. 50, no. 11, pp. 1176-1182, 1999. · Zbl 1054.90507 |

[24] | K. Skouri and S. Papachristos, “A continuous review inventory model, with deteriorating items, time-varying demand, linear replenishment cost, partially time-varying backlogging,” Applied Mathematical Modelling, vol. 26, no. 5, pp. 603-617, 2002. · Zbl 1029.90010 |

[25] | J.-T. Teng, H.-J. Chang, C.-Y. Dye, and C.-H. Hung, “An optimal replenishment policy for deteriorating items with time-varying demand and partial backlogging,” Operations Research Letters, vol. 30, no. 6, pp. 387-393, 2002. · Zbl 1013.90006 |

[26] | 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 |

[27] | L. A. San José, J. Sicilia, and J. García-Laguna, “An inventory system with partial backlogging modeled according to a linear function,” Asia-Pacific Journal of Operational Research, vol. 22, no. 2, pp. 189-209, 2005. · Zbl 1078.90009 |

[28] | L. A. San José, J. Sicilia, and J. García-Laguna, “Analysis of an inventory system with exponential partial backordering,” International Journal of Production Economics, vol. 100, no. 1, pp. 76-86, 2006. |

[29] | C.-K. Chen, T.-W. Hung, and T.-C. Weng, “Optimal replenishment policies with allowable shortages for a product life cycle,” Computers & Mathematics with Applications, vol. 53, no. 10, pp. 1582-1594, 2007. · Zbl 1152.90305 |

[30] | C.-K. Chen, T.-W. Hung, and T.-C. Weng, “A net present value approach in developing optimal replenishment policies for a product life cycle,” Applied Mathematics and Computation, vol. 184, no. 2, pp. 360-373, 2007. · Zbl 1162.90305 |

[31] | E. Naddor, Inventory Systems, John Wiley & Sons, New York, NY, USA, 1966. · Zbl 0315.90019 |

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