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**Inflation and the optimal inventory replenishment schedule within a finite planning horizon.**
*(English)*
Zbl 1304.90011

Summary: The subject of this paper is the problem of finding the optimal replenishment schedule for an inventory, subject to time-dependent demand and deterioration, within a finite time planning horizon. It is shown that taking inflation into account has a profound effect on the solution of the problem. For instance, there is a critical number of replenishment periods, in excess of which the optimal schedule is characterized by the inclusion of token orders at the end of the planning horizon. This and other conclusions, obtained via a careful mathematical analysis of the problem, rectify those of earlier studies.

### MSC:

90B05 | Inventory, storage, reservoirs |

### Keywords:

inventory; finite time planning horizon; optimal schedule; demand; deterioration; inflation
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\textit{B. H. Gilding}, Eur. J. Oper. Res. 234, No. 3, 683--693 (2014; Zbl 1304.90011)

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### References:

[2] | Bakker, M.; Riezebos, J.; Teunter, R. H., Review of inventory systems with deterioration since 2001, European Journal of Operational Research, 221, 275-284 (2012) · Zbl 1253.90017 |

[3] | Balkhi, Z. T.; Benkherouf, L., On an inventory model for deteriorating items with stock dependent and time-varying demand rates, Computers and Operations Research, 31, 223-240 (2004) · Zbl 1087.90006 |

[4] | Benkherouf, L., On an inventory model with deteriorating items and decreasing time-varying demand and shortages, European Journal of Operational Research, 86, 293-299 (1995) · Zbl 0906.90050 |

[5] | Benkherouf, L., On the optimality of a replenishment policy for an inventory model with deteriotating items and time-varying demand and shortages, Arab Journal of Mathematical Sciences, 3, 59-67 (1997) · Zbl 0893.90051 |

[6] | Benkherouf, L.; Balkhi, Z. T., On an inventory model for deteriorating items and time-varying demand, Mathematical Methods of Operations Research, 45, 221-233 (1997) · Zbl 0882.90027 |

[7] | Benkherouf, L.; Boushehri, D., Optimal policies for a finite-horizon production inventory model, Advances in Operations Research, 768929-1-768929-16 (2012) · Zbl 1246.90004 |

[8] | Benkherouf, L.; Gilding, B. H., On a class of optimization problems for finite time horizon inventory models, SIAM Journal on Control and Optimization, 48, 993-1030 (2009) · Zbl 1198.90031 |

[9] | Benkherouf, L.; Mahmoud, M. G., On an inventory model for deteriorating items with increasing time-varying demand and shortages, Journal of the Operational Research Society, 47, 188-200 (1996), 842 · Zbl 0842.90027 |

[10] | Benkherouf, L.; Omar, M., Optimal integrated policies for a single-vendor single-buyer time-varying demand model, Computers and Mathematics with Applications, 60, 2066-2077 (2010) · Zbl 1205.90024 |

[11] | Bierman, H.; Thomas, J., Inventory decisions under inflationary conditions, Decision Sciences, 8, 151-155 (1977) |

[12] | Bose, S.; Goswami, A.; Chaudhuri, K. S., An EOQ model for deteriorating items with linear time-dependent demand rate and shortages under inflation and time discounting, Journal of the Operational Research Society, 46, 771-782 (1995) · Zbl 0832.90026 |

[13] | Buzacott, J. A., Economic order quantities with inflation, Operational Research Quarterly, 26, 553-558 (1975) |

[14] | Chandra, M. J.; Bahner, M. L., The effects of inflation and the time value of money on some inventory systems, International Journal of Production Research, 23, 723-730 (1985) |

[15] | Chern, M.-S.; Yang, H.-L.; Teng, J.-T.; Papachristos, S., Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation, European Journal of Operational Research, 191, 127-141 (2008) · Zbl 1144.90004 |

[16] | Chung, K.-J.; Liu, J.; Tsai, S.-F., Inventory systems for deteriorating items taking account of time value, Engineering Optimization, 27, 303-320 (1997) |

[17] | Datta, T. K.; Pal, A. K., Effects of inflation and time-value of money on an inventory model with linear time-dependent demand rate and shortages, European Journal of Operational Research, 52, 326-333 (1991) |

[18] | Donaldson, W. A., Inventory replenishment policy for a linear trend in demand—An analytical solution, Operational Research Quarterly, 28, 663-670 (1977) · Zbl 0372.90052 |

[19] | Dye, C.-Y.; Hsieh, T.-P., Deterministic ordering policy with price- and stock-dependent demand under fluctuating cost and limited capacity, Expert Systems with Applications, 38, 14976-14983 (2011) |

[20] | Friedman, M. F., Inventory lot-size models with general time-dependent demand and carrying cost functions, INFOR, 20, 157-167 (1982) · Zbl 0502.90018 |

[21] | Ghare, P. M.; Schrader, G. F., A model for an exponentially decaying inventory, Journal of Industrial Engineering, 14, 238-243 (1963) |

[23] | Goyal, S. K.; Giri, B. C., Recent trends in modeling of deteriorating inventory, European Journal of Operational Research, 134, 1-16 (2001) · Zbl 0978.90004 |

[24] | Hariga, M. A., Effects of inflation and time-value of money on an inventory model with time-dependent demand rate and shortages, European Journal of Operational Research, 81, 512-520 (1995) · Zbl 0920.90049 |

[25] | Henery, R. J., Inventory replenishment policy for increasing demand, Journal of the Operational Research Society, 30, 611-617 (1979) · Zbl 0424.90019 |

[26] | Hou, K.-L.; Huang, Y.-F.; Lin, L.-C., An inventory model for deteriorating items with stock-dependent selling rate and partial backlogging under inflation, African Journal of Business Management, 5, 3834-3843 (2011) |

[27] | Hsieh, T.-P.; Dye, C.-Y., Pricing and lot-sizing policies for deteriorating items with partial backlogging under inflation, Expert Systems with Applications, 37, 7234-7242 (2010) |

[28] | Misra, R. B., A study of inflationary effects on inventory systems, Logistics Spectrum, 9, 51-55 (1975) |

[29] | Misra, R. B., A note on optimal inventory management under inflation, Naval Research Logistics Quarterly, 26, 161-165 (1979) · Zbl 0396.90031 |

[30] | Moon, I.; Giri, B. C.; Ko, B., Economic order quantity models for ameliorating/deteriorating items under inflation and time discounting, European Journal of Operational Research, 162, 773-785 (2005) · Zbl 1067.90004 |

[31] | Papachristos, S.; Skouri, K., An optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential type - backlogging, Operations Research Letters, 27, 175-184 (2000) · Zbl 1096.90518 |

[32] | Pentico, D. W.; Drake, M. J., A survey of deterministic models for the EOQ and EPQ with partial backordering, European Journal of Operational Research, 214, 179-198 (2011) |

[33] | Raafat, F., Survey of literature on continuously deteriorating inventory models, Journal of the Operational Research Society, 42, 27-37 (1991) · Zbl 0718.90025 |

[34] | Skouri, K.; Papachristos, S., Note on “Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand” by Yang et al, Naval Research Logistics, 49, 527-529 (2002) · Zbl 1013.90005 |

[35] | Teng, J.-T.; Chern, M.-S.; Yang, H.-L.; Wang, Y. J., Deterministic lot-size inventory models with shortages and deterioration for fluctuating demand, Operations Research Letters, 24, 65-72 (1999) · Zbl 0956.90002 |

[36] | Uthayakumar, R.; Rameswari, M., Economic order quantity for deteriorating items with time discounting, International Journal of Advanced Manufacturing Technology, 58, 817-840 (2012) · Zbl 1260.90028 |

[37] | Yang, H.-L.; Teng, J.-T.; Chern, M.-S., Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand, Naval Research Logistics, 48, 144-158 (2001) · Zbl 0981.90003 |

[38] | Yang, H.-L.; Teng, J.-T.; Chern, M.-S., An inventory model under inflation for deteriorating items with stock-dependent consumption rate and partial backlogging shortages, International Journal of Production Economics, 123, 8-19 (2010) |

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