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**Optimal ordering policy for deteriorating items with partial backlogging under permissible delay in payments.**
*(English)*
Zbl 1099.90004

Summary: In [Economic order quantity under conditions of permissible delay in payments, J. Oper. Res. Soc. 36, 335–338 (1985)], S. K. Goyal developed an economic order quantity (EOQ) model under conditions of permissible delay in payments. A. M. M. Jamal, B. R. Sarker and S. Wang [J. Oper. Res. Soc. 48, No. 8, 826–833 (1997; Zbl 0890.90049)] then generalized Goyal’s model for deteriorating items with completely backlogging. However, they only ran several simulations to indicate that the total relevant cost may be convex. Recently, J. T. Teng [J. Oper. Res. Soc. 53, No. 8, 915–918 (2002; Zbl 1098.90006)] amended Goyal’s model by considering the difference between unit price and unit cost, and provided an alternative conclusion that it makes economic sense for some retailers to order less quantity and take the benefits of the permissible delay more frequently. However, he did not consider deteriorating items and partial backlogging.

In this paper, we establish a general EOQ model for deteriorating items when the supplier offers a permissible delay in payments. For generality, our model allows not only the partial backlogging rate to be related to the waiting time but also the unit selling price to be larger than the unit purchase cost. Consequently, the proposed model includes numerous previous models as special cases. In addition, we mathematically prove that the total relevant cost is strictly pseudo-convex so that the optimal solution exists and is unique. Finally, our computational results reveal six managerial phenomena.

In this paper, we establish a general EOQ model for deteriorating items when the supplier offers a permissible delay in payments. For generality, our model allows not only the partial backlogging rate to be related to the waiting time but also the unit selling price to be larger than the unit purchase cost. Consequently, the proposed model includes numerous previous models as special cases. In addition, we mathematically prove that the total relevant cost is strictly pseudo-convex so that the optimal solution exists and is unique. Finally, our computational results reveal six managerial phenomena.

### MSC:

90B05 | Inventory, storage, reservoirs |

90B25 | Reliability, availability, maintenance, inspection in operations research |

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\textit{L.-Y. Ouyang} et al., J. Glob. Optim. 34, No. 2, 245--271 (2006; Zbl 1099.90004)

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### References:

[6] | Chang, C.T. and Teng, J.T. (2004), Retailer’s optimal ordering policy under supplier credits, to appear in Mathematical Methods of Operations Research. · Zbl 1104.90007 |

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