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**Optimal inventory policy involving ordering cost reduction, back-order discounts, and variable lead time demand by minimax criterion.**
*(English)*
Zbl 1187.90031

Summary: This paper allows the backorder rate as a control variable to widen applications of a continuous review inventory model. Moreover, we also consider the backorder rate that is proposed by combining L.-Y. Ouyang and B.-R. Chuang [Mixture inventory model involving variable lead time and controllable backorder rate,’ Comput. Ind. Eng. 40, No. 4, 339–348 (2001; doi:10.1016/S0360-8352(01)00033-X)] (or W.-Ch. Lee [Appl. Math. Comput. 160, No. 3, 701–717 (2005; Zbl 1087.90009)]) with J. C. Pan and Y. C. Hsiao [Int. J. Syst. Sci. 32, No. 7, 925–929 (2001; Zbl 1005.90007)] to present a new form. Thus, the backorder rate is dependent on the amount of shortages and backorder price discounts. Besides, we also treat the ordering cost as a decision variable. Hence, we develop an algorithmic procedure to find the optimal inventory policy by minimax criterion. Finally, a numerical example is also given to illustrate the results.

### MSC:

90B05 | Inventory, storage, reservoirs |

### Keywords:

backorder rate
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XMLCite

\textit{J.-W. Wu} et al., Math. Probl. Eng. 2009, Article ID 928932, 19 p. (2009; Zbl 1187.90031)

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