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**Computational algorithmic procedure for optimal inventory policy involving ordering cost reduction and back-order discounts when lead time demand is controllable.**
*(English)*
Zbl 1401.90032

Summary: In many practical situations, the ordering cost can be reduced by capital investment and the back-order rate is dependent on the amount of shortages and back-order price discounts. Hence, in this paper, we consider an inventory model with random yield in which the ordering cost can be reduced through capital investment, lead time can be shortened at an extra crashing cost and allow the back-order rate as a control variable to widen applications of J.-W. Wu and H.-Y. Tsai’s model [Int. J. Syst. Sci. 32, No. 2, 259–268 (2001; Zbl 1006.90010)]. Moreover, we also consider the back-order rate that 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.-C. Lee, Appl. Math. Comput. 160, No. 3, 701–717 (2005; Zbl 1087.90009)]) with [J. C. H. Pan and Y.-C. Hsiao, Int. J. Syst. Sci. 32, No. 7, 925–929 (2001; Zbl 1005.90007); “Integrated inventory models with controllable lead time and backorder discount considerations”, Int. J. Prod. Econ. 93–94, 387–397 (2005; doi:10.1016/j.ijpe.2004.06.035)] (also see [J. C. H. Pan et al., Eur. J. Oper. Res. 158, No. 2, 488–505 (2004; Zbl 1067.90005)]) to present a new general form. The objective is to simultaneously optimize the order quantity, ordering cost, back-order discount and lead time. In addition, we also develop an algorithmic procedure and use the computer software Compaq Visual Fortran V6.0 (inclusive of IMSL) to find the optimal inventory policy. Finally, a numerical example is also given to illustrate the results.

### MSC:

90B05 | Inventory, storage, reservoirs |

### Keywords:

order quantity; back-order rate; ordering cost reduction; lead time; mixture of normal distributions; discount; algorithm
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\textit{W.-C. Lee} et al., Appl. Math. Comput. 189, No. 1, 186--200 (2007; Zbl 1401.90032)

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### References:

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