##
**A note on lead time and distributional assumptions in continuous review inventory models.**
*(English)*
Zbl 1042.90509

Summary: There is a rapidly growing literature on modelling the effects of investment strategies to control givens such as setup time, setup cost, quality level and lead time. Recently, a continuous review inventory model with a mixture of backorders and lost sales in which both lead time and the order quantity are decision variables has been studied. The objectives of this paper are twofold. Firstly, we want to correct and improve the recently studied model by simultaneously optimizing both the order quantity and the reorder point. A significant amount of savings over the model can be achieved. We illustrate these savings by solving the same examples in the study. Secondly, we then develop a minimax distribution free procedure for the problem.

Recently, there have been some studies on lead time reduction to provide more meaningful mathematical models to decision makers. Ouyang et al. study a continuous review inventory model in which lead time is a decision variable. However, their algorithm cannot find the optimal solution due to the flaws in the modeling and the solution procedure. We present a complete procedure to find the optimal solution for the model. In addition to the above contribution, we also apply the minimax distribution free approach to the model to devise a practical procedure which can be used without specific information on demand distribution.

Recently, there have been some studies on lead time reduction to provide more meaningful mathematical models to decision makers. Ouyang et al. study a continuous review inventory model in which lead time is a decision variable. However, their algorithm cannot find the optimal solution due to the flaws in the modeling and the solution procedure. We present a complete procedure to find the optimal solution for the model. In addition to the above contribution, we also apply the minimax distribution free approach to the model to devise a practical procedure which can be used without specific information on demand distribution.

### MSC:

90B05 | Inventory, storage, reservoirs |

PDFBibTeX
XMLCite

\textit{I. Moon} and \textit{S. Choi}, Comput. Oper. Res. 25, No. 11, 1007--1012 (1998; Zbl 1042.90509)

Full Text:
DOI

### References:

[1] | Silver, E., Modelling in support of continuous improvements towards achieving world class operations. Perspectives in Operations Management; Silver, E., Modelling in support of continuous improvements towards achieving world class operations. Perspectives in Operations Management |

[2] | Silver, E., Pyke, D. and Peterson, R., Decision Systems for Inventory Management and Production Planning; Silver, E., Pyke, D. and Peterson, R., Decision Systems for Inventory Management and Production Planning |

[3] | Liao, C.; Shyu, C., An analytical determination of lead time with normal demand, Int. J. Oper. Prod. Management, 11, 72-78 (1991) |

[4] | Ben-Daya, M.; Raouf, A., Inventory models involving lead time as decison variables, J. Oper. Res. Soc., 45, 579-582 (1994) · Zbl 0805.90037 |

[5] | Ouyang, L.; Yeh, N.; Wu, K., Mixture inventory model with backorders and lost sales for variable lead time, J. Oper. Res. Soc., 47, 829-832 (1996) · Zbl 0856.90041 |

[6] | Scarf, H., A min-max solution of an inventory problem. In Studies in The Mathematical Theory of Inventory and Production; Scarf, H., A min-max solution of an inventory problem. In Studies in The Mathematical Theory of Inventory and Production |

[7] | Gallego, G.; Moon, I., The distribution free newsboy problem: review and extensions, J. Oper. Res. Soc., 44, 825-834 (1994) · Zbl 0781.90029 |

[8] | Shore, H., General approximate solutions for some common inventory models, J. Oper. Res. Soc., 37, 619-629 (1986) · Zbl 0597.90026 |

[9] | Moon, I.; Choi, S., Distribution free procedures for make-to-order, make-in-advance and composite policies, Int. J. Prod. Eco., 48, 21-28 (1997) |

[10] | Gallego, G., Ryan, J. and Simchi-Levi, D., Minimax analysis for finite horizon inventory models. Working Paper. Northwestern University, 1997; Gallego, G., Ryan, J. and Simchi-Levi, D., Minimax analysis for finite horizon inventory models. Working Paper. Northwestern University, 1997 |

[11] | Hadley, G. and Whitin, T., Analysis of Inventory Systems; Hadley, G. and Whitin, T., Analysis of Inventory Systems · Zbl 0133.42901 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.