##
**Fuzzy mixture inventory model with variable lead-time based on probabilistic fuzzy set and triangular fuzzy number.**
*(English)*
Zbl 1055.90008

Summary: This article considers the fuzzy problems for the mixture inventory model involving variable lead-time with backorders and lost sales. We first use the probabilistic fuzzy set to construct a new random variable for lead-time demand, and derive the total expected annual cost in the fuzzy sense. Then, the average demand per year is fuzzified as the triangular fuzzy number. For this case, two methods of defuzzification, namely signed distance and centroid, are employed to find the value of total expected annual cost in the fuzzy sense. Next, the backorder rate of the demand during the stock-out period is also fuzzified as the triangular fuzzy number, and the value of total expected annual cost in the fuzzy sense is derived using the signed distance. For the proposed models, we provide a solution procedure to find the optimal lead-time and the optimal order quantity such that the total expected annual cost in the fuzzy sense has a minimum value.

### MSC:

90B06 | Transportation, logistics and supply chain management |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

PDFBibTeX
XMLCite

\textit{H.-C. Chang} et al., Math. Comput. Modelling 39, No. 2--3, 287--304 (2004; Zbl 1055.90008)

Full Text:
DOI

### References:

[1] | Tersine, R. J., Principle of Inventory and Materials Management (1982), North-Holland: North-Holland New York |

[2] | Liao, C. J.; Shyu, C. H., An analytical determination of lead time with normal demand, International Journal of Operations and Production Management, 11, 72-78 (1991) |

[3] | Ben-Daya, M.; Raouf, A., Inventory models involving lead time as decision variable, Journal of the Operational Research Society, 45, 579-582 (1994) · Zbl 0805.90037 |

[4] | Ouyang, L. Y.; Yeh, N. C.; Wu, K. S., Mixture inventory model with backorders and lost sales for variable lead time, Journal of the Operational Research Society, 47, 829-832 (1996) · Zbl 0856.90041 |

[5] | Hirota, K., Concepts of probabilistic set, Fuzzy Sets and Systems, 5, 31-46 (1981) |

[6] | Zadeh, L., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606 |

[7] | Petrovic, D.; Sweeney, E., Fuzzy knowledge-based approach to treating uncertainty in inventory control, Computer Integrated Manufacturing Systems, 7, 147-152 (1994) |

[8] | Vujošević, M.; Petrovic, D.; Petrovic, R., EOQ formula when inventory cost is fuzzy, International Journal of Production Economics, 45, 499-504 (1996) |

[9] | Chen, S. H.; Wang, C. C., Backorder fuzzy inventory model under functional principle, Information Sciences, 95, 71-79 (1996) |

[10] | Roy, T. K.; Maiti, M., A fuzzy EOQ model with demand-dependent unit cost under limited storage capacity, European Journal of Operational Research, 99, 425-432 (1997) · Zbl 0953.90501 |

[11] | Gen, M.; Tsujimura, Y.; Zheng, P. Z., An application of fuzzy set theory to inventory control models, Computers and Industrial Engineering, 33, 553-556 (1997) |

[12] | Ishii, H.; Konno, T., A stochastic inventory with fuzzy shortage cost, European Journal of Operational Research, 106, 90-94 (1998) |

[13] | Chang, S. C.; Yao, J. S.; Lee, H. M., Economic reorder point for fuzzy backorder quantity, European Journal of Operational Research, 109, 183-202 (1998) · Zbl 0951.90003 |

[14] | Lee, H. M.; Yao, J. S., Economic production quantity for fuzzy demand quantity and fuzzy production quantity, European Journal of Operational Research, 109, 203-211 (1998) · Zbl 0951.90019 |

[15] | Lin, D. C.; Yao, J. S., Fuzzy economic production for production inventory, Fuzzy Sets and Systems, 111, 465-4955 (2000) · Zbl 0993.91024 |

[16] | Yao, J. S.; Chang, S. C.; Su, J. S., Fuzzy inventory without backorder for fuzzy quantity and fuzzy total demand quantity, Computers and Operations Research, 27, 935-962 (2000) · Zbl 0970.90010 |

[17] | Ouyang, L. Y.; Yao, J. S., A minimax distribution free procedure for mixed inventory model involving variable lead time with fuzzy demand, Computers and Operations Research, 29, 471-487 (2002) · Zbl 0995.90004 |

[18] | Yao, J. S.; Wu, K. M., Ranking fuzzy numbers based on decomposition principle and signed distance, Fuzzy Sets and Systems, 116, 275-288 (2000) · Zbl 1179.62031 |

[19] | Pu, P. M.; Liu, Y. M., Fuzzy Topology 1, Neighborhood structure of a fuzzy point and Moore-Smith convergence, Journal of Mathematical Analysis and Applications, 76, 571-599 (1980) · Zbl 0447.54006 |

[20] | Kaufmann, A.; Gupta, M. M., Introduction to Fuzzy Arithmetic: Theory and Applications (1991), Van Nostrand Reinhold: Van Nostrand Reinhold New York · Zbl 0754.26012 |

[21] | Zimmermann, H. J., Fuzzy Set Theory and its Application (1996), Kluwer Academic: Kluwer Academic Dordrecht · Zbl 0845.04006 |

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.