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**Incorporating one-way substitution policy into the newsboy problem with imprecise customer demand.**
*(English)*
Zbl 1188.90008

Summary: This paper presents an approach for solving an inventory model for single-period products with maximizing its expected profit in a fuzzy environment, in which the retailer has the opportunity for substitution. Though various structures of substitution arise in real life, in this study, we consider the fuzzy model for two-item with one-way substitution policy. This one-way substitutability is reasonable when the products can be stored according to certain attribute levels such as quality, brand or package size. Again, to describe uncertainty usually probability density functions are being used. However, there are many situations in real world that utilize knowledge-based information to describe the uncertainty. The objective of this study is to provide an analysis of single-period inventory model in a fuzzy environment that enables us to compute the expected resultant profit under substitution. An efficient numerical search procedure is provided to identify the optimal order quantities, in which the utilization of imprecise demand and the use of one-way substitution policy increase the average expected profit. The benefit of product substitution is illustrated through numerical example.

### MSC:

90B05 | Inventory, storage, reservoirs |

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\textit{P. Dutta} and \textit{D. Chakraborty}, Eur. J. Oper. Res. 200, No. 1, 99--110 (2010; Zbl 1188.90008)

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### References:

[1] | Urban, T. L.; Baker, R. C., Optimal ordering and pricing policies in a single period environment with multivariate demand and markdowns, European Journal of Operational Research, 103, 573-583 (1997) · Zbl 0921.90065 |

[2] | Nahmias, S.; Schmidt, C. P., An efficient heuristic for the multi-item newsboy problem with a single constraint, Naval Research Logistics, 31, 463-474 (1984) · Zbl 0544.90023 |

[3] | Ben-Daya, M.; Raouf, A., On the constrained multi-item single-period inventory problem, International Journal of Production and Operations Management, 13, 104-112 (1993) |

[4] | Lau, Amy H. L.; Lau, H. S., Maximizing the probability of achieving a target profit level in a two-product newsboy problem, Decision Science, 19, 392-408 (1988) |

[5] | Bayindir, Z. P.; Erkip, N.; Güllü, R., Assessing the benefits of remanufacturing option under one-way substitution and capacity constraint, Computers and Operations Research, 34, 487-514 (2007) · Zbl 1113.90004 |

[6] | Parlar, M.; Goyal, S. K., Optimal ordering decisions for two substitutable products with stochastic demand, Operations Research, 21, 1-15 (1984) · Zbl 0545.90030 |

[7] | Khouja, M., The single-period (news-vender) inventory problem: a literature review and suggestions for future research, Omega, 27, 537-553 (1999) |

[8] | Khouja, M.; Mehrez, A.; Robinowitz, G., A two-item newsboy problem with substitutability, International Journal of Production Economics, 44, 267-275 (1996) |

[9] | Rajaram, K.; Tang, C., The impact of product substitution on retail merchandising, European Journal of Operational Research, 135, 582-601 (2001) · Zbl 0989.90050 |

[10] | Axsater, S., Evaluation of unidirectional lateral transshipments and substitutions in inventory systems, European Journal of Operational Research, 149, 438-447 (2003) · Zbl 1033.90001 |

[11] | Bassok, Y.; Anupindi, R.; Akella, R., Single-period multiproduct inventory models with substitution, Operations Research, 47, 632-642 (1999) · Zbl 0979.90005 |

[12] | Inderfurth, K., Optimal policies in hybrid manufacturing/remanufacturing systems with product substitution, International Journal of Production Economics, 90, 325-343 (2004) |

[13] | Petrovic, D.; Petrovic, R.; Vujosevic, M., Fuzzy models for the newsboy problem, International Journal of Production Economics, 45, 435-441 (1996) |

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

[15] | Li, L.; Kabadi, S. N.; Nair, K. P.K., Fuzzy models for single-period inventory problem, Fuzzy Sets and Systems, 132, 273-289 (2002) · Zbl 1013.90003 |

[16] | Kao, C.; Hsu, W. K., A single period inventory model with fuzzy demand, Computers and Mathematics with Applications, 43, 841-848 (2002) · Zbl 0994.90002 |

[17] | Dutta, P.; Chakraborty, D.; Roy, A. R., A single period inventory model with fuzzy random variable demand, Mathematical and Computer Modeling, 41, 915-922 (2005) · Zbl 1121.90302 |

[18] | Dutta, P.; Chakraborty, D.; Roy, A. R., An inventory model for single-period products with reordering opportunities under fuzzy demand, Computers and Mathematics with Applications, 53, 1502-1517 (2007) · Zbl 1152.90309 |

[19] | Ji, X.; Shao, Z., Models and algorithm for bi-level newsboy problem with fuzzy demands and discounts, Applied Mathematics and Computation, 172, 163-174 (2006) · Zbl 1169.90496 |

[20] | Dubois, D.; Prade, H., The mean value of a fuzzy number, Fuzzy Sets and Systems, 24, 279-300 (1987) · Zbl 0634.94026 |

[21] | Zimmermann, H. J., Fuzzy Sets Theory and its Application (1991), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0719.04002 |

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