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**Integrated inventory model with quantity discount and price-sensitive demand.**
*(English)*
Zbl 1219.90012

Summary: Quantity discount has been a subject of study for a long time; however, little is known about its effect on integrated inventory models when price-sensitive demand is placed. The objective of this study is to find the optimal pricing and ordering strategies for an integrated inventory system when a quantity discount policy is applied. The pricing strategy discussed here is one in which the vendor offers a quantity discount to the buyer. Then, the buyer will adjust his retail price based on the purchasing cost, which will influence the customer demand as a result. Consequently, an integrated inventory model is established to find the optimal solutions for order quantity, retail price, and the number of shipments from vendor to buyer in one production run, so that the joint total profit incurred has the maximum value. Also, numerical examples and a sensitivity analysis are given to illustrate the results of the model.

### MSC:

90B05 | Inventory, storage, reservoirs |

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\textit{Y.-J. Lin} and \textit{C.-H. Ho}, Top 19, No. 1, 177--188 (2011; Zbl 1219.90012)

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### References:

[1] | Allenby GM, Shively TS, Yang S, Garratt MJ (2004) A choice model for packaged goods: dealing with discrete quantities and quantity discounts. Mark Sci 23(1):95–108 |

[2] | Burke GJ, Carrillo J, Vakharia AJ (2008) Heuristics for sourcing from multiple suppliers with alternative quantity discounts. Eur J Oper Res 186:317–329 · Zbl 1138.90333 |

[3] | Chang HC, Ouyang LY, Wu KS, Ho CH (2006) Integrated vendor–buyer cooperative inventory models with controllable lead time and ordering cost reduction. Eur J Oper Res 170:481–495 · Zbl 1085.90002 |

[4] | Chung CS, Hum SH, Kirca O (1996) The coordinated replenishment dynamic lot-sizing problems with quantity discounts. Eur J Oper Res 94:122–133 · Zbl 0930.90001 |

[5] | Corbett CJ, De Groote X (2000) A supplier’s optimal quantity discount policy under asymmetric information. Manag Sci 46:444–450 · Zbl 1231.90024 |

[6] | Dolan RJ (1987) Quantity discounts: managerial issues and research opportunities. Mark Sci 6:1–22 |

[7] | Goyal SK (1976) An integrated inventory model for a single supplier–single customer problem. Int J Prod Res 15(1):107–111 |

[8] | Goyal SK (1988) ”A joint economic-lot-size model for purchaser and vendor”: a comment. Decis Sci 19:236–241 |

[9] | Hadley G, Whitin T (1963) Analysis of inventory systems. Prentice Hall, New Jersey · Zbl 0133.42901 |

[10] | Hariga M, Ben-Daya M (1999) Some stochastic inventory models with deterministic variable lead time. Eur J Oper Res 113:42–51 · Zbl 0933.90005 |

[11] | Hofmann C (2000) Supplier’s pricing policy in a just-in-time environment. Comput Oper Res 27:1357–1373 · Zbl 0992.90001 |

[12] | Joglekar P (1988) Comments on ”A quantity discount pricing model to increase vendor profits”. Manag Sci 34:1391–1398 |

[13] | Lee HL, Rosenblatt MJ (1986) A generalized quantity discount pricing model to increase supplier’s profits. Manag Sci 32(9):1177–1185 · Zbl 0605.90022 |

[14] | Li SX, Huang Z (1995) Managing buyer–seller system cooperation with quantity discount considerations. Comput Oper Res 22(9):947–958 · Zbl 0854.90055 |

[15] | Li J, Liu L (2006) Supply chain coordination with quantity discount policy. Int J Prod Econ 101:89–98 |

[16] | Lin YJ (2008) Minimax distribution free procedure with backorder price discount. Int J Prod Econ 111:118–128 |

[17] | Monahan JP (1984) A quantity discount pricing model to increase vendor profits. Manag Sci 30(6):720–726 |

[18] | Moon I, Choi S (1998) A note on lead time and distributional assumptions in continuous review inventory models. Comput Oper Res 25:1007–1012 · Zbl 1042.90509 |

[19] | Munson CL, Rosenblatt MJ (1998) Theories and realities of quantity discounts: an exploratory study. Prod Oper Manag 7(4):352–369 |

[20] | Munson CL, Rosenblatt MJ (2001) Coordinating a three-level supply chain with quantity discount. IIE Trans 33:371–384 |

[21] | Ouyang LY, Chuang BR, Lin YJ (2007) Effective investment to reduce lost sales in a periodic review inventory model. OR Spectr 29:681–697 · Zbl 1168.90335 |

[22] | Pan JCH, Yang JS (2002) A study of an integrated inventory with controllable lead time. Int J Prod Res 40(5):1263–1273 · Zbl 1027.90024 |

[23] | Parlar M, Wang Q (1994) Discounting decisions in a supplier–buyer relationship with a linear buyer’s demand. IIE Trans 26:34–41 |

[24] | Qin Y, Tang H, Guo C (2007) Channel coordination and volume discounts with price-sensitive demand. Int J Prod Econ 105:43–53 |

[25] | Sheen GJ, Tsao YC (2007) Channel coordination, trade credit and quantity discounts for freight cost. Transp Res Part E 43:112–128 |

[26] | Tsai JF (2007) An optimization approach for supply chain management models with quantity discount policy. Eur J Oper Res 177:982–994 · Zbl 1114.90005 |

[27] | Viswanathan S, Wang Q (2003) Discount pricing decisions in distribution channels with price-sensitive demand. Eur J Oper Res 149:571–587 · Zbl 1033.90006 |

[28] | Weng ZK (1995) Modeling quantity discounts under general price-sensitive demand functions: optimal policies and relationships. Eur J Oper Res 86:300–314 · Zbl 0906.90102 |

[29] | Weng ZK, Wong RT (1993) General models for the supplier’s all-unit quantity discount policy. Nav Res Logist 40:971–991 · Zbl 0800.90117 |

[30] | Yang PC (2004) Pricing strategy for deteriorating items using quantity discount when demand is price sensitive. Eur J Oper Res 157:389–397 · Zbl 1103.90313 |

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.