A Stackelberg game and its improvement in a VMI system with a manufacturing vendor.

*(English)*Zbl 1157.91320Summary: Vendor managed inventory (VMI) is an inventory management strategy to let a vendor manage his retailers’ inventories, which makes the vendor have the opportunity to obtain some inventory and market-related information of his retailers. This paper discusses how the vendor can take advantage of this information for increasing his own profit by using a Stackelberg game in a VMI system. The vendor here is a manufacturer who procures raw materials to produce a finished product and supplies it at the same wholesale price to multiple retailers. The retailers then sell the product in independent markets at retail prices. Solution procedures are developed to find the Stackelberg game equilibrium that each enterprise is not willing to deviate from for maximizing his own profit. The equilibrium makes the manufacturer benefited, and the retailers’ profits maximized. The equilibrium can then be improved for further benefiting the manufacturer and his retailers if the retailers are willing to cooperate with the manufacturer by using a cooperative contract. Finally, a numerical example and the corresponding sensitivity analysis are given to illustrate that: (1) the manufacturer can benefit from his leadership, and monopolize the added profit of the VMI system in some cases; (2) The manufacturer can further improve his own profit, and then the retailers’ profits by the cooperative contract, as compared to the Stackelberg equilibrium; (3) market and raw material related parameters have significant influence on every enterprise’s net profit.

##### MSC:

91A35 | Decision theory for games |

91A80 | Applications of game theory |

90B05 | Inventory, storage, reservoirs |

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\textit{Y. Yu} et al., Eur. J. Oper. Res. 192, No. 3, 929--948 (2009; Zbl 1157.91320)

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