交叉销售产品的报童模型与博弈分析

Newsvendor model and game analysis of cross-selling products

当产品间存在互补关联关系时,会出现交叉销售:顾客在购买一种产品的同时也会以一定可能性购买另一种关联产品;反过来,某产品也会因其关联产品的缺货而失去交叉销售机会.本文考虑交叉销售,首先建立带缺货惩罚的单周期多产品集中决策报童模型,推导其最优订货量的一阶必要条件,并给出最优解的上下界.考虑多个报童独立竞争决策,建立交叉销售产品的报童博弈模型,证明该博弈是超模博弈,并给出了一阶博弈均衡条件以及均衡解的唯一性条件和上下界.分析了集中决策和分散博弈决策的差异,给出了博弈模型中需求相关系数对期望利润的影响规律.通过计算研究讨论了交叉销售系数、需求相关系数以及缺货惩罚成本对订货量和期望收益的影响.

Cross-selling emerges when complementary associations exist among products： A customer who has purchased a product may be willing to purchase another associated product with a certain probability; otherwise,the cross-selling opportunity of a stocked product can also dimish because of the shortage of its associated products. In this paper,a single-period multi-product centralized newsvendor model considering cross-selling and shortage penalty is formulated. The first-order necessary conditions and the upper and lower bounds of the optimal order quantity are given. For multiple newsvendors who make decisions individually and competitively,the newsvendor non-cooperative game of cross-selling product is modeled,which is proved supermodular. The first-order conditions,the uniqueness conditions and the bounds of the Nash equilibrium are developed. The difference between the decisions of the two models is presented and the analysis shows how the correlation of demand influences the expected profit. Finally,a computational study is conducted to observe the impacts of cross-selling,demand correlation,and shortage penalty on the order quantities and expected profits.