Abstract Taking fairness concerns of retailer into account, we extend the classical newsvendor model to a new type with Nash bargaining preference. Depending on the demand forms, three models are proposed: one benchmark case for deterministic demand, and two stochastic demand cases for multiplicative and additive patterns, respectively. We theoretically prove the existence and uniqueness of the optimal joint decision on pricing and ordering by maximising the fairness-concerned retailer’s utility function theoretically. The optimal strategy of the supplier is acquired via one dimensional search method numerically. The results show that the optimal price is increasing in terms of the fairness-concerned parameter, Nash bargaining power and wholesale price. But the optimal ordering changes in an opposite way. Numerical examples and experiments agree well with our theoretical analysis. It is worth noting that the degree of retailer’s fairness concerns can improve the retailer’s utility and performance of the supply chain, which is different from the traditional fairness-neutral scenario.

中文翻译：

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基于Nash讨价还价公平的随机需求下的定价和订货联合决策

摘要 考虑到零售商的公平问题，我们将经典报摊模型扩展为具有纳什讨价还价偏好的新类型。根据需求形式，提出了三种模型：确定性需求的一个基准案例，以及乘法和加法模式的两个随机需求案例。我们通过最大化关注公平的零售商的效用函数，从理论上证明了定价和订购最优联合决策的存在性和唯一性。供应商的最优策略是通过一维搜索方法数值获取的。结果表明，最优价格在公平相关参数、纳什议价能力和批发价格方面均呈递增趋势。但最佳排序以相反的方式变化。数值例子和实验与我们的理论分析非常吻合。值得注意的是，零售商对公平的关注程度可以提高零售商的供应链效用和绩效，这与传统的公平中立情景不同。