随机需求下考虑缺货损失变动的最优订购与定价决策  

Optimal Ordering and Pricing Decisions of a Retailer Under Stochastic Demand with Considering Variable Stockout Cost

作　　者：肖玉徽[1] 楼振凯 戴晓震 Xiao Yuhui;Lou Zhenkai;Dai Xiaozhen(Gathering Stars Digital Eoonormic College,Hakou University of Economics,Haikou 571127,China;School of Management and Eonomics,Beijing Institute of Technology,Beijing 100081,China;School of Management,Wenzhou Business College,Wenzhou 325035,China)

机构地区：[1]海口经济学院聚星数字经济学院,海南海口571127 [2]北京理工大学管理与经济学院,北京100081 [3]温州商学院管理学院,浙江温州325035

出　　处：《南京师大学报（自然科学版）》2022年第3期9-14,共6页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金面上项目(71571019);海南省哲学社会科学规划课题(HNSK(YB)21-11)。

摘　　要：研究了需求关于销售价格线性敏感且随机的零售商最优订购与定价问题.考虑到不同销售价格下单位商品的缺货损失对零售商来说是不同的,给出了机会缺货损失的概念.接着建立了随机需求下的平衡机会损失与实际利润的最优订购与定价模型,得到了最大化净收益目标下进货量与销售价格的函数关系,并利用该函数将原模型转化为只含一个决策变量的模型.通过极值存在性的分析给出了零售商最大期望利润为正的必要条件,并进一步给出了需求随机项的概率密度函数可导时利润函数极大值存在的充分条件.通过所能获得的最大利润,可分析零售商是否值得进行此次的订购与销售.最后给出一个算例,对文中所获得的结论做一些补充.This paper studies optimal ordering and pricing issues of a retailer who faces price-linear-sensitive and stochastic demand. By considering variable stockout cost of one item under different retail price, the conception of variable opportunity loss is proposed. Then an ordering and pricing model is constucted under stochastic demand for the purpose of trading off opportunity loss and overordering cost. It is shown that the ordering quantity and the retail price of the retailer meet a unique relation formula, by which the previous model is transformed to another model which only involves one decision variable. By analyzing the existence of the extremum value of the profit function, a necessary condition in which the retailer’s profit is positive is presented. Further, a sufficient condition in which the maximal value of the profit function exists is obtained under the assumption that the probability density function of the stochastic item of demand is differentiable. By analyzing the maximal profit, the retailer is able to draw the conclusion for whether or not to order and sales. Finally, a numerical illustration is presented to make some supplements.

关 键 词：随机需求 订购与定价 机会损失 极值存在性 

分 类 号：F224[经济管理—国民经济] F274