替代竞争情境下考虑期初库存水平和存储能力约束的多周期订货博弈问题研究  

Multi-period Inventory Substitute Competition under the Initial Inventory Level and the Capacity Constraints

作　　者：张剑 何爽 师璞杰 张菊亮[2] Zhang Jian;He Shuang;Shi Pujie;Zhang Juliang(School of Business Administration,Inner Mongolia University of Finance and Economics,Hohhot 010080,China;School of Economics and Management,Beijing Jiaotong University,Beijing 100044,China)

机构地区：[1]内蒙古财经大学工商管理学院,内蒙古呼和浩特010080 [2]北京交通大学经济管理学院,北京100044

出　　处：《中国管理科学》2024年第1期319-324,共6页Chinese Journal of Management Science

基　　金：国家自然科学基金项目(71962026);教育部人文社会科学基金项目(19YJA630111);内蒙古自然科学基金项目(2019MS07004);内蒙古自治区高等学校创新团队发展计划资项目(NMGIRT2202)。

摘　　要：本文研究了期初库存水平和存储能力约束下缺货替代竞争的多周期订货博弈问题。两种可相互替代的产品分别由两个零售商销售,当购买某一产品的顾客遇到缺货时会转而购买另外一种产品。零售商通过选择订货量来争取替代需求,订货后的库存量大于期初库存水平且小于各自的存储能力。研究发现,多周期博弈存在纳什均衡解。当仅考虑期初库存水平约束时,零售商的均衡订货策略是一种广义的Base-stock策略。在存储能力约束下,本文提出了一种改进的Base-stock策略。这两种均衡订货策略包含了非竞争条件下的最优订货策略。数值实验表明,替代竞争会导致零售商订更多的货;与短视策略相比,本文提出的订货策略能够增加零售商收益。Substitute competition is a common phenomenon in economy and business that affects inventory management significantly.The competition problem between two firms is studied with the initial inventory level and the capacity constraints.Two substitutable products are operated by two firms respectively.The unmet demand of one product can be met by the other product’s leftover stock,if available,and is lost otherwise.The firms compete for the substitute demand by choosing their own order quantities in multi-period.The problem is formulated as a dynamic game under independent stochastic demands and it is shown that the inventory game is submodular and the response functions are contraction maps,so the existence of a unique Nash equilibrium is guaranteed.It is found that the best response function is strictly decreasing in the rival’s decisions and decreas⁃ing in the initial inventory levels of the two products.It is found that the base-stock policy is the equilibrium policy.The capacitated case is considered where each firm can hold no more than a certain quantity of the product in each period and find that the equilibrium policy is a modified base-stock strategy.Finally,numerical studies are conducted to compare our strategy with the myopic policy and to generate managerial insights from the analytical findings.Compared with the existing literature,it contributes to the fields of multi-period inven⁃tory management and dynamic game in this paper.

关 键 词：期初库存水平 存储能力约束 动态订货博弈 Base-stock策略 

分 类 号：F224[经济管理—国民经济] C931[经济管理—管理学]