带注资的生产动态控制和优化  

Dynamic Control and Optimization of Production with Capital Injection

作　　者：郑宽宽 谭激扬[1] 吕志科 牛龙龙 Zheng Kuankuan;Tan Jiyang;Lv Zhike;Niu Longlong(School of Mathematics and Computation Science,Xiangtan University,Xiangtan 411105,China;Business Shool,Xiangtan University,Xiangtan 411105,China)

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105 [2]湘潭大学商学院,湖南湘潭411105

出　　处：《中国管理科学》2024年第11期115-124,共10页Chinese Journal of Management Science

基　　金：湖南省教育厅重点项目(20A485);湖南省自然科学基金项目(2019JJ40278);国家自然科学基金项目(62172294,11371301)。

摘　　要：本文考虑控制企业的采购生产及资金的流动,使得股东未来的累积期望贴现收益达到最大。在一个生产周期结束时,若公司持有现金量超过给定边界,则超出部分作为红利分发给股东;若公司盈余不足以支付随后的最优生产成本,则允许股东注入资金满足生产需求。文中建立了一个马尔可夫决策模型,假设任意周期的单位生产成本和上一期的单位售价、需求量相关,并服从一个联合分布;本文提供了计算最优值函数和最优生产策略的方法,其中包括考察期时长有限时值函数满足的迭代关系式,以及考察期时长无限制时值函数满足的Bellman方程,并用压缩映射原理证明最优值函数是Bellman方程的唯一解。本文最后给出了数值算例,采用文中的方法计算最优值函数和最优策略并分析结果。A common problem in the production and management of enterprises,especially retail enterprises,how to make reasonable purchasing and production plans to achieve the business objectives of enterprises,is studied in this paper.In addition to production,sales,inventory and other activities,paying dividends to shareholders and accepting capital injection from shareholders are also essential links of enterprises.It is of practical significance to formulate purchasing and production strategies with the goal of maximizing shareholders’interests.On the basis of previous relevant studies,it is considered that enterprises operate a class of products,similar to the multi-cycle newsboy model.An enterprise controls the purchase or production and capitalflow,adopts the barrier dividend strategy to pay dividends to shareholders at the end of each cycle,or accepts capital injection from shareholders when the amount of cash held is insufficient to pay the optimal production cost in the next period.In addition,it is assumed that the unit production cost of any period,the unit selling price of the previous period and the quantity demanded obey a joint distribution.In this paper,a discrete time Markov decision model is proposed to maximize the future cumulative expected discounted returns of shareholders,the aim is tofind the optimal production strategy and the corresponding optimal value function.Under the condition that the assessment period is limited,the iterative relation satisfied by the optimal value function is given by the formula of total expectation.When the assessment period is unlimited,the Bellman equation satisfied by the value function is given,and the optimal value function is proved to be the only solution by the contraction mapping principle.Finally,a numerical example is given according to the method provided in this paper,and the results mainly provide the following information:1)When the duration of the assessment period is limited,the optimal production strategy of each period which is far away from the

关 键 词：注资策略 边界分红策略 最优生产策略 Bellman方程 压缩映射 

分 类 号：C934[经济管理—管理学]