突变需求条件下带监测窗口和外购策略的生产与库存模型及性质  

A Production-inventory Model with Monitoring Window and Outsourcing Strategies and Its Properties under Demand Disruption

作　　者：王孟正 万中[1] 褚书含 WANG Mengzheng;WAN Zhong;CHU Shuhan(School of Mathematics and Statistics,Central South University,Changsha 410083)

机构地区：[1]中南大学数学与统计学院,长沙410083

出　　处：《工程数学学报》2025年第1期77-96,共20页Chinese Journal of Engineering Mathematics

基　　金：国家社会科学基金(21BGL122)。

摘　　要：生产库存管理经常遭受突发事件的影响,常常导致市场需求的“断层”。从生产商角度,采用生产与外购混合策略,研究了在生产计划总周期内当突发事件发生时带监测窗口和外购策略的生产库存模型。通过引入监测窗口,生产商能够确定突变的需求率;通过构建和求解突发事件条件下库存问题的微分方程组,推导了生产率调整策略的解析表达式,以及生产外购混合策略下外购时间和外购量的解析表达式,以实现供应与需求的再次匹配。案例研究中,以新冠肺炎疫情对中小型企业需求的影响为例开展了数值仿真,分析了需求突变强度、监测窗口时长、生产与外购混合策略(外购占比)对生产库存规律的影响,得到了一系列对生产和库存管理实践有指导意义的结论。Production and inventory management often suffers from emergency events,which always lead to the phenomenon of“stratification”in market demand.By the mixed producing and outsourcing strategy,we propose a new production and inventory model with monitoring window from the perspective of manufacturers when an emergency event occurs during a fixed production period.With help of the monitoring strategy,the manufacturer determines a sudden change of demand rate.By building and solving the proposed production and inventory model defined by a system of differential equations,the analytical expressions of the productivity adjustment,the outsourcing time and the outsourcing quantity so that the supply matches the demand again.In case study,we apply the developed model and its theoretical properties to analyze impacts of COVID-19 on the production and inventory of small and medium enterprises,including the impacts of the demand fluctuation intensity,the size of monitoring window,and the producing and outsourcing structure.The results from the numerical simulation reveal a series of valuable practical managerial insights underlying the proposed model in this paper.

关 键 词：突发事件 监测窗口 需求突变 生产库存模型 

分 类 号：F253.4[经济管理—国民经济]