双需求类静态配给策略  

Constant Critical Level Policy for Inventory Systems with Two Demand Classes

作　　者：张勇 张盛浩[1] ZHANG Yong;ZHANG Shenghao(School of Management,Xi’an Jiaotong University,Xi’an 710049,China)

机构地区：[1]西安交通大学管理学院,陕西西安710049

出　　处：《工业工程与管理》2020年第4期9-15,24,共8页Industrial Engineering and Management

基　　金：国家自然科学基金资助项目(71771185,71271167,71832011)。

摘　　要：考虑一个周期盘点、无限期、缺货回补、双需求类的库存系统,其中高优先级需求的单位缺货成本高于低优先级需求。系统采用基准库存策略补充库存,提前期期数为正整数;采用静态配给策略分配库存,即总是优先满足高优先级需求,且在持有库存水平不高于一个固定配给阈值时拒绝满足低优先级需求。优化目标是最小化系统运行的期望平均成本。为克服"维数灾难"影响,引入"预留库存假设",即必要时允许通过提高低优先级需求缺货水平的方式补充库存,使得期末持有库存水平不低于本期高优先级需求缺货水平与固定配给阈值之和。对于预留库存假设下的库存系统,给出绩效衡量的解析表达式,刻画关键绩效指标关于控制参数的单调性,证明期望平均成本关于配给阈值水平的凸性,并设计最优控制参数的求解算法。由于基于预留库存假设的库存系统与原系统的动态特征高度接近,前者的最优控制参数和相应绩效可作为后者对应指标的近似解。数值分析表明,基于预留库存假设的绩效衡量方法和参数求解算法不仅准确性好,而且计算效率高。This research studied a periodic-review,infinite-horizon,backlogging inventory system with two demand classes,where unsatisfied demands from high priority class incur higher backlogging costs than those from low priority class.Inventory replenishment followd a base-stock policy with a positive integer replenishment lead time.A constant critical level policy was applied to manage inventory rationing,under which demands from high priority class were always satisfied first and then demands from low priority one were fulfilled only if the on-hand inventory level was above the constant critical level.The objective was to minimize the expected long-run average cost.To eliminate the problem of"the curse of dimensionality",a"Reservation Assumption"was proposed,under which the ending on-hand inventory level was kept no less than the sum of the backorder level of high priority class and the constant critical level by increasing the backorder level of low priority class(if necessary).With such an assumption,we derived closed-form expressions for the system performance,proved monotone properties with respect to control parameters,showed convexity of the critical level,and developed an iterative solution procedure.Because the dynamics of the system with the Reservation Assumption was almost identical to that of the exact system,optimal control parameters and corresponding performance of the former system served as good approximations for those of the latter system.A numerical study validated high solution accuracy and computation efficiency of the approximation approach.

关 键 词：库存控制 双需求类 静态配给策略 绩效衡量 解析表达式 

分 类 号：F253.4[经济管理—国民经济]