服务水平约束下双需求类静态配给策略

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目标服务水平较高。系统采用基准库存策略补充库存，依据静态配给策略分配库存，即优先满足高优先级需求，仅当持有库存水平不低于固定配给阈值时满足低优先级需求。优化目标是在服务水平约束下最小化期望库存持有量。为提升计算效率，引入“预留库存假设”,即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。基于预留库存假设，给出两类需求服务水平和期望库存持有量的解析表达式，证明上述绩效指标关于控制参数的单调性，刻画满足服务水平约束的控制参数可行域，得到原系统最优控制参数的近似求解算法。算例分析表明，基于预留库存假设的绩效衡量方法和参数求解算法准确性好且计算效率高。

Constant Critical Level Policy for Two-class Inventory Systems under Service Level Constraints

We consider a periodic review, infinite horizon, backlogging inventory system with two demand classes, where the high priority class has a higher target service level than the low priority one. The system applies a base-stock policy and a constant critical level policy, under which high priority demands are fulfilled firstly while low priority ones are satisfied only if on-hand inventory is more than a constant critical level. The objective is to minimize the expected ending on-hand inventory subject to two service level constraints. To improve computation efficiency, we propose a “Reservation Assumption”, under which the ending on-hand inventory is no less than the sum of high priority backorder level and the constant critical level by increasing low priority backorder level. We derive closed-form expressions for the approximate system performance, prove various monotone properties with respect to control parameters, characterize the zones of feasible solutions, and develop a solution procedure of the service level constraint problem. The numerical experiments show that our solution procedure performs well in both solution accuracy and computation efficiency.