Inventory Positioning/Partitioning for Backorders Optimization for a Class of Multi‐Echelon Inventory Problems*
针对多级库存网络，提出一个非线性优化模型来确定基础库存水平，利用拉格朗日松弛得到最优解和预算约束的影子价格，帮助管理者在最小成本下保证客户服务。
Inventory management has undergone significant philosophical changes in recent decades such as the advent of the zero inventory concept. However, as attractive as the concept of minimal inventories may be, it is often unrealistic in application. Attention to basic features of inventory control systems such as order quantities, base stock levels, and reorder points remain crucial to ensure customer service at minimal cost. A nonlinear optimization model for determining base stock levels in a multi‐echelon inventory network is presented. Lagrangian relaxation results in (1) newsboy‐style relations that provide the optimal solutions, and (2) instantaneous shadow prices for the budget constraint. Sensitivity analysis of this model will facilitate making decisions concerning the desired investment in inventory for the entire system. This model may be solved on standard nonlinear programming software and is generalizable to problems in both production and distribution settings.