This paper considers an integrated supplier selection and inventory control problem for a multi-echelon inventory system with an order-splitting policy. A buyer firm consisting of one warehouse and $N$ identical retailers procures a type of product from a group of potential suppliers; the acquisition of the warehouse takes place when the inventory level depletes to a reorder point $R$, and the order $Q$ is simultaneously split among $m$ selected suppliers. We develop an exact analytical model for the order-splitting problem in a multi-echelon system, and formulate the supplier selection problem in a Mixed Integer Nonlinear Programming (MINLP) model. This model determines the optimal inventory policy that coordinates stock levels between each echelon of the systems while properly allocating orders among selected suppliers to maximize the expected profit. For verification and validation of the proposed mathematical model, we conduct several numerical analyses and implement simulation models which helps us demonstrate the model’s solvability and effectiveness.

本文考虑了具有订单拆分策略的多级库存系统的集成供应商选择和库存控制问题。由一个仓库和一个仓库组成的买方公司$N$相同的零售商从一组潜在供应商那里采购一种产品；当库存水平耗尽到再订货点时，就会发生仓库的收购$\mathrm{电阻}$, 和顺序 $问$ 同时被分配到 $米$选定的供应商。我们为多梯队系统中的订单拆分问题开发了一个精确的分析模型，并在混合整数非线性规划 (MINLP) 模型中制定了供应商选择问题。该模型确定了最佳库存策略，该策略协调系统每个梯队之间的库存水平，同时在选定的供应商之间正确分配订单以最大化预期利润。为了验证和验证所提出的数学模型，我们进行了多次数值分析并实现了仿真模型，这有助于我们证明模型的可解性和有效性。