We consider a location-inventory optimization model for supply chain (SC) configuration. It includes a supplier, multiple distribution centers (DCs), and multiple retailers. Customer demand and replenishment lead time are considered to be stochastic. Two classes of customer orders, priority and ordinary, are assumed based on their demand. The goal is to find the optimal locations for DCs and their inventory policy simultaneously. For this purpose, a two-phase approach based on queuing theory and stochastic optimization was developed. In the first phase, the stock level of DCs is modeled as a Markov chain process and is analyzed, while in the second phase, a mathematical program is used to determine the optimal number and locations of DCs, the assignment of retailers to DCs, and the order quantity and safety stock level at DCs. As solving this problem is NP-hard, a hybrid Genetic Algorithm (GA) was developed to make the problem computationally tractable.

我们考虑用于供应链（SC）配置的位置库存优化模型。它包括一个供应商，多个分销中心（DC）和多个零售商。客户需求和补货提前期被认为是随机的。根据客户的需求，假定有两类客户订单，即优先客户订单和普通客户订单。目标是同时找到DC的最佳位置及其库存策略。为此，开发了一种基于排队论和随机优化的两阶段方法。在第一阶段，将配送中心的库存水平建模为马尔可夫链过程并进行分析，而在第二阶段，使用数学程序确定配送中心的最佳数量和位置，零售商对配送中心的分配以及配送中心的订单数量和安全库存水平。