Abstract In this article, we introduce two novel multi-commodity inventory-location models considering continuous and periodic review inventory control policies and modular stochastic capacity constraints. The models address a logistic problem in which a single plant supplies a set of commodities to warehouses where they serve a set of customers or retailers. The problem consists of determining which warehouses should be opened, which commodities are assigned, and which customers should be served by the located warehouses; as well as their reorder points and order sizes in order to minimize costs of the system while satisfying service level requirements. This problem can be formulated as a mixed-integer nonlinear programming model, which is non-convex in terms of modular stochastic capacity constraints and the objective function. A Lagrangian relaxation and the subgradient method solution approach is proposed. We consider the relaxation of three sets of constraints, including customer assignment, warehouse demand, and variance constraints. Thus, we develop a Lagrangian heuristic to determine a feasible integer solution at each iteration of the subgradient method. An experimental study shows that the proposed algorithm provides good quality gaps and near-optimal solutions in a short time. It also evinces significant impacts of the selected inventory control policy into total costs and network design, including risk pooling effects, when it is compared with different review period values and continuous review.

中文翻译：

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具有两种不同审查库存控制策略和模块化随机容量约束的多商品库存位置问题

摘要 在本文中，我们介绍了两种新的多商品库存位置模型，考虑到连续和定期审查库存控制策略和模块化随机容量约束。这些模型解决了一个物流问题，其中单个工厂向仓库供应一组商品，在那里它们为一组客户或零售商提供服务。问题包括确定应该开设哪些仓库，分配哪些商品，以及所在仓库应该为哪些客户提供服务；以及他们的再订货点和订单大小，以便在满足服务水平要求的同时最大限度地降低系统成本。这个问题可以表述为一个混合整数非线性规划模型，它在模块化随机容量约束和目标函数方面是非凸的。提出了拉格朗日松弛和次梯度法求解方法。我们考虑放宽三组约束，包括客户分配、仓库需求和差异约束。因此，我们开发了一个拉格朗日启发式算法来在次梯度方法的每次迭代中确定一个可行的整数解。一项实验研究表明，所提出的算法在短时间内提供了良好的质量差距和接近最优的解决方案。当与不同的审查期值和持续审查进行比较时，它还表明所选库存控制政策对总成本和网络设计的重大影响，包括风险分担效应。仓库需求和差异约束。因此，我们开发了一个拉格朗日启发式算法来在次梯度方法的每次迭代中确定一个可行的整数解。一项实验研究表明，所提出的算法在短时间内提供了良好的质量差距和接近最优的解决方案。当与不同的审查期值和持续审查进行比较时，它还表明所选库存控制政策对总成本和网络设计的重大影响，包括风险分担效应。仓库需求和差异约束。因此，我们开发了一个拉格朗日启发式算法来在次梯度方法的每次迭代中确定一个可行的整数解。一项实验研究表明，所提出的算法在短时间内提供了良好的质量差距和接近最优的解决方案。当与不同的审查期值和持续审查进行比较时，它还表明所选库存控制政策对总成本和网络设计的重大影响，包括风险分担效应。