In this paper we study a Multi-Attribute Inventory Routing Problem (MAIRP). A mathematical formulation and exact solution algorithms are introduced for this problem. More precisely, we extend the Multi-Depot Inventory Routing Problem (MDIRP) in order to consider the multi-product case with a heterogeneous fleet of vehicles and explicit constraints for the route duration. The MAIRP is an NP-hard problem more complex than the classical Inventory Routing Problem. Moreover, it captures many features that can be found in real applications of a vendor-managed inventory strategy. We introduce a hybrid exact algorithm to solve it, in which several Mixed Integer Programming (MIP) models are solved to explore the neighborhoods of a Variable Neighborhood Search (VNS) scheme applied to the MAIRP. We design several neighborhoods that are based on the features of the problem. The impact of this hybridization is a faster convergence of the model and an accelerated resolution process with respect to a branch-and-cut algorithm applied to the regular MIP formulation. Extensive computational results on new and existing instances from the literature on two benchmark problems and a real data set confirm the high efficiency of our algorithm.

在本文中，我们研究了多属性库存路由问题（MAIRP）。为此引入了数学公式和精确的求解算法。更准确地说，我们扩展了多仓库库存路由问题（MDIRP），以考虑具有异构车辆群和路线持续时间的明确约束的多产品案例。MAIRP是一个NP难题，比经典的清单路由问题更为复杂。而且，它捕获了许多功能，这些功能可以在供应商管理的库存策略的实际应用中找到。我们引入了一种混合精确算法来解决该问题，在该算法中，解决了几种混合整数编程（MIP）模型，以探索应用于MAIRP的可变邻域搜索（VNS）方案的邻域。我们根据问题的特征设计了几个街区。相对于应用于常规MIP公式的分支剪切算法，这种混合的影响是模型的更快收敛和加速的解析过程。来自文献的关于两个基准问题和真实数据集的关于新的和现有实例的大量计算结果证实了我们算法的高效率。