The Inventory Routing Problem (IRP) arises in logistics operations when routing and inventory decisions are made simultaneously. In this work, some ideas to improve the long-term performance of the rolling horizon strategy are explored. First, three simple modifications to the IRP are tested to improve its long-term performance: using safety stocks, defining minimum inventory levels for the last period of the planning horizon, and using an artificial discount rate in the objective function. We use this improved IRP as a benchmark. Then, a solution strategy is proposed where an approximation is used in the final periods of the planning horizon, which is based on the linear relaxation of the IRP. The algorithm is calibrated and, through simulation, compared to the benchmark on a set of randomly generated instances with up to 30 customers, three vehicles, and 20 periods, and different costs and uncertainty levels. It is shown that the proposed algorithm is, on average, three times faster than the benchmark and generates savings between 1% and 2%. Under favorable conditions (low uncertainty, low inventory cost, and one vehicle), it can generate savings of around 10% in long-term costs.

中文翻译：

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使用线性松弛优化库存路径问题的长期成本

当同时做出路线和库存决策时，物流操作中就会出现库存路线问题 (IRP)。在这项工作中，探讨了一些提高滚动策略长期绩效的想法。首先，测试了对 IRP 的三个简单修改，以提高其长期绩效：使用安全库存、定义计划范围最后一个时期的最低库存水平以及在目标函数中使用人为贴现率。我们使用这个改进的 IRP 作为基准。然后，提出了一种解决策略，其中在规划范围的最后时期使用近似值，该策略基于 IRP 的线性松弛。该算法经过校准，并通过模拟与一组随机生成的实例（最多有 30 个客户、三辆车、20 个周期以及不同的成本和不确定性水平）的基准进行比较。结果表明，所提出的算法平均比基准快三倍，并节省 1% 到 2% 的成本。在有利的条件下（不确定性低、库存成本低、一辆车），它可以节省约 10% 的长期成本。