This paper studies the cyclic inventory routing problem with stochastic demand. A geographically dispersed set of retailers with stochastic demand rates is replenished from a single depot using vehicles with limited capacity. For an infinite horizon, a fixed-partition policy is adopted that partitions the retailers into subsets that are always replenished together in the same route being cyclically repeated. The objective is to provide cost efficient buffering of the demand variability within a cyclic distribution plan by providing carefully calibrated safety stock levels at the retailers. In doing so, the vehicle capacity needs to be taken into account, since cumulative demand during a cycle of the retailers in a route may exceed this capacity. In that case, shortfall remains at the retailer inventories because they are not fully replenished, which affects the service level (and cost balance) in the consecutive cycle(s). An approximate method is presented for determining the safety stock levels and is integrated into a state-of-the-art metaheuristic solution approach for cyclic inventory routing. An illustrative example and experiments on benchmark instances show (i) the effect of the vehicle capacity on the cost balance in a route, (ii) the accuracy of the approximation, and (iii) the added value of taking demand variability and shortfall due to limited vehicle capacity into account during the route design.

本文研究了具有随机需求的循环库存路由问题。使用容量有限的车辆从单个仓库补充地理上分散的具有随机需求率的零售商集。对于无限期，采用固定分区策略，将零售商划分为子集，这些子集总是在同一路径中一起补充，并循环重复。目标是通过在零售商处提供仔细校准的安全库存水平，在循环分配计划中提供具有成本效益的需求变化缓冲。这样做时，需要考虑车辆容量，因为路线中零售商在一个周期内的累积需求可能会超过该容量。在这种情况下，短缺因为它们没有完全补充，所以仍然留在零售商库存中，这会影响连续周期中的服务水平（和成本平衡）。提出了一种确定安全库存水平的近似方法，并将其集成到用于循环库存路由的最先进的元启发式解决方案方法中。一个说明性示例和对基准实例的实验表明（i）车辆容量对路线成本平衡的影响，（ii）近似值的准确性，以及（iii）考虑需求可变性和短缺造成的附加值在路线设计过程中考虑到有限的车辆容量。