We consider the Inventory Routing Problem (IRP) with one vendor replenishing the inventories of many retailers who face stochastic demands. To hedge against demand uncertainty, dynamic lot-sizing and safety stock planning are integrated using chance-constrained programming to adapt to the varying demand uncertainty across planning periods and allow for variable replenishment periods. We present a tactical approach towards obtaining cyclic delivery schedules that avoid given starting inventories and account for non-stationary interdependent demands. The assumption of independent, identically distributed (i.i.d.) demands often oversimplifies the stochasticity of the underlying demand time series by neglecting, among other things, seasonality and correlation. In IRPs, the evolution of the demand time series highly affects the consolidation of retailer replenishments in delivery routes. The problem is modeled as a mixed-integer linear program (MILP), including several real-world characteristics. To obtain solutions faster than by using MILP solvers, we propose a multi-start adaptive local search and an adaptive large neighborhood search (ALNS) heuristic. The influence of several problem parameters on the solutions is investigated. The benefit of an integrated planning of lot-sizing and routing over sequential planning is assessed. The results show that the proposed approach for cyclic delivery schedules allows a (de-)synchronization of retailer replenishments and their consolidation in vehicle routes while meeting real-world constraints in both routing and inventory management. Under non-stationary demands, it yields savings of 2.8% and 1.9% on average compared to given or zero starting inventories by setting initial inventories endogenously. The presented heuristics render near-optimal results. The ALNS deviates by only 0.6% from optimal on instances where $\mathit{cv}=0,$ and by an average of 1.6% from optimal on all small-sized instances. On larger problems, it outperforms the other heuristics and obtains an average deviation from the best solution found of only 0.1%.

我们考虑一个供应商补充许多面临随机需求的零售商的库存的库存路径问题（IRP）。为了应对需求不确定性，使用机会受限的编程将动态的批量确定和安全库存计划集成在一起，以适应整个计划周期内变化的需求不确定性，并允许可变的补货周期。我们提出一种获取周期性交货计划的战术方法，该计划可避免给定的初始库存并考虑非固定的相互依存的需求。假设独立的，均匀分布的（iid）需求通常会忽略季节性和相关性，从而过分简化了潜在需求时间序列的随机性。在IRP中，需求时间序列的演变在很大程度上影响了配送路线中零售商补货的整合。该问题被建模为包含多个实际特征的混合整数线性程序（MILP）。为了比使用MILP求解器更快地获得解决方案，我们提出了多起点自适应局部搜索和自适应大邻域搜索（ALNS）启发式方法。研究了几个问题参数对解的影响。评估了批量计划和工艺路线的综合计划相对于顺序计划的好处。结果表明，所提出的周期性交货计划方法可以实现零售商补货的（去同步）及其在车辆路线中的合并，同时满足路线和库存管理中的实际限制。在非平稳需求下，通过内生设置初始库存，与给定的零库存或零初始库存相比，它平均可节省2.8％和1.9％。提出的启发式方法提供了接近最佳的结果。在以下情况下，ALNS与最佳值仅相差0.6％$\mathit{简历}=0，$在所有小型实例中，平均比最佳平均值低1.6％。在较大的问题上，它优于其他启发式方法，并且与最佳解决方案的平均偏差仅为0.1％。