In this paper we present a multi-stage stochastic optimization model to solve an inventory routing problem for the collection of recyclable municipal waste. The objective is the maximization of the total expected profit of the waste collection company. The decisions are related to the selection of the bins to be visited and the corresponding routing plan in a predefined time horizon. Stochasticity in waste accumulation is modeled through scenario trees generated via conditional density estimation and dynamic stochastic approximation techniques. The proposed formulation is solved through a rolling horizon approach, providing a rigorous worst-case analysis on its performance. Extensive computational experiments are carried out on small- and large-sized instances based on real data provided by a large Portuguese waste collection company. The impact of stochasticity on waste generation is examined through stochastic measures, showing the importance of adopting a stochastic model over a deterministic formulation when addressing a waste collection problem. The performance of the rolling horizon approach is evaluated, demonstrating that this heuristic provides cost-effective solutions in short computational time. Managerial insights related to different geographical configurations of the instances and varying levels of uncertainty are finally discussed.

中文翻译：

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用于多阶段随机废物收集问题的滚动水平启发式方法


在本文中，我们提出了一个多阶段随机优化模型，用于解决可回收城市垃圾收集的库存路由问题。目标是使废物收集公司的总预期利润最大化。这些决策与选择要访问的 bin 以及预定义时间范围内的相应路由计划有关。废物积累的随机性是通过条件密度估计和动态随机逼近技术生成的情景树建模的。所提出的公式通过滚动视距法求解，对其性能进行了严格的最坏情况分析。根据葡萄牙一家大型垃圾收集公司提供的真实数据，在小型和大型实例上进行了广泛的计算实验。通过随机度量来检查随机性对废物产生的影响，表明在解决废物收集问题时采用随机模型而不是确定性公式的重要性。评估了滚动视野方法的性能，表明这种启发式方法在较短的计算时间内提供了经济高效的解决方案。最后讨论了与实例的不同地理配置和不同程度的不确定性相关的管理见解。