We solve a rich routing problem inspired from practice, in which a heterogeneous fixed fleet is used for collecting recyclable waste from large containers over a finite planning horizon. Each container is equipped with a sensor that communicates its level at the start of the day. Given a history of observations, a forecasting model is used to estimate the expected demands and a forecasting error representing the level of uncertainty. The problem falls under the framework of the stochastic inventory routing problem and our main contribution is the modeling of the dynamic probability-based cost of container overflows and route failures over the planning horizon. We cast the problem as a mixed integer non-linear program and, to solve it, we develop an adaptive large neighborhood search algorithm that integrates a purpose-designed forecasting model, tested and validated on real data. We demonstrate the strength of our modeling approach on a set of rich inventory routing instances derived from real data coming from the canton of Geneva, Switzerland. Our approach significantly outperforms alternative deterministic policies in its ability to limit the occurrence of container overflows for the same routing cost. Finally, we show the benefit of a rolling horizon solution and derive lower and upper bounds on its cost.

We introduce a unified framework for rich vehicle and inventory routing problems with complex physical and temporal constraints. Demands are stochastic, can be non-stationary, and are forecast using any model that provides the expected demands and their error term distribution, which can be any theoretical or empirical distribution. We offer a detailed discussion on the modeling of demand stochasticity, focusing on the probabilities and cost effects of undesirable events, such as stock-outs, breakdowns and route failures, and their associated recourse actions. Tractability is achieved through the ability to pre-compute or at least partially pre-process the stochastic information, which is possible under mild assumptions for a general inventory policy. We integrate the stochastic aspect into a mixed integer non-linear program, illustrate applications to various problem classes, and show how to model specific problems through the lens of inventory routing. The case study is based on two sets of realistic instances, representing a waste collection inventory routing problem and a facility maintenance problem, respectively. We analyze the effects of our assumptions on modeling realism and tractability, and demonstrate that our framework significantly outperforms deterministic policies in its ability to limit the number of undesirable events for the same routing cost.