This article describes the problem in which the edges of a network represent customers, and a quantity of material is delivered to them so that each one achieves a desired inventory level while finding the lowest-cost route of delivery. Routing and inventory decisions are made at the same time. An example of an application of this problem is dust suppression in open-pit mines. A fleet of vehicles spray water along the roads of a mine. Humidity increases the effectiveness of dust-particle retention. Because the level of humidity decreases, replenishment is done periodically. Other examples of applications include dust suppression in forest roads and plants watering in street medians and sidewalks. We develop a mathematical model that combines two objectives: An inventory objective that minimizes the penalty for the lack of humidity and a routing objective that minimizes watering and traversing costs. Due to the complexity of the mathematical model, we developed an adaptive large neighborhood search algorithm that combines several destroy and repair operators dynamically.