The purpose of this paper is to study the periodic arc routing problem when the arcs of a network behave as customers, and sufficient material is delivered so that each achieves its desired inventory level. Therefore, routing and inventory decisions are made simultaneously. Applications include dust suppression in open-pit mines or forest roads and plant watering along sidewalks or street medians. A truck periodically sprays water along the edges of a network. The humidity reaches a desired level and is then consumed over time until water is delivered again. The quantity of water delivered can be fixed or variable; we consider both scenarios and propose a mathematical model for each. Results are reported to validate the model.