The 1-Commodity Pickup and Delivery Vehicle Routing Problem (1-PDVRP) asks to deliver a single commodity from a set of supply nodes to a set of demand nodes, which are unpaired. That is, a demand node can be served by any supply node. In this paper, we further assume that the supply and demand is unsplittable, which implies that we can visit each node only once. The 1-PDVRP arises in several practical contexts, ranging from bike-sharing programs in which bikes at each station need to be redistributed at various points in time, to food rescue programs in which excess food is collected from, e.g., restaurants and schools, and redistributed through agencies to people in need. The latter application is the main motivation of our study.