The elementary shortest path problem with resource constraints (ESPPRC) is an NP-hard problem that often arises in the context of column generation for vehicle routing problems. We propose an exact solution method that relies on implicit enumeration with a novel bounding scheme that dramatically narrows the search space. We embedded our algorithm within a column generation to solve the linear relaxation (root node) of the vehicle routing problem with time windows (VRPTW) and found that the proposed algorithm performs well when compared against state-of-the-art algorithms for the ESPPRC on the well-known Solomon’s test bed for the VRPTW.