It's a novel rather than a short story, but I think you're looking for The Scheme for Full Employment by Magnus Mills, published in 2003, which is about exactly the situation you describe.
The scheme referred to in the title involves the driving of "UniVans" from depot to depot picking up and unloading cargo - the cargo being replacement parts for UniVans. "Gloriously self-perpetuating, the scheme was designed to give an honest day's wage for an honest day's labour", "the envy of the world: the greatest undertaking ever conceived by man". The novel is a satire of labour relations and describes how the scheme is brought to the brink of disaster.