  Flows over time have received substantial attention from both an optimization
and (more recently) a game-theoretic perspective. In this model, each arc has
an associated delay for traversing the arc, and a bound on the rate of flow
entering the arc; flows are time-varying. We consider a setting which is very
standard within the transportation economic literature, but has received little
attention from an algorithmic perspective. The flow consists of users who are
able to choose their route but also their departure time, and who desire to
arrive at their destination at a particular time, incurring a 'scheduling cost'
if they arrive earlier or later. The total cost of a user is then a combination
of the time they spend commuting, and the scheduling cost they incur. We
present a combinatorial algorithm for the natural optimization problem, that of
minimizing the average total cost of all users (i.e., maximizing the social
welfare). Based on this, we also show how to set tolls so that this optimal
flow is induced as an equilibrium of the underlying game.
