We present a new two-commodity flow formulation for the traveling salesman problem. Each commodity corresponds to a resource that is either distributed or picked-up along the tour of all nodes. This formulation is particularly well-suited to handle time window constraints; the resource used is then the time. This formulation can be extended to the makespan problem. For a n-node problem, the linear relaxation of the formulation involves only O(n) constraints and O(n²) variables. Implementation issues are discussed and numerical experimentations have been realized for problems of up to 60 nodes.