The delivery man problem on a tree network

This note considers a variant of the traveling salesman problem in which a route is sought that minimizes the total of the vertex arrival times. This problem is called the delivery man problem. The traveling salesman problem is NP-complete on a general network and trivial on a tree network. The delivery man problem is also NP-complete on a general network but far from trivial on a tree network. Various characteristics of the delivery man problem for tree networks are explored and a pseudo-polynomial time solution algorithm is proposed.