Cost allocation in the Chinese postman problem

This paper considers a cost allocation problem that arises from a delivery problem associated with the Chinese postman problem. A delivery problem is described by a connected undirected graph in which each edge belongs to a different player, a cost function on the edges of this graph and a fixed vertex which is referred to as the post office. Assume that the post office is providing some service to the players. The nature of this service, which can be thought of as mail delivery, requires that a server will travel along the edges of the graph and return to the post office. The cost allocation problem is concerned with the cost of providing the service to all players. A specific cost allocation rule is introduced and characterized. Further, the class of delivery problems gives rise to a new class of cooperative combinatorial optimization games called delivery games. It is shown that the outcome of the allocation rule with respect to a bridge-connected Euler graph is a core element of the corresponding delivery game.