On analyzing cost allocation problems: Cooperation building structures and order problem representations

To analyze cost allocation problems, this paper identifies associated cooperation building structures, with joint cost functions, and corresponding efficient order problem representations, with individualized cost functions. This paper presents an approach that, when applicable, offers a way not only to adequately model a cost allocation problem by means of a cooperative cost game, but also to construct a core element of such a game by means of a generalized Bird allocation. We apply the approach to both existing and new classes of cost allocation problems related to operational research problems: sequencing situations without initial ordering, maintenance problems, minimum cost spanning tree situations, permutation situations without initial allocation, public congestion network situations, traveling salesman problems, shared taxi problems and traveling repairman problems.