Game theoretic approaches to cost allocation in the dynamic total tardiness problem

We examine a dynamic Total Tardiness Problem (TTP) arising out of a decentralized job acquisition by several agents. Since the underlying static TTP is NP-hard, we first present a heuristic in order to solve the dynamic TTP without regard to the participation constraints of the agents. In the main part of the paper a cost allocation based on the results of the heuristic is developed by applying game theoretic concepts. Introducing the concept of a fair cost allocation according to Nash in a special case, the results are subsequently transformed to suit the general situation. Two cost allocation schemes are discussed.