Schedule Situations and their Cooperative Game Theoretic Representations

In this paper, we optimize and allocate the costs of a non-rival common-pool resource among several users. In such a so-called schedule situation the players have different demands given by distinct subsets of periods satisfying their needs. The total costs resulting from shared use of the resource are allocated by natural allocations called Equal Pooling allocations, in which the cost of each needed period is shared equally among the users of this period. The associated schedule game gives, for each coalition of players, the minimal cost of a period configuration satisfying the needs of all its members. We have three main contributions. First, we provide several sufficient conditions for the non-emptiness of the core of a schedule game. Second, we prove that under some of these conditions the Shapley value is in the core and coincides with some Equal pooling allocation. Third, we establish connections with other classes of operational research games. Furthermore, we present an application to the allocation of the common costs of the mail carrier route of La Poste, the french postal operator.