Partitioning sequencing situations and games

The interaction between sequencing situations and cooperative games starting from the paper of Curiel et al. [Curiel, I., Pederzoli, G., Tijs S., 1989. Sequencing games. European Journal of Operational Research 40, 344–351], has become an established line of research within the theory of operation research games. The current paper introduces a new model in this field: partitioning sequencing situations and associated games. The characteristic of partitioning sequencing situations is that the jobs arrive in batches, and those jobs that arrive in earlier batches have some privileges over jobs in later arrived batches. For partitioning sequencing situations we introduce and characterise the partitioning equal gain splitting rule. We define cooperative games corresponding to partitioning sequencing situations and show that these games are convex. Moreover, we present a game independent expression for the Shapley value of these games. Finally, it is shown that the partitioning equal gain splitting rule leads to a core allocation which is the average of two specific marginal vectors.