A core-allocation family for generalized holding cost games

Inventory situations, introduced in Meca et al. (Eur J Oper Res 156: 127–139, 2004), study how a collective of firms can minimize its joint inventory cost by means of co-operation. Depending on the information revealed by the individual firms, they analyze two related cooperative TU games: inventory cost games and holding cost games, and focus on proportional division mechanisms to share the joint cost. In this paper we introduce a new class of inventory games: generalized holding cost games, which extends the class of holding cost games. It turns out that generalized holding cost games are totally balanced.We then focus on the study of a core-allocation family which is called N-rational solution family.It is proved that a particular relation of inclusion exists between the former and the core. In addition, an N-rational solution called minimum square proportional ruleis studied. This work was partially supported by the Spanish Ministry of Education and Science, and the Generalitat Valenciana (grants MTM2005-09184-C02-02, CSD2006-00032, ACOMP06/040). The author thanks Javier Toledo, Josefa Cá novas, and two anonymous referees for helpful comments.