Luis A. Guardiola (Departamento de Fundamentos del Análisis Económico, Universidad de Alicante), Ana Meca (I.U. Centro de Investigación Operativa, Universidad Miguel Hernández) and Justo Puerto (Mathematical Research Institute of the University of Seville (IMUS), Sevilla)
Abstract: Production-Inventory settings with heterogeneous agents appear frequently in the study of supply chain management. For instance, there are Production-Inventory situations in which certain agents are essential as they can reduce the costs of other agents (followers) when they cooperate with each other. The study of such a cooperation can be modelled by means of a cooperative game and studied finding fair cost allocations. These class of cooperative games was introduced in Guardiola et al. (in Games Econ Behav 65:205–219, 2009) where it was also proposed the Owen point. This cost allocation is an appealing solution concept that for Production-Inventory games (PI-games) is always stable, in the sense of the core. The Owen point allows all the players in the game to operate at minimum cost but it does not take into account the cost reduction induced by essential players over their followers. Thus, it may be seen as an altruistic allocation for essential players what can be criticized. The aim of this paper is two-fold: to introduce new core allocations for PI-games improving the weaknesses of the Owen point and to study the structure and complexity of set of stable cost allocations (the core) of PI-games.