In this paper we propose a context-specific cost allocation rule for inventory transportation systems. We consider the setting defined in Fiestras-Janeiro et al. (2012)  and propose a new cost allocation rule, the so-called AMEF value, which is inspired by the Shapley value. We prove that, under suitable conditions, the AMEF value provides core allocations. Besides, we provide a characterization of the AMEF value based on properties of balanced contributions, solidarity, and transfer.