In this paper, we study cooperation among multiple organizations (e.g., retailers) that jointly place orders from an external supplier and manage their inventories. We use the well-known Economic Lot-Sizing (ELS) model with general concave ordering and holding costs to model the retailers’ decision problem and analyze the resulting cooperation games (i.e., ELS games). The existence of population monotonic allocation schemes for ELS games has been an open question in the literature. Recently, a positive answer was obtained for two-period ELS games with linear holding and backorder costs; however, a general result has remained unknown. In this paper, we show by means of a counterexample that ELS games do not admit a population monotonic cost allocation scheme in general. We then discuss a class of candidate core allocations for ELS games with general concave ordering and holding costs.