  We consider a cooperative game defined by an economic lot-sizing problem with
heterogeneous costs over a finite time horizon, in which each firm faces demand
for a single product in each period and coalitions can pool orders. The model
of cooperation works as follows: ordering channels and holding and backlogging
technologies are shared among the members of the coalitions. This implies that
each firm uses the best ordering channel and holding technology provided by the
participants in the consortium. That is, they purchase, hold inventory, pay
backlogged demand and make orders at the minimum cost of the coalition members.
Thus, firms aim at satisfying their demand over the planing horizon with
minimal operation cost. Our contribution is to show that there exist fair
allocations of the overall operation cost among the firms so that no group of
agents profit from leaving the consortium. Then we propose a parametric family
of cost allocations and provide sufficient conditions for this to be a stable
family against coalitional defections of firms. Finally, we focus on those
periods of the time horizon that are consolidated and we analyze their effect
on the stability of cost allocations.
