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We formulate the downlink cross-carrier resource allocation problem in LTE-Advanced carrier aggregation (CA) systems as an unbalanced transportation problem (TP). The component carriers (CC's), or their associated sub-bands, represent the supply points whereas the users requesting traffic represent the demand points. The cost of shipping from a supply point to a demand point is set as a function of the proportional fairness (PF) metric. To balance the problem, an artificial supply point is added to represent the shortage in satisfying the demand in case of an overloaded system. Backward compatibility with LTE Release 8 (Rel-8) is guaranteed by adjusting the cost of shipping to Rel-8 users to restrict them to operate on a single CC. The results show that using Vogel approximation method (VAM), which is a sub-optimal efficient method, provides near-optimum results in terms of throughput and fairness and is much faster than the simplex method for optimal solution. The proposed TP-based scheduler is shown to achieve considerable performance improvement over a PF scheduler that handles multiple CC's in the presence of both Rel-8 and LTE-A users.