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The problem of aggregating multiple criteria to form overall objective functions is of considerable importance in many disciplines. The most commonly used aggregation is based on the weighted sum. The ordered weighted averaging (OWA) aggregation, introduced by Yager, uses the weights assigned to the ordered values (i.e. to the worst value, the second worst and so on) rather than to the specific criteria. This allows to model various aggregation preferences, preserving simultaneously the impartiality (neutrality) with respect to the individual criteria. In this paper we analyze solution procedures for linear programs with the OWA objective functions. Two alternative linear programming formulations are introduced and their computational efficiency is analyzed.