In this paper, we study the biobjective assignment problem, a NP-hard version of the classical assignment problem. We employ an effective two-phase method with certain enhancements: in Phase I, we use a distributed auction algorithm to solve the single objective assignment problems to obtain the so-called supported Pareto optimal solutions; we apply a ranking approach with tight upper/lower bounds in Phase II to obtain the non-supported Pareto optimal solutions. Moreover, a randomized algorithm

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... for Phase II is proposed that supports finding the approximation on a polynomial time basis. Extensive experiments are conducted using SGI Altix 3700 and computational results are reported based on a large set of randomly generated problem instances. Also, some experimental results of the distributed auction algorithm on large data-size assignment problems are provided.