The Auction Algorithm for Assignment and Other Network Flow Problems

The auction algorithm is an intuitive method for solving the classical assignment problem. It outperforms substantially its main competitors for important types of problems, both in theory and in practice, and is also naturally well suited for parallel computation. The algorithm represents a significant departure from the cost improvement idea that underlies primal simplex and dual ascent methods; at any one iteration, it may deteriorate both the primal and the dual cost, although in the end it does find an optimal primal solution. We derive the algorithm from first principles, explain its computational properties, and discuss its extensions to transportation and transhipment problems.

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