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. In this article, we will sketch the basic principles of the algorithm, we will explain its computational properties, and we will discuss its extensions to more general network flow problems. For a detailed presentation, see the survey paper [3] and the textbooks [2], [4]. For an extensive computational study, see [8]. The algorithm was first proposed in the 1979 report [1].
In the classical assignment problem there are n persons and n objects that we have to match on a one-to-one basis. There is a benefit a ij for matching person i with object j and we want to assign persons to objects so as to maximize the total benefit. Mathematically, we want to find a one-to-one assignment [a set of person-object pairs (1, j...
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References
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Bertsekas, D.P. (2001). Auction Algorithms . In: Floudas, C.A., Pardalos, P.M. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/0-306-48332-7_15
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DOI: https://doi.org/10.1007/0-306-48332-7_15
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