Abstract
In this paper auction algorithms for solving several types of assignment problems with inequality constraints are proposed. Included are asymmetric problems with different numbers of persons and objects, and multiassignment problems, where persons may be assigned to several objects and vice versa. A central new idea in all these algorithms is to combine regular auction, where persons bid for objects by raising their prices, with reverse auction, where objects compete for persons by essentially offering discounts. Reverse auction can also be used to accelerate substantially (and sometimes dramatically) the convergence of regular auction for symmetric assignment problems.
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