Reverse Auction and the Solution of Inequality Constrained Assignment Problems

In this paper we propose auction algorithms for solving several types of assignment problems with inequality constraints. Included are asymmetric problems with different numbers of persons and objects, and multiassignment problems, where persons may be assigned to several objects and reversely. 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. 1 This work was supported in part by the BM/C3 Technology branch of the United States Army Strategic Defense Command. 2 Department of Electrical Engineering and Computer Science, M. I. T., Cambridge, Mass., 02139. 3 Department of Electrical Engineering, Boston University, and ALPHATECH, Inc., Burlington, Mass., 01803. 4 ALPHATECH, Inc., Burlington, Mass., 01803. 1