A forward/reverse auction algorithm for asymmetric assignment problems

In this paper we consider the asymmetric assignment problem and we propose a new auction algorithm for its solution. The algorithm uses in a novel way the recently proposed idea of reverse auction, where, in addition to persons bidding for objects by raising their prices, we also have objects competing for persons by essentially offering discounts. In practice, the new algorithm apparently deals better with price wars than the currently existing auction algorithms. As a result, it tends to terminate substantially (and often dramatically) faster than its competitors.

[1]  Richard V. Helgason,et al.  Algorithms for network programming , 1980 .

[2]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[3]  D. Bertsekas.  A distributed asynchronous relaxation algorithm for the assignment problem , 1985, 1985 24th IEEE Conference on Decision and Control.

[4]  D. Bertsekas.  The auction algorithm: A distributed relaxation method for the assignment problem , 1988 .

[5]  Dimitri P. Bertsekas,et al.  Dual coordinate step methods for linear network flow problems , 1988, Math. Program..

[6]  Dimitri P. Bertsekas,et al.  The Auction Algorithm for Assignment and Other Network Flow Problems: A Tutorial , 1990 .

[7]  J. M. Wein,et al.  Massively parallel auction algorithms for the assignment problem , 1990, [1990 Proceedings] The Third Symposium on the Frontiers of Massively Parallel Computation.

[8]  David A. Castañón,et al.  Reverse Auction Algorithms for Assignment Problems , 1991, Network Flows And Matching.

[9]  Dimitri P. Bertsekas,et al.  Linear network optimization - algorithms and codes , 1991 .

[10]  Dimitri P. Bertsekas,et al.  Parallel synchronous and asynchronous implementations of the auction algorithm , 1991, Parallel Comput..

[11]  Stavros A. Zenios,et al.  On the Massively Parallel Solution of the Assignment Problem , 1991, J. Parallel Distributed Comput..

[12]  Jeffery L. Kennington,et al.  Performance Characteristics of the Jacobi and the Gauss-Seidel Versions of the Auction Algorithm on the Alliant FX/8 , 1991, INFORMS J. Comput..

[13]  Dimitri P. Bertsekas,et al.  Reverse Auction and the Solution of Inequality Constrained Assignment Problems , 1993, SIAM J. Optim..