A Distributed Auction Algorithm for the Assignment Problem

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Lab Papers (GRASP)
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commerce
distributed control
facility location
linear programming
distributed auction algorithm
distributed control
facility allocation
linear assignment problem
linear programming
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The assignment problem constitutes one of the fundamental problems in the context of linear programming. Besides its theoretical significance, its frequent appearance in the areas of distributed control and facility allocation, where the problemspsila size and the cost for global computation and information can be highly prohibitive, gives rise to the need for local solutions that dynamically assign distinct agents to distinct tasks, while maximizing the total assignment benefit. In this paper, we consider the linear assignment problem in the context of networked systems, where the main challenge is dealing with the lack of global information due to the limited communication capabilities of the agents. We address this challenge by means of a distributed auction algorithm, where the agents are able to bid for the task to which they wish to be assigned. The desired assignment relies on an appropriate selection of bids that determine the prices of the tasks and render them more or less attractive for the agents to bid for. Up to date pricing information, necessary for accurate bidding, can be obtained in a multi-hop fashion by means of local communication between adjacent agents. Our algorithm is an extension to the parallel auction algorithm proposed by Bertsekas et al to the case where only local information is available and it is shown to always converge to an assignment that maximizes the total assignment benefit within a linear approximation of the optimal one.

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2008-12-09
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Lab Papers (GRASP)
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2023-05-17T03:10:18.000
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Copyright 2008 IEEE. Reprinted from: Zavlanos, M.M.; Spesivtsev, L.; Pappas, G.J., "A distributed auction algorithm for the assignment problem," Decision and Control, 2008. CDC 2008. 47th IEEE Conference on , vol., no., pp.1212-1217, 9-11 Dec. 2008 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4739098&isnumber=4738560 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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