Abstract
We define a problem called “used car salesman problem” in which sale, purchase and barter bids can be simultaneously put forward for trading cars. A sale or a purchase bid is expressed in terms of a single car and a sale or purchase price that is required for the car. A barter bid, on the other hand, can be augmented by a differential money amount that is offered or required in addition to the cars that are to be traded. Restrictions are also allowed to be placed on sale and purchase bids. A minimum cost circulation network flow algorithm is presented which produces a solution that maximizes the profit made by the used car salesman.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Federal communications commission spectrum auction site. [Online], http://wireless.fcc.gov/auctions/.
R.K. Ahuja, T.L. Magnanti and J.B. Orlin, Network Flows, Theory, Algorithms and Applications (Prentice Hall, 1993).
J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications (Springer-Verlag, 2000).
S. de Vries and R.V. Vohra, Combinatorial auctions: A survey, Informs Journal of Computing (to appear).
M. Engineer, Bargains, barter and money, Review of Economic Dynamics 4 (2001) 188–209.
A. Goldberg, CS2, “Andrew Goldberg’s Network Optimization Library”, [Online], http://www.avglab.com/andrew/soft.html.
G. Gutin, Finding a longest path in a complete multipartite digraph, SIAM J. Discrete Math. 6 (1993) 270–273.
W.S. Jevons, Theory of Political Economy (MacMillan and Co., New York, 1888).
R. Jones, The origin and development of Media of Exchange, J. of Political Economy 84 (1976) 757–776.
J.R. Kalagnanam, A. Davenport and H.S. Lee, Computational aspects of clearing continuous call double auctions with assignment constraints and indivisible demand, Electronic Commerce Research Journal 1 (2001) 221–238.
C.H.C. Little and H. Wang, Vertex disjoint cycles in a directed graph, Australasian Journal of Combinatorics 12 (1995) 113–119.
C. Özturan, Direct single instance multi-item bartering problem, Technical Report FBE-CMPE-02/2002-4, Dept. of Computer Engineering, Bogazici University, Istanbul, July 2002. Available: http://www.cmpe.boun.edu.tr/~ozturan/cmpe2002-4.ps.
S. Shinohara and Y.P. Gunji, Emergence and collapse of money through reciprocity, Applied Math. and Computation 117 (2001) 131–150.
H. Wang, On the maximum number of independent cycles in a graph, Discrete Mathematics 205 (1999) 183–190.
H. Wang, On the maximal number of vertices covered by disjoint cycles, Australasian Journal of Combinatorics 21 (2000) 179–186.
P.R. Wurman, W.E. Walsh and M.P. Wellman, Flexible double auctions for electronic commerce, Decision Support Systems 24 (1998) 17–27.
Author information
Authors and Affiliations
Corresponding author
Additional information
AMS subject classification
91B26, 90B10, 05C38
Rights and permissions
About this article
Cite this article
Özturan, C. Used car salesman problem: A differential auction–barter market. Ann Math Artif Intell 44, 255–267 (2005). https://doi.org/10.1007/s10472-005-4691-z
Issue Date:
DOI: https://doi.org/10.1007/s10472-005-4691-z