A double auction based mathematical market model and heuristics for internet-based secondhand durable good markets

•A double auction based electronic market model with budget constraints is introduced.•A linear integer program for the winner determination problem (WDP) is provided.•Three problem specific heuristic methods for WDP are proposed.•Computational results are provided on a comprehensive test suite.•Possible economical contribution of the proposed model is evaluated. Trading of used goods in secondhand markets is considered to have both environmental and economic benefits. For the trading of used goods as well as new ones, this study proposes a periodic double auction model for Internet-based electronic markets whereby each bidder can place both asks and bids for selling and purchasing goods respectively during a trading period. The proposed model allows each bidder to place a spending limit order such that the difference between the cost of the purchased goods and the income obtained from the sold goods does not exceed this limit. Furthermore, since a bidder may be indifferent to multiple goods, e.g. copies of a same title, the model also provides a mechanism so that bidders may combine a number of bids inside a set and put a limit on the number of goods to be purchased in this set. The model is mathematically defined, and the corresponding winner determination problem is formulated using linear integer programming. Since the problem is shown to be NP-hard, a number of heuristic methods are also proposed. Performances of these methods are evaluated on a comprehensive test suite and statistical analyses of the results are presented. Furthermore, possible economical contribution of the model is also evaluated. The results indicate that the proposed model can be used efficiently in large-scale markets with tens of thousands of bidders.