Differential auction-barter (DAB) model augments the well-known double auction (DA) model with barter bids so that besides the usual purchase and sale activities, bidders can also carry out direct bartering of items. The DAB model also provides a mechanism for making or receiving a differential money payment as part of the direct bartering of items, hence, allowing bartering of different valued items. In this paper, we propose an extension to the DAB model, called the multi-unit differential auction-barter (MUDAB) model for e-marketplaces in which multiple instances of commodities are exchanged. Furthermore, a more powerful and flexible bidding language is designed which allows bidders to express their complex preferences of purchase, sell and exchange requests, and hence increases the allocative efficiency of the market compared to the DAB. The winner determination problem of the MUDAB model is formally defined, and a fast polynomial-time network flow based algorithm is proposed for solving the problem. The fast performance of the algorithm is also demonstrated on various test cases containing up to one million bids. Thus, the proposed model can be used in large-scale online auctions without worrying about the running times of the solver. (C) 2010 Elsevier B. V. All rights reserved.