In this paper, we describe the operation of barter trade exchanges by identifying key techniques used by trade brokers to stimulate trade and satisfy member needs, and present algorithms to automate some of these techniques. In particular, we develop algorithms that emulate the practice of trade brokers by matching buyers and sellers in such a way that trade volume is maximized while the balance of trade is maintained as much as possible. We show that the buyer/seller matching and trade balance problems can be decoupled, permitting efficient solution as well as numerous options for matching strategies. We model the trade balance problem as a minimum cost circulation problem (MCC) on a network. When the products have uniform cost or when the products can be traded in fractional units, we solve the problem exactly. Otherwise, we present a novel stochastic rounding algorithm that takes the fractional optimal solution to the trade balance problem and produces a valid integer solution. We ...