Given a network with flow costs and arc capacities, the classical min-cost flow problem is to send a given amount of flow from the source node to the sink node at least cost. This paper proposes a new variant of the min-cost flow problem by including a fixed cost into the model and by changing the goal as to minimize the average cost. In other words, we assume that the total cost includes two terms: one is the fixed cost of using the network to send flow; the other is a variable cost per unit of flow on the arc. Under this cost assumption, our goal is to minimize the average cost of sending flow. This paper develops an efficient algorithm for this problem.
