A network is a pair of sets (N, A), where N is a set of nodes (points, vertices) and A is a set of arcs (edges, lines, links). If i and j are nodes, then the arc joining them is denoted by the ordered pair (i, j). An arc may have a cost c_ij that denotes the cost per unit flow across that arc, and an upper bound flow capacity denoted by u_ij. For some applications, a node may be a supply node in which goods enter the network, a demand node in which goods leave the network, or a transshipment node through which goods are shipped without a gain or a loss. In most network applications, it is assumed that the flow of goods that enter a node is equal to the flow that leaves the node. This is the conservation of flow assumption.How-ever, in some applications, the amount of goods that enter a node can be more than the amount that leaves the node (e.g., due to the expansion of a liquid) or can be less than the amount that leaves a node (e.g., due to a leak or pilferage). These latter...