Bilinear Programming: Applications in the Supply Chain Management.

Many problems in the supply chain management can be formulated as a network flow problem with specified arc cost functions. Let G(N, A) represent a network where N and A are the sets of nodes and arcs, respectively, and fa(xa) denotes an arc cost function. In the network, there are supply and demand nodes, and the main objective of the problem is to minimize the total cost by satisfying the demand from the available supply. In addition, one can assume that the arc flows are bounded, which corresponds to the cases where a shipment along an arc should not exceed a specified capacity. The mathematical formulation of the problem can be stated as