Solving to optimality the uncapacitated fixed-charge network flow problem

Given a directed network, the uncapacitated fixed-charge network flow problem is to find a minimum-cost arc combination that provides flows from the supply nodes to the demand nodes. Associated with all arcs are two costs: the fixed charge of using the arc and the variable cost depending on the amount of flow the arc actually carries. This generic model has applications for problems of distribution, transportation, communication, and routing. In this paper, we use the well-known branch-and-bound algorithm to exactly solve the problem. We develop a computationally efficient branching strategy and a reduction technique based on Lagrangean Relaxation. We also propose a simplification of the branch-and-bound algorithm. As a result of these strategic improvements, we achieve a significant speed-up in the solution process.