Capacity improvement lower bound for fixed charge network design problems

Network design problems concern flows over networks in which a fixed charge must be incurred before an arc becomes available for use. The uncapacitated, multicommodity network design problem is modeled with aggregate and disaggregate forcing constraints. (Forcing constraints ensure logical relationships between the fixed charge-related and the flow-related decision variables.) A new lower bound for this problem - referred to as the capacity improvement (CI) bound - is presented; and an efficient implementation scheme using shortest path and linearized knapsack programs is described. A key feature of the CI lower bound is that it is based on the LP relaxation of the aggregate version of the problem. A numerical example illustrates that the Cl lower bound can converge to the optimal objective function value of the IP formulation.