## A Lower Bound for Uncapacitated, Multicommodity Fixed Charge Network Design ProblemsInstitute of Transportation Studies, University of California, Irvine, 1987 - Branch and bound algorithms - 37 pages |

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aggregate formulation aggregate LP relaxation aggregate problem arc b€A arc flow vector Balakrishnan 1984 Benders Decomposition bound to z*[FCND Capacity Improvement Lower capacity parameter vector charge network design CI lower bound commodity k€K compute current improved capacity decision variables denote the optimal DFCND disaggregate formulation disaggregate LP relaxation Facilities Location Problem fixed charge network flow on arc improved capacity parameter Institute of Technology Institute of Transportation integer program Knapsack Problem Lagrangian relaxation laxation least as tight linearized knapsack programs Magnanti and Wong marginal cost Mireault network design problem nodes nonincreasing NP-hard objective function value obtained Operations Research optimal objective function optimal solution Parametric Analysis program FCND program LKb(t program SP R.T. Wong Rardin relaxation of FCND relaxation of program routing cost sequence of target shortest path program SP(u T.L. Magnanti target values decrease tighter lower bound tion ub(t umax uncapacitated valid lower bound wb(t