A method determines an optimal or near-optimal conveyance network layout in which revenue from serviced customer locations is maximized while the cost of installing and/or maintaining the conveyance is minimized. The conveyance may, for example, be a fiber optic telecommunications cable or a power or utility distribution system. Algorithms in the method generate primal and dual bounds in a Prize-Collecting Steiner Tree Problem in Graphs (PCSPG). Those algorithms originate from a Lagrangian Non-Delayed Relax-and-Cut (NDRC) based approach and incorporate ingredients such as a new PCSPG reduction test, an effective Local Search procedure and a modification in the NDRC framework that allows additional reductions in duality gaps to be attained.