This paper has a dual purpose. First, it proposes a virtual path management model for ATM networks. The model unifies VPC overlay network configuration, VCC routing, and capacity allocation in a single framework. It accommodates multiple end-to-end offered traffics of various QoS requirements and traffic types. Especially, it also supports point-to-multipoint as well as point-to-point connections in a resource-efficient manner. The objective is to minimize the overall network resource cost. To do so, it pursues an optimal trade-off among the gains offered by ATM technology. The application of the proposed model is naturally extended to the multiprotocol label switching framework. Second, it proposes an efficient algorithm to solve the model. The mathematical formulation of such a unifying model typically involves a very large-scale intractable optimization which, treated by a straightforward method, requires excessive computational efforts. In this paper, we show how the computational structure of formulation can be exploited to tailor a solution method providing good solutions in dramatically reduced computational efforts.