Local access network design often involves the solution of a capacitated concentrator location problem (CCLP). In contrast to the conventional single-capacitated CCLP, this paper presents a generalized CCLP (GCCLP) in which n given end-user nodes are to be connected to concentrators located at m available sites, and each concentrator is subject to two capacity constraints - its effective data processing rate (Kbits/sec) and the available number of circuit ports. The objective of GCCLP is to ensure that each end-user node is connected to exactly one concentrator such that neither of its capacity constraints is violated while the total communication costs are minimized. Since GCCLP is combinatorially explosive, large problems may not be practically solved by an exact method. In this paper, rather, an artificial intelligence solution engine, a Gaussian Machine, is developed for solving GCCLP. Our preliminary computational results indicate that this AI-based solution algorithm is a feasible alternative for solving GCCLP.