In this paper we consider the optimization of teleprocessing (TP) networks with concentrators. Each terminal may in general have multiple connections to several concentrators. The first part of the paper is concerned with the optimal assignment of terminals to a given set of concentrators. A sequential assignment algorithm is presented with its efficiency and optimality established. The second part of the paper is concerned with the optimal number and location of the concentrators to be installed. A generalized “ADD” algorithm is suggested. It is shown that the total cost function is convex with respect to the number ofconcentrators installed in such an algorithm. Copyright © 1978 by The Institute of Electrical and Electronics Engineers. Inc.