In terms of nonlinear discrete mathematical programming with Boolean variables, the choice of the placement for remote information concentrators (RIC) in a centralized data transmission network (DTS) is described as a mathematical problem. Each terminal complex is connected to just one RIC by a main communication channel and, at most, to one more RIC by a backup channel. The sum of reduced costs for building an operating DTS, and the loss incurred by channel downtime because of failure, are minimized. A local optimization algorithm has been developed for the solution of this problem.