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In this paper, we study the problem of the design of telecommunication access networks with reliability constraints. These networks form an important part of the telecommunications infrastructure of large organizations, such as banks. Using data patterned after an actual bank network in the U.S., we formulate an optimization model for this problem which specifically takes into account the various cost, and discount structures offered by telecommunication carriers. We then develop dedicated solution procedures for obtaining solutions. Starting from a cluster solution, we then use perturbation techniques which we developed specifically for this problem within an overall simulated annealing solution algorithm. We show how to make the solution procedure more efficient by implicitly determining the values for many variables. We then report the results of our computational testing for a variety of problems. We compare our solution to a lower bound obtained using a linear programming relaxation. We show that substantial cost savings can be realized with our model, and solution procedure. Finally, we discuss which types of annealing steps in the simulated annealing algorithm are important.