We consider the problem of establishing an optimal link capacity expansion plan over multiple periods on the telecommunication network that uses a Digital Cross-connect System (DCS) at each node. It is assumed that predetermined working channels on each link of the network are given for each period. Each link must have sufficient channel capacities to ensure the working channels and spare channels that are needed to restore the traffic when a link fails. We give an integer programming model for this problem which determines the number of facilities to be installed on each link to meet the aggregated requirements of working and spare channels at each period. We proposed a branch-and-cut algorithm for this problem which applies the cutting plane approach at each node of the branch-and-bound tree. Computational results show that the algorithm solves all randomly generated problems optimally in reasonable time bound.