Regenerator location problem and survivable extensions: a hub covering location perspective

In a telecommunications network the reach of an optical signal is the maximum distance it can traverse before its quality degrades. Regenerators are devices to extend the optical reach. The regenerator placement problem seeks to place the minimum number of regenerators in an optical network so as to facilitate the communication of a signal between any node pair. In this study, the Regenerator Location Problem is revisited from the hub location perspective directing our focus to applications arising in transportation settings. Two new dimensions involving the challenges of survivability are introduced to the problem. Under partial survivability, our designs hedge against failures in the regeneration equipment only, whereas under full survivability failures on any of the network nodes are accounted for by the utilization of extra regeneration equipment. All three variations of the problem are studied in a unifying framework involving the introduction of individual flow-based compact formulations as well as cut formulations and the implementation of branch and cut algorithms based on the cut formulations. Extensive computational experiments are conducted in order to evaluate the performance of the proposed solution methodologies and to gain insights from realistic instances.