Exact solutions for the robust prize-collecting steiner tree problem

We consider a combinatorial optimization problem that models an expansion of fiber optic telecommunication networks. Thereby, we are given a set of customers with potential gains of revenue and the set of edges with fixed installation costs. The goal is to decide which customers to connect to a given root node so that the sum of edge costs plus the node revenues for the nodes that are left out from the solution is minimized. The problem is known in the literature as the Prize-Collecting Steiner Tree Problem (PCStT). In many applications it is unrealistic to assume that the gains of revenue or installation costs are known in advance. In this paper, we extend this well-studied deterministic problem by considering the robust optimization approach in which the input parameters are subject to interval uncertainty. To control the level of conservatism of the solution, we consider Bertsimas & Sim robust optimization approach. We propose a branch-and-cut approach to solve this problem to optimality and provide an extensive computational study on a set of benchmark instances that are adapted from those previously used to solve the deterministic version of the problem. We show how the price of robustness influences the costs of the solutions and the algorithm performance.