A branch and price approach for the robust bandwidth packing problem with queuing delays

This paper considers a variant of the bandwidth packing problem that determines paths for selected demands on a telecommunication network with given arc capacities to maximize the total revenue. Facilities on the arcs can be seen as M / M /1 queuing systems, which incur queuing delays that should be minimized by adding them to the objective function as a penalty. We also consider the case in which the demands are uncertain, so both the capacity and queuing delay of an arc should take the uncertainty of demand into account. The mathematical formulation for the problem is stated as a nonlinear integer programming problem due to the queuing delays added in the objective function. We first show that the formulation can be linearized to a mixed integer linear programming problem that can be solved by off-the-shelf MIP solvers like Cplex. We then propose a branch-and-price approach by showing that the column generation problem can be solved efficiently by a dynamic programming algorithm. Computational experiments with benchmark instances show that the proposed approach significantly outperforms the state-of-the-art MIP solver in terms of computational times. We also report a Monte-Carlo simulation study with randomly generated demand scenarios to assert the benefits of the robust approach.