Solution Strategies for the Multi-Hour Network Design Problem

The problem of finding the most cost efficient network design by considering two or more demand matrices that represent varying network traffic over several time periods, is referred to as multi-hour network design. Capacity installations need to be determined such that the network is robust enough to allow routing of the demand matrices non-simultaneously. In the paper the multi-hour network design problem is formulated as a mixed-integer programming model and the solution approach is based on a branch-and-cut framework that incorporates several classes of valid inequalities. The aim of the paper is to investigate the effect of problem reduction on computing times. Results from domination theory are applied to reduce the number of non-simultaneous traffic demand matrices to a so-called dominant (sub-)set. That is, matrices from the original data set are removed which do not change the solution space of a feasible network. In addition, strategies for strengthening the right-hand side of metric inequalities are presented and computational results are provided based on measurements from an operational network.